Defining Ecological Network Structure and Function: A Cross-Disciplinary Framework for Biomedical Research

Abstract

This article provides a comprehensive framework for defining the structure and function of ecological networks, tailored for researchers, scientists, and drug development professionals. It explores the core concepts of nodes, links, and network architecture, and details methodologies for network construction and analysis, including specialized software tools. The content addresses challenges in network robustness and optimization, and covers validation techniques and comparative analysis across biological systems. By integrating principles from landscape ecology and systems biology, this guide aims to equip biomedical researchers with the analytical frameworks needed to model complex biological networks, from protein-protein interactions to cellular signaling pathways, thereby informing drug discovery and therapeutic targeting.

The Blueprint of Complexity: Core Concepts for Defining Ecological Network Architecture

Biological systems, from molecular interactions within a cell to species relationships within an ecosystem, are fundamentally composed of interconnected entities. This whitepaper deconstructs the core components of biological networks—nodes and links—to establish a unified framework for understanding their structure and function. By framing ecological and molecular systems as computable graphs, we provide researchers with methodologies to infer, analyze, and perturb these networks, thereby bridging the gap between high-throughput data generation and mechanistic biological insight. The integrative approaches detailed herein are essential for advancing research in systems biology, ecology, and therapeutic development.

The complexity of biological systems, whether observing a microbial community or a signal transduction pathway, arises not from the mere presence of individual components but from the intricate web of interactions between them. A network-based perspective provides a powerful scaffold for conceptualizing, quantifying, and predicting the behavior of these systems. This guide deconstructs biological networks into their fundamental units—nodes (representing biological entities) and links (representing their interactions)—to explore how their arrangement dictates system-wide function and resilience [1] [2].

This computational approach allows for the systematic integration of multi-omics data (e.g., transcriptomics, proteomics) and the identification of emergent properties that are not apparent when studying components in isolation [2]. The principles are universally applicable, enabling a common language for researchers studying ecological networks of species and habitats, as well as for drug development professionals mapping disease-associated gene regulatory networks.

The Core Components: Nodes and Links

The architecture of any biological network is built upon two elemental components, each with specific semantic meaning.

• Nodes (Vertices): Nodes are the fundamental entities within a network. In biological contexts, they can represent a wide array of entities, including:
  • Molecular Elements: Genes, proteins, metabolites, transcripts [1] [2].
  • Biological Entities: Promoters, cells, species, habitats [1] [3].
  • Ecological Elements: Ecological sources, patches, corridors [3].
• Links (Edges): Links define the interactions or relationships between nodes. These interactions can be:
  • Physical: Protein-protein interactions, binding events [2].
  • Regulatory: A transcription factor regulating a target gene [2].
  • Functional: Metabolic conversions, signal transduction [1] [2].
  • Spatial: Species dispersal or ecological flows between habitat patches [3].

The semantics of nodes and edges are formally defined using ontologies and meta-data, which ensure consistent interpretation and computational analysis across different studies and biological domains [1].

Representing Biological Systems as Networks

Many distinct types of biological information can be coherently represented and stored as graphs, facilitating unified analysis [1]. The table below summarizes common types of biological networks.

Table 1: Common Types of Biological Networks and Their Components

Network Type	Node Examples	Link Examples	Primary Function
Protein-Protein Interaction (PPI)	Proteins, Complexes	Physical Binding, Stabilization	Map functional protein complexes and cellular machinery [2].
Gene Regulatory	Genes, Transcription Factors, Promoters	Transcriptional Regulation, Inhibition	Control gene expression programs and cellular states [1] [2].
Metabolic	Metabolites, Enzymes	Biochemical Conversion, Catalysis	Model metabolic flux and product synthesis [1] [2].
Signal Transduction	Receptors, Kinases, Signaling Molecules	Phosphorylation, Activation, Relay	Transduce signals from extracellular to intracellular environments [1].
Ecological	Species, Habitat Patches	Predation, Competition, Dispersal	Safeguard regional ecological security and biodiversity [3].

Figure 1: Logical relationships in biological networks. Different network types are defined by the nature of their nodes and links, from regulatory interactions to biochemical transformations.

Methodologies for Network Reconstruction and Analysis

Network Reconstruction from Data

Network reconstruction, or inference, involves deducing the causal, regulatory connections between molecular entities from high-dimensional omics data [2]. The goal is to infer connectivity that changes across conditions such as time, cell types, or disease states.

Table 2: Data Requirements and Methods for Network Inference

Data Input	Inference Method Examples	Network Type	Key Output
Gene Expression (RNA-seq, microarrays)	GENIE3 [2], Bayesian Networks [2], Tree-Based Methods [2]	Gene Regulatory	Context-specific regulatory interactions.
Protein Abundance (Mass spectrometry)	Integrative Random Forest [2], Graphical Models [2]	Protein-Protein Interaction	Functional protein modules and complexes.
Epigenomic Data (ChIP-seq, ATAC-seq)	NCA [2], Footprinting Analysis [2]	Gene Regulatory	Transcription factor binding and promoter-enhancer links.
Metabolomic Profiles	Genome-Scale Metabolic Models (GEMs) [2]	Metabolic	Biochemical pathways and flux states.
Land Use & Climate Data	Random Forest Regression [3], GTWR [3]	Ecological	Species corridors and habitat connectivity.

A generalized workflow for network reconstruction and analysis is outlined below, integrating multiple data sources and validation steps.

Figure 2: A generalized workflow for network reconstruction and analysis. The process is iterative, where experimental validation refines the initial computational model.

Network-Based Interpretation and Prioritization

Once a network is reconstructed, it serves as a scaffold for interpreting new experimental data and prioritizing key elements (e.g., genes, species) for further study [2]. Key approaches include:

• Integration of Gene Sets: Overlaying results from high-throughput experiments (e.g., differentially expressed genes from microarray or RNA-seq studies) onto a pre-existing network to identify enriched modules or neighborhoods [2].
• Network Perturbation Analysis: Simulating the effect of node or link removal (e.g., gene knockout, habitat fragmentation) to assess network resilience and identify critical vulnerabilities [3] [2]. For instance, applying "corridor-fragmentation" disturbance strategies to an ecological network quantifies the impact on structural and functional resilience [3].
• Gene Prioritization: Using network properties (e.g., centrality measures, which identify highly connected nodes) to rank genes for follow-up experimental validation in disease contexts, thereby streamlining the drug discovery pipeline [2].

Experimental Protocols: A Case Study in Ecological Network Resilience

The following detailed methodology provides a template for assessing the dynamics and resilience of biological networks under external pressure, as demonstrated in a study on the ecological networks of the Guangdong-Hong Kong-Macao Greater Bay Area (GBA) [3].

Protocol: Assessing Structural and Functional Resilience of Ecological Networks

Objective: To quantitatively assess the impacts of different disturbance strategies on both the structural and functional resilience of Ecological Networks (ENs) under climate change and urbanization scenarios [3].

Background: Ecological networks safeguard regional security by connecting ecological sources (nodes) via corridors (links). Their resilience is critical for maintaining ecosystem services under stress [3].

Materials:

• Land use and land cover (LULC) maps for the study region for historical (e.g., 1990-2020) and future (e.g., up to 2060) time points.
• Climate projection data aligned with Shared Socioeconomic Pathways (SSPs), such as SSP126 (sustainability) and SSP585 (fossil-fueled development).
• GIS software (e.g., ArcGIS, QGIS).
• Statistical computing environment (e.g., R, Python).

Procedure:

• Network Construction:

  • Delineate ecological sources using LULC data, identifying core habitat patches.
  • Extract corridors between sources using circuit theory or least-cost path models to represent potential species dispersal routes.
  • Construct the composite ecological network for each time period.

• Define Disturbance Strategies:

  • Random: Random removal of nodes or links to establish a baseline.
  • Climate-stress: Targeted disturbance based on climate projection data (e.g., areas of high temperature stress or sea-level rise).
  • Source-degradation: Targeted removal of key ecological source nodes.
  • Corridor-fragmentation: Targeted removal of corridor links to disrupt connectivity [3].

• Resilience Simulation:

  • Systematically apply each disturbance strategy to the constructed networks in a simulation environment.
  • Quantify changes in structural metrics (e.g., connectivity, landscape fragmentation index, node importance).
  • Quantify changes in functional metrics (e.g., ecosystem service flow, potential for species migration).
  • Model the coupling mechanism between structural damage, functional decline, and resilience loss [3].

• Drivers Analysis:

  • Employ a random forest regression model to explore the driving effects of LULC changes on the evolution of the EN's structure and function [3].
  • Identify which land use conversions (e.g., forest to urban, cropland to forest) most significantly enhance or degrade network integrity.

Expected Output:

• Quantification of historical and projected future resilience.
• Identification of the most disruptive disturbance type (e.g., source-degradation typically causes the most severe disruption [3]).
• Maps of critical nodes and corridors essential for maintaining network resilience, informing conservation prioritization.

The Scientist's Toolkit: Essential Research Reagents and Materials

Table 3: Key Research Reagent Solutions for Network Biology

Item	Function in Network Analysis	Example Use Case
ONTEX Data Warehouse	An open-source (GPL) framework for integrating, storing, and querying diverse biological networks as graphs with ontologies [1].	Linking microarray results, biological networks, and sequence analysis methods in a unified system [1].
Optical Transceivers (e.g., LINK-PP 400G-FR4)	High-speed data transmission hardware; critical for visualizing and monitoring the physical network infrastructure that underpins large-scale bioinformatics computations and data centers [4].	Enabling real-time visualization of network performance metrics in a data center supporting cloud-based network analysis [4].
Random Forest Regression Model	A machine learning algorithm used to explore the driving effects of multiple factors (e.g., LULC) on the evolution of a network's structure and function [3].	Identifying which land use conversions are the strongest drivers of connectivity and node importance in an ecological network [3].
Bayesian Network Inference Tools	Computational methods that use probabilistic graphical models to infer causal regulatory connections from gene expression data, often incorporating prior knowledge [2].	Reconstructing context-specific gene regulatory networks from RNA-seq data across multiple cellular conditions [2].

Deconstructing biological systems into networks of nodes and links provides a powerful, unifying framework for research. This approach enables the integration of disparate data types into a semantically compact model, facilitating the transition from descriptive observation to predictive understanding. For ecologists, this means identifying critical leverage points for conservation. For drug development professionals, it means pinpointing disease modules and robust therapeutic targets within the cellular interactome. Mastering the reconstruction, analysis, and perturbation of these networks is therefore fundamental to advancing our ability to explain and influence the complex fabric of biological systems.

Understanding the structure of ecological networks is fundamental to predicting their function and stability. Ecological networks simplify the vast complexity of the real world by representing interacting species—be they in trophic, mutualistic, or competitive relationships—as nodes (species) connected by links (interactions) [5]. This architectural blueprint, defined by its connectivity, nestedness, and modularity, dictates the flow of energy, the robustness of the community to perturbation, and the overall dynamics of the ecosystem [6] [5]. The matrix A = [aij], where each element aij describes the effect of species j on species i, serves as the foundational data structure from which these metrics are derived [5]. Quantifying this structure is not merely an academic exercise; it is a critical tool for managing biodiversity and ecosystem services in an era of unprecedented planetary change [5].

This guide provides a technical deep dive into the core metrics used to define ecological network structure, framing them within the broader research objective of linking structure to function. It is intended for researchers and scientists who require a clear, actionable overview of the quantitative tools available for network analysis.

Core Structural Metrics

The following tables summarize the key metrics for quantifying the three primary aspects of ecological network structure.

Table 1: Metrics for Network Connectivity/Density

Metric	Formula/Description	Ecological Interpretation	Data Input
Linkage Density	( L/S ) The average number of links per species.	Measures the average level of connectedness in the network. Higher values indicate denser, more complex webs.	S (Species Richness), L (Number of Links) [5]
Connectance	( C = L/S^2 ) For directed networks; ( C = L/[\frac{1}{2}S(S-1)] ) for undirected.	The proportion of all possible links that are realized. A fundamental measure of network complexity and sparsity.	S (Species Richness), L (Number of Links) [5]
Interaction Strength	( a_{ij} ) The per-capita effect of species j on the growth rate of species i.	In weighted networks, the distribution of aij values describes the heterogeneity of influence among species.	Weighted interaction matrix A [5]

Table 2: Metrics for Network Nestedness

Metric	Formula/Description	Ecological Interpretation	Data Input
NODF (Nestedness based on Overlap and Decreasing Fill)	Measures the degree to which specialists interact with subsets of species that generalists interact with. Ranges from 0 (not nested) to 100 (perfectly nested).	Promotes community stability and coexistence in mutualistic networks. Generalists form a core, with specialists interacting with them.	Binary (unweighted) interaction matrix, often for bipartite networks (e.g., plant-pollinator) [5].
WINE (Weighted-Interaction Nestedness)	An extension of NODF that incorporates the strength (weight) of interactions, not just their presence/absence.	Provides a more nuanced view of nested structure by considering the intensity of ecological relationships.	Weighted interaction matrix A [5].

Table 3: Metrics for Network Modularity

Metric	Formula/Description	Ecological Interpretation	Data Input
Newman-Girvan Modularity (Q)	( Q = \sum (e{ii} - ai^2) ) Compares the fraction of links within modules to the expected fraction in a random network.	Identifies compartments (modules) where species interact more frequently amongst themselves than with species in other modules.	Binary or weighted interaction matrix A [6].
GraphRECAP Algorithm	A method that finds compartments with a larger minimum number of habitat patches, ensuring greater robustness to local extinctions.	Used in spatial habitat networks to find modules that are more traversable and have more alternative routes for dispersal.	Spatial graph representing a habitat network (nodes=patches, links=dispersal routes) [6].
Edge Ratio-based Hierarchical Region Discovery (EHRD)	Regionalizes a graph such that movements (or interactions) are more frequent within regions than across regions, without relying on a null model.	Effectively captures animal movement patterns by identifying spatial or functional modules with high internal cohesion.	Graph where nodes represent locations or entities, and links represent flows or interactions (e.g., animal trajectories) [6].

Experimental Protocols for Metric Calculation

The process of moving from raw data to structural insights involves a series of methodological steps. The workflow below outlines the general protocol for calculating the metrics described in the previous section.

Diagram 1: Workflow for network structure analysis.

Detailed Methodological Steps

• Data Collection and Matrix Construction (Protocol): The first step is to construct the interaction matrix A.

  • For Trophic Networks: Conduct field observations, gut content analysis, or stable isotope analysis to determine predator-prey relationships. The element aij can be quantified as the consumption rate of predator i on prey j [5].
  • For Mutualistic Networks: Record visitor-plant interactions through field surveys to build a bipartite network. Links can be weighted by the frequency of visits or the degree of species dependence [5].
  • For Spatial/Habitat Networks: Use Geographic Information Systems (GIS) data to define habitat patches (nodes) and estimate potential dispersal routes (links) based on species movement data or landscape resistance models [6] [7].

• Metric Calculation and Structure Identification (Protocol):

  • Modularity Analysis (GraphRECAP vs. Girvan-Newman): As detailed in a study on ring-tailed lemur habitat networks, GraphRECAP can be applied to find compartments that are more robust to local extinctions. The protocol involves:
    • Inputting a graph where nodes are habitat patches and links represent lemur movement.
    • Running the GraphRECAP algorithm, which was found to produce compartments with stronger within-compartment dispersal and greater traversability compared to the Girvan-Newman method, which can create unbalanced partitions [6].
  • Nestedness Analysis (AJS vs. EAJS): For a mammalian food web, the Extended Additive Jaccard Similarity (EAJS) index can be used to aggregate species with equivalent trophic roles.
    • Calculate the EAJS, which considers species' feeding relations at broader trophic levels, not just adjacent ones.
    • Cluster species using the EAJS index. This has been shown to yield clusters with higher trophic similarities within clusters and stronger separation between clusters compared to the Additive Jaccard Similarity (AJS) index [6].

The Scientist's Toolkit: Research Reagent Solutions

Table 4: Essential Reagents and Tools for Ecological Network Research

Tool/Reagent	Function in Analysis	Example Use Case
Interaction Matrix (A)	The primary data structure; a mathematical representation of the network where elements aij describe the effect of species j on species i [5].	Foundation for all subsequent metric calculations and modeling efforts.
Stable Isotopes (e.g., N15, C13)	To trace energy flow and trophic positions in food webs, helping to quantify the strength of trophic links [5].	Empirically weighting the links in a trophic network matrix.
GIS & Remote Sensing Data	To map and quantify landscape features for constructing spatial ecological networks, defining nodes and resistance surfaces for links [7].	Identifying habitat patches and modeling connectivity corridors for conservation planning.
Cluster Analysis Algorithms	Software routines (e.g., for GraphRECAP, EHRD) that group nodes into modules or regions based on linkage patterns [6].	Automatically detecting compartments in a habitat network or functional groups in a food web.
Null Models	Computational models that generate randomized versions of the network for statistical comparison to validate metric values [6].	Testing whether observed modularity or nestedness is significantly different from chance.

Quantifying connectivity, nestedness, and modularity is not an end in itself. These structural metrics are the levers through which researchers can hypothesize and test theories about ecological function and stability. A network's complexity, embodied by these structures, is intrinsically linked to its propensity to return to a functioning regime after a stress or perturbation [5]. For instance, a modular structure (high Q), as identified by algorithms like GraphRECAP, can enhance robustness by localizing the impact of disturbances, such as a disease outbreak or a species extinction, within one compartment [6]. Conversely, a highly nested structure is often associated with stability and persistence in mutualistic networks [5].

The choice of metric and algorithm is critical, as each carries underlying assumptions. The superior performance of EHRD over Modularity-based Hierarchical Region Discovery (MHRD) in capturing cattle, mule deer, and elk movement patterns underscores this point; EHRD succeeded because it did not rely on an invalid null model for that specific application [6]. Therefore, the ongoing challenge and opportunity for researchers is to continue refining these quantitative tools, ensuring they are ecologically meaningful and capable of illuminating the complex relationship between the architecture of nature's networks and their capacity to endure.

The classical approach to studying ecological networks has often treated their structure—the pattern of who interacts with whom—as a static, intrinsic property that determines community robustness. For decades, network and community ecology has been centered on understanding the importance of these structural patterns in species interaction networks, typically synthesizing data on interactions occurring in a given location and time [8]. This perspective has led to widespread belief that certain network structures, such as modular or nested patterns, are universally advantageous for community persistence. However, emerging research demonstrates that this static structural perspective presents an incomplete picture that fails to capture the dynamic relationship between networks and their environmental contexts.

A groundbreaking synthesis proposes that the importance of any network structure is inherently environment-dependent [8]. This paradigm shift moves beyond cataloging structural patterns to understanding how environmental conditions activate potential network functions. Where traditional approaches might assess a network's importance by its capacity to tolerate external perturbations through random or targeted species removal, the new framework recognizes that network importance changes with perturbation type, direction, and magnitude [8]. This explains why inconsistent conclusions emerge when comparing structures across single environmental contexts—a structure that enhances persistence under one set of conditions may undermine it under another.

This technical guide establishes the theoretical and methodological foundations for studying ecological networks through an environment-dependent lens, providing researchers with tools to bridge the gap between potential structure and realized function across diverse environmental contexts.

Theoretical Foundations: From Static Structure to Dynamic Function

Traditional Structural Assessment and Its Limitations

Ecological networks have traditionally been characterized by their topology—the binary representation of interactions between species within a community. This structural approach has revealed recurring patterns across ecosystems:

• Modular structures where groups of species have dense interactions within groups but sparse interactions between groups [8]
• Nested structures where highly connected species interact with both highly and poorly connected species, while poorly connected species interact primarily with highly connected species [8]

The conventional research agenda has linked these structures to community persistence—the capacity of a community to sustain positive abundances for all constituent species [8]. Through simulations involving sequential species removal or parameter randomization, studies have attempted to identify universally "robust" network structures. This approach has led to generalizations such as modular structures benefiting antagonistic communities and nested structures enhancing mutualistic community persistence [8].

The Environment-Dependent Framework

The emerging paradigm rejects the notion of universally superior network structures, instead proposing that environmental conditions activate specific structural functions [8]. This framework recognizes that:

• Environmental variation is not noise but a central determinant of network function
• The same structure may confer different functional advantages under different conditions
• Network importance must be assessed relative to local environmental settings

This perspective aligns with Stephen J. Gould's proposition that "variation stands out as the only meaningful reality" in biological systems [8]. The critical implication is that temporal or spatial changes in network structure should not be automatically interpreted as changes in robustness, but rather as potential adaptations to changing environmental conditions.

Table 1: Comparison of Network Ecology Paradigms

Aspect	Traditional Structural Approach	Environment-Dependent Framework
Primary focus	Intrinsic network topology	Network-environment interactions
Perspective on structure	Static property determining function	Dynamic capacity activated by conditions
Approach to variation	Noise to be controlled	Central object of study
Generalization goal	Identify universally robust structures	Contextualize structural benefits
Perturbation role	Standardized test of robustness	Environmental context shaping function

Methodological Approaches: Quantitative Frameworks for Environment-Structure-Function Analysis

Structural Stability and Feasibility Domain Analysis

The structural stability approach provides a powerful quantitative methodology for implementing the environment-dependent framework. This approach investigates how the qualitative behavior of a dynamical system changes as a function of its parameters [8]. For ecological networks, this translates to:

• Defining the feasibility domain: The parameter space (environmental conditions) where all species in a community can persist
• Mapping domain boundaries: Identifying environmental thresholds where species extinctions occur
• Comparing domain properties: Analyzing how different network structures shape the feasibility domain

For a two-species community, this can be visualized with axes representing species vital rates and colored regions showing parameter combinations compatible with species coexistence [8]. The size and shape of this feasibility domain depend directly on network structure, creating a quantifiable link between structure and environmental tolerance.

Experimental Protocol: Feasibility Domain Mapping

Objective: Quantify the feasibility domain of a given ecological network structure across environmental gradients.

Materials and Reagents:

• Species interaction data (direct observation, stable isotopes, or molecular gut content analysis)
• Environmental parameter monitoring equipment
• Population tracking methodology (mark-recapture, telemetry, or census protocols)
• Statistical computing environment (R, Python with NumPy/SciPy)

Procedure:

• Parameterize population dynamics using a generalized Lotka-Volterra model: dX_i/dt = X_i * (r_i + Σ_j A_ij * X_j) Where X_i is abundance of species i, r_i is intrinsic growth rate, and A_ij is interaction matrix

• Systematically sample environmental conditions by varying growth rate parameters (r_i) across empirically observed ranges

• Simulate population dynamics for each parameter combination until equilibrium

• Record persistence outcomes (1 for positive abundance, 0 for extinction) for each species

• Calculate feasibility domain volume as the proportion of parameter space where all species persist

• Repeat for alternative network structures while maintaining same number and type of interactions

• Compare domain shapes and volumes across structures and environmental contexts

This protocol generates quantitative data on how network structures perform across environmental conditions, moving beyond single-context assessments.

Quantitative Analysis of Environment-Structure Interactions

The environment-dependent framework requires specialized analytical approaches to detect context-dependent structural effects:

Multi-environment Meta-Analysis:

• Compile network data from multiple environmental contexts
• Standardize persistence metrics across studies
• Test for structure × environment interaction effects
• Model optimal structures along environmental gradients

Temporal Network Analysis:

• Track network structure across environmental fluctuations
• Calculate lagged responses to environmental changes
• Identify structural resilience indicators

Table 2: Key Metrics for Environment-Network Analysis

Metric	Calculation	Interpretation
Feasibility Domain Volume	Proportion of parameter space permitting full species persistence	Environmental tolerance range of a network structure
Domain Overlap Index	Shared parameter space between structures under comparison	Functional equivalence across environments
Environmental Sensitivity	Change in persistence per unit environmental change	Responsiveness to environmental variation
Structure-Environment Fit	Correlation between structural properties and environmental conditions	Adaptation of structure to environment

Visualization and Data Representation

Network-Environment Relationship Mapping

Effective visualization must communicate the dynamic relationship between network structure and environmental context. The following Graphviz diagram illustrates the conceptual framework of environment-structure-function relationships:

This diagram highlights the central premises that: (1) environmental context shapes both network structure and function, (2) structure enables but does not determine function, and (3) environment activates specific functions from structural potential.

Experimental Workflow for Environment-Dependent Network Analysis

The methodological approach for implementing the environment-dependent framework requires integrated data collection and analysis:

This workflow emphasizes the parallel characterization of network structure and environmental parameters, integrated through feasibility domain mapping, to establish context-structure-function relationships.

Data Visualization Best Practices

Effective visualization of ecological networks requires careful color application to enhance interpretation while maintaining accessibility:

Color Selection Guidelines:

• Limit palette complexity: Avoid overwhelming viewers with too many colors; 6-8 distinct colors typically represents the maximum for clear differentiation [9]
• Ensure adequate contrast: Select colors with sufficient luminance difference for clear distinction, considering color vision deficiencies [9]
• Maintain consistency: Use identical hues for the same variables across multiple visualizations to avoid confusion [9]
• Choose appropriate color scales: Match color scale type (categorical, sequential, diverging) to data characteristics and analysis goals [9]

Accessibility Considerations:

• Test color contrast using Advanced Perceptual Contrast Algorithm (APCA) rather than traditional WCAG ratios [9]
• Avoid problematic color combinations (red/green, blue/purple) that challenge color vision deficiencies [9]
• Provide alternative encodings (pattern, shape) alongside color differentiation [9]

Table 3: Research Reagent Solutions for Ecological Network Analysis

Tool/Resource	Function/Purpose	Implementation Considerations
Interaction Matrix	Binary or quantitative representation of species interactions	Foundation for topological analysis; determines structural metrics
Feasibility Domain Mapping	Identifies environmental conditions supporting full species persistence	Requires parameter sampling across realistic environmental ranges
Structural Stability Analysis	Quantifies tolerance to parameter changes	Links topological structure to dynamical outcomes
Null Model Ensembles	Benchmark for detecting significant structural patterns	Must carefully select appropriate randomization constraints
Environmental Gradient Analysis	Tests structure-function relationships across conditions	Requires replication across environmental contexts
Dynamic Network Modeling	Simulates temporal structural changes	Captures network responses to environmental variation

Discussion: Implications for Research and Application

Advancing Ecological Forecasting

The environment-dependent framework transforms how we approach ecological forecasting and management. Rather than seeking universal structural indicators of ecosystem health, conservation strategies can identify context-appropriate structural targets. This enables:

• Condition-specific management: Tailoring interventions to current and projected environmental conditions
• Precision conservation: Identifying structural interventions most likely to succeed in specific contexts
• Climate adaptation planning: Projecting how network structures will function under future climates

Methodological Innovations Needed

Fully realizing the potential of environment-dependent network analysis requires methodological advances:

• High-throughput interaction mapping to capture structural variation across contexts
• Automated feasibility domain calculation for complex, large-scale networks
• Standardized environmental metadata to enable cross-study comparison
• Longitudinal network monitoring to track structure-environment coevolution

Applications Beyond Ecology

The environment-dependent framework extends to other network systems where structure-function relationships are context-dependent:

• Biomedical networks: Protein-protein interactions across cellular environments
• Social networks: Information flow across cultural and institutional contexts
• Economic networks: Trade relationships across market conditions

In each case, the shift from cataloging static structures to understanding environment-activated functions provides a more powerful predictive framework.

The paradigm shift from static structural assessment to environment-dependent function represents a maturation of network ecology. By recognizing that environmental conditions activate specific functions from structural potential, researchers can develop more accurate predictive models and more effective conservation strategies. The methodological toolkit presented here—centered on feasibility domain mapping across environmental gradients—provides a roadmap for implementing this framework.

Future research must prioritize multi-context network data collection, develop standardized metrics for environment-structure-function relationships, and create analytical tools specifically designed for detecting context-dependent effects. Through these advances, ecological network science will transition from classifying structures to predicting functions across the environmental variation that characterizes natural systems.

The convergence of ecology and biomedical science represents a paradigm shift in how we understand complex biological systems, from the human body to drug interactions. Ecological principles, particularly the study of ecological networks (ENs), provide powerful frameworks for understanding the complex, interconnected systems that characterize human physiology, disease pathology, and therapeutic interventions [10]. This guide establishes core ecological concepts as fundamental tools for biomedical researchers and drug development professionals, translating methodologies from landscape ecology into analyzable, quantitative frameworks for biomedical innovation.

Ecological networks model interactions between species and their environment, focusing on structure (physical patterns and connections) and function (dynamic processes and flows) [11] [12]. Similarly, human biological systems comprise intricate networks—from molecular signaling pathways to microbial communities—where structure dictates function. The degradation of an ecological network's integrity through habitat fragmentation has direct conceptual parallels to the breakdown of cellular communication in disease states or the collapse of beneficial gut microbiota due to antibiotic treatment [11] [10]. By adopting this ecological lens, researchers can develop more predictive models of disease progression and therapeutic response.

Core Ecological Principles for Biomedical Applications

Integrating ecology into biomedical research requires a foundational understanding of key principles and their corresponding biomedical interpretations.

Table 1: Core Ecological Principles and Their Biomedical Correlates

Ecological Principle	Ecological Context & Definition	Biomedical Application	Relevant Quantitative Metrics
Network Structure & Connectivity	The physical configuration of ecological sources, patches, and corridors that maintain landscape integrity [11] [12].	Architecture of organ systems, vascular networks, neural circuits, and protein-protein interaction networks.	Connectivity indices, corridor centrality, node degree (network analysis) [12].
Functional Sustainability	The capacity of an ecological network to consistently maintain ecosystem services despite external pressures [12].	System resilience (e.g., organ functional reserve, immune system robustness) and its decline in disease or aging.	Rate of functional decline, service provision under stress [12].
Structural Stability	The ability of a network to maintain overall connectivity and function when components are disrupted [12].	Robustness of biological systems to perturbation (e.g., cancer resistance to therapy, metabolic stability).	Maximum connectivity, transitivity, efficiency (Graph theory metrics) [12].
Information Processing	The role of information (genetic, behavioral, chemical) in structuring ecological interactions and system dynamics [10].	Cellular signaling (autocrine/paracrine), neural communication, and immunological memory.	Information entropy, signal fidelity, network rewiring capacity [10].
Spatiotemporal Dynamics	The evolution of network patterns and functions over time and space in response to drivers like climate change [11] [12].	Disease progression (e.g., metastasis, neurodegeneration), circadian rhythms, and pharmacokinetics/pharmacodynamics.	Dynamics of spatial correlation, range shifts, flow resistance [11].

The fifth principle, Information Processing, is particularly foundational. Ecological science recognizes information as a fundamental feature of living systems, alongside energy and matter [10]. This principle manifests in two forms: syntactic information (the statistical, thermodynamic properties of biological structures) and semiotic information (the meaning or interpretation of signals within a biological context, such as a ligand binding to its receptor) [10]. In biomedicine, this translates to the analysis of both the physical flow of biomolecules and the contextual "meaning" of those flows within a cellular network, driving processes like apoptosis, proliferation, and differentiation.

Quantitative Frameworks and Data Analysis

Translating ecological principles into biomedical research requires robust quantitative frameworks. The following table summarizes key data types and analytical approaches adapted from ecological network analysis.

Table 2: Quantitative Data Types and Analytical Methods for Biomedical Ecology

Data Category	Definition & Ecological Example	Biomedical Example	Recommended Analysis Tools
Discrete Data	Countable, whole numbers. Example: Number of species in a patch [13].	Number of metastatic foci, count of specific immune cell types (e.g., CD4+ T-cells) in a tumor.	Tally charts, bar graphs, Poisson regression models.
Continuous Data	Measurable, infinitely divisible values. Example: Biomass, temperature [13].	Tumor volume, blood pressure, enzyme concentration, gene expression levels.	Linear regression, correlation analysis, time-series modeling.
Spatial Data	Georeferenced information on patterns. Example: Land use/land cover (LULC) maps [11] [12].	Histopathology slide images, spatial transcriptomics data, metastatic spread patterns on medical imaging.	Geographic Information Systems (GIS), spatial autocorrelation (Moran's I), circuit theory models [11].
Network Data	Data defining nodes and edges. Example: Species interactions, corridor linkages [14] [12].	Protein-protein interactions, neuronal connectivity maps, metabolic pathways.	Graph theory (NetworkX, Cytoscape), centrality measures, community detection algorithms [14] [12].

A critical step in analysis is assessing the granularity of the data—what a single row in a dataset represents [15]. In a tumor microenvironment dataset, a record could be a single cell (high granularity), a tumor region, or an entire patient (low granularity). This determines the appropriate level for statistical analysis and inference. Furthermore, understanding the domain of each field—the possible values it should contain—is crucial for data validation and cleaning. For instance, the domain for a "cell viability" field should be values between 0 and 100, and any outliers should be investigated as potential errors or biologically significant anomalies [15].

Experimental Protocols: From Ecology to Biomedicine

Protocol 1: Assessing Network Structural Stability

This protocol adapts ecological methods for evaluating network robustness to biomedical contexts, such as analyzing a protein-protein interaction (PPI) network in a cancer cell.

1. Define Network Nodes and Edges:

• Ecological Method: Identify ecological sources (core habitats) and corridors (linkages) using GIS and circuit theory [11] [12].
• Biomedical Adaptation: Define nodes (e.g., proteins, genes, cells) and edges (e.g., physical interactions, regulatory relationships) from databases like STRING or via high-throughput yeast-two-hybrid screens.

2. Construct the Network Model:

• Ecological Method: Use tools like Linkage Mapper to map corridors and build the network graph [12].
• Biomedical Adaptation: Use NetworkX (Python) or Cytoscape to construct an undirected graph representing the PPI network [14] [12].

3. Calculate Structural Metrics:

• Calculate key stability metrics for the entire network:
  • Maximum Connectivity (Component Size): The size of the largest connected subgraph.
  • Transitivity (Clustering Coefficient): The probability that adjacent nodes are connected.
  • Global Efficiency: The average inverse of the shortest path length, measuring parallel information flow [12].

4. Simulate Node/Edge Failure:

• Systematically remove nodes (simulating gene knockout or protein inhibition) or edges (simulating disrupted interactions).
• After each removal, recalculate the structural metrics from Step 3.

5. Analyze Stability:

• Plot the change in network metrics against the proportion of removed components.
• A robust network will show a slow decline in connectivity and efficiency, identifying fragile hubs critical for network integrity which represent potential therapeutic targets [12].

Protocol 2: Mapping Functional Corridors and Flows

This protocol adapts ecological corridor analysis to map the flow of signals or metabolites in a tissue.

1. Define Sources and Resistance Surface:

• Ecological Method: Identify ecological sources from land cover data. Create a resistance surface where landscape features (e.g., roads, urban areas) impede species movement [11].
• Biomedical Adaptation:
  • Sources: Define source points (e.g., cytokine-secreting cells, metabolite-producing regions).
  • Resistance Surface: Create a raster where each cell's value represents resistance to signal diffusion. Factors include: density of physical barriers (e.g., extracellular matrix), presence of degrading enzymes (e.g., phosphatases), or distance from vasculature.

2. Model Functional Corridors:

• Ecological Method: Use circuit theory (e.g., Circuitscape) or Least-Cost Path analysis to predict movement routes [11].
• Biomedical Adaptation: Apply the same algorithms to the biomedical resistance surface to map probable "corridors" of high signal flow and "pinch points" where communication is easily disrupted.

3. Validate with Spatial Analysis:

• Ecological Method: Use spatial autocorrelation (e.g., Moran's I) to correlate network patterns with ecological risk [11].
• Biomedical Adaptation: Use spatial transcriptomics or proteomics data to validate if gene/protein expression correlates with predicted corridors of high functional connectivity.

Diagram 1: Functional corridor mapping workflow.

The Scientist's Toolkit: Essential Reagents and Materials

This table details key reagents and their functions for implementing the ecological-network-based protocols in a biomedical laboratory setting.

Table 3: Research Reagent Solutions for Ecological Network Analysis in Biomedicine

Reagent / Material	Supplier Examples	Function in Experimental Protocol
Recombinant Signaling Proteins (Cytokines, Growth Factors)	PeproTech, R&D Systems	Serve as defined "sources" in functional corridor mapping (Protocol 2) to experimentally manipulate network inputs.
Small Molecule Inhibitors/Agonists	Tocris Bioscience, Selleckchem	Used in node/edge failure simulations (Protocol 1) to specifically disrupt nodes (proteins) in a network.
Tissue Dissociation Kits	Miltenyi Biotec, STEMCELL Technologies	Enable single-cell suspension creation from tissues for high-granularity network analysis via scRNA-seq.
Antibodies for Multiplexed Imaging (CODEX, CyCIF)	BioLegend, Abcam	Generate spatial protein expression data for constructing and validating spatial resistance surfaces and corridors.
scRNA-seq Library Prep Kits	10x Genomics, Parse Biosciences	Provide high-dimensional data to define cell states (nodes) and infer regulatory interactions (edges) for network construction.
CRISPR Knockout Libraries	Addgene, Sigma-Aldrich	Enable large-scale, parallelized node removal studies to empirically test network stability and identify fragile hubs.
Graph Analysis Software (NetworkX, Cytoscape)	Open Source, Cytoscape Consortium	Primary tools for calculating network metrics, visualizing topology, and simulating disruptions [14] [12].

Visualization of Biomedical Networks

Effective visualization is critical for interpreting complex network data and communicating findings. Adherence to foundational rules ensures clarity and prevents misinterpretation [14].

Rule 1: Determine the Figure's Purpose. Before creation, decide if the message is about network functionality (e.g., signal flow, requiring directed edges/arrows) or network structure (e.g., protein complexes, requiring undirected edges) [14].

Rule 2: Consider Alternative Layouts. While node-link diagrams are common, dense networks can become cluttered.

• Adjacency matrices are excellent for dense networks and easily display edge attributes via cell color [14].
• Fixed layouts position nodes based on external data (e.g., a node's position on a linear chromosome or within a cellular compartment) [14].

Rule 3: Beware of Unintended Spatial Interpretations. In node-link diagrams, viewers inherently interpret proximity and centrality as indicating similarity or importance. Use layout algorithms (force-directed, multidimensional scaling) that spatially group nodes based on actual biological similarity or interaction strength [14].

Rule 4: Provide Readable Labels and Captions. All labels must be legible at publication size. If labels cannot be fit without clutter, provide a high-resolution version and use leader lines. The caption should fully explain symbols, colors, and layouts [14].

Diagram 2: Example signaling pathway with functional flow.

The integration of ecological principles into biomedical research marks a significant advancement toward a more holistic and predictive understanding of human biology and disease. By treating physiological systems, tumors, and microbial communities as ecological networks with defined structures and functions, researchers can leverage powerful analytical tools from ecology. This cross-disciplinary approach, utilizing quantitative metrics, spatial analysis, and robust visualizations, provides a framework for uncovering the fundamental rules governing system robustness, vulnerability, and dynamic adaptation. Ultimately, this ecological perspective is poised to drive innovation in drug discovery, the development of combination therapies that target network fragility, and the creation of sophisticated diagnostic and prognostic models based on systemic integrity rather than isolated biomarkers.

From Theory to Practice: Tools and Techniques for Network Construction and Analysis

Ecological network research provides a critical framework for understanding complex species interactions and their influence on ecosystem functioning. The ability to accurately define, analyze, and visualize these networks directly impacts our capacity to predict ecological stability, biodiversity patterns, and ecosystem responses to environmental change. Within this scientific domain, specialized software tools have become indispensable for handling the computational complexity of ecological networks. This technical guide examines three pivotal platforms—Cytoscape, NetworkX, and BEFANA—that enable researchers to transform raw ecological data into meaningful ecological insights. Each tool offers distinct methodological advantages for particular research scenarios, from sophisticated visualization to flexible programming interfaces and integrated ecological analysis. Understanding their complementary capabilities allows ecological researchers to select appropriate methodologies that strengthen the empirical foundation of ecological network science and advance our understanding of ecosystem structure-function relationships.

Comparative Tool Analysis

The selection of an appropriate analytical platform significantly influences research outcomes in ecological network studies. The table below provides a systematic comparison of three specialized tools across multiple technical dimensions:

Table 1: Technical Comparison of Ecological Network Analysis Tools

Feature	Cytoscape	NetworkX	BEFANA
Primary Focus	Network visualization & exploration	Graph algorithm development & analysis	Biodiversity-ecosystem functioning assessment
Programming Base	Java-based desktop application	Python library	Free & open-source software [16]
Key Strength	Advanced visual encoding & styling [17]	Flexible graph manipulation & algorithm implementation [18]	Integrated topological analysis & machine learning [16]
Visualization Capability	High-quality renderings with extensive style options [17]	Basic matplotlib integration with customization [19] [20]	Specialized for ecological network representation
Learning Curve	Moderate (GUI-based)	Steep (programming required)	Moderate (ecology-specific interface)
Data Compatibility	SIF, GML, XGMML, CSV	Edge lists, dictionaries, NumPy arrays	Ecological data formats (food webs, interaction matrices)
Ecological Applications	Protein-protein interaction, gene regulatory networks	Custom ecological models, network metrics	Soil food webs, biodiversity-ecosystem functioning [16] [21]

Each platform serves a distinct niche within the research ecosystem. Cytoscape excels in producing publication-quality visualizations through its sophisticated style mapping system, which allows visual properties like color, size, and shape to be encoded based on node or edge attributes [17]. NetworkX provides researchers with unparalleled flexibility for developing custom analyses, implementing novel metrics, and prototyping ecological models through Python's expressive programming environment [18]. BEFANA occupies a specialized position with its dedicated focus on biodiversity-ecosystem functioning relationships, incorporating both topological analysis and machine learning approaches specifically tailored to ecological questions [16] [21].

Experimental Applications in Ecological Research

Case Study: Soil Food Web Analysis with BEFANA

BEFANA provides researchers with a structured methodology for investigating biodiversity-ecosystem functioning relationships in soil environments. The tool was specifically applied to analyze a detrital soil food web of an agricultural grassland, demonstrating its capability to handle complex ecological interactions [16]. The experimental protocol encompasses several critical phases:

• Data Collection and Integration: Researchers compile interaction data representing trophic relationships among soil organisms, typically obtained from field sampling, literature review, or databases like EUdaphobase.

• Network Construction: Species or functional groups are represented as nodes, while trophic interactions form the directed edges, creating a comprehensive food web structure.

• Topological Analysis: BEFANA calculates structural metrics including connectance, modularity, and centrality indices to identify key species and interaction patterns.

• Dynamics Assessment: The tool incorporates population dynamics models to simulate perturbation responses and stability properties.

• Machine Learning Application: Selected algorithms identify non-linear relationships between biodiversity components and ecosystem process rates.

This methodology has revealed critical insights into how soil community structure influences decomposition processes and nutrient cycling, providing empirical evidence for the functional importance of soil biodiversity in agricultural ecosystems.

Ecological Network Optimization Protocol

Research on ecological network optimization employs a sophisticated simulation approach to improve landscape connectivity, as demonstrated in the Nanping case study [22]. The experimental workflow involves:

• Scenario Development: Create future land-use scenarios (e.g., natural development vs. ecological protection) using the CLUE-S model to simulate spatial patterns.

• Ecosystem Service Quantification: Apply the InVEST model to estimate key services including habitat quality, soil retention, and water yield under each scenario.

• Trade-off Analysis: Calculate correlation coefficients between paired ecosystem services to identify synergies and trade-offs across the landscape.

• Network Construction: Define ecological sources, corridors, and nodes using circuit theory or least-cost path approaches based on habitat connectivity.

• Structural Enhancement: Implement optimization measures including additional ecological sources, corridor restoration, and stepping stone patches.

This protocol successfully demonstrated that optimized ecological networks in Nanping showed significantly improved connectivity metrics, with circuitry increasing to 0.45, edge/node ratio to 1.86, and network connectivity to 0.64 [22]. This methodological framework provides a reproducible approach for enhancing ecological network functionality in fragmented landscapes.

Visualization Techniques and Workflows

Cytoscape Styling Workflow

Cytoscape's sophisticated visual encoding system enables researchers to create highly informative network representations through a structured styling process:

The workflow begins with data importation, followed by style creation and visual property mapping. A critical decision point involves selecting appropriate color palettes based on data characteristics: sequential for gradient values, qualitative for categorical data, and diverging for positive/negative value differentiations [23] [24]. Cytoscape supports multiple palette systems including ColorBrewer and Viridis, which provide scientifically rigorous color schemes optimized for data visualization [23]. Researchers can map visual properties including node size (degree centrality), color (expression data), border width (betweenness centrality), and shape (functional group) to create multidimensional representations of complex ecological networks.

NetworkX Analysis Pipeline

NetworkX enables programmatic network creation and analysis through a structured coding approach, particularly valuable for prototyping ecological models:

This pipeline demonstrates NetworkX's flexible approach to network construction, beginning with graph initialization and progressing through node/edge addition with optional attribute attachment [18]. The analytical phase computes standard network metrics including degree distributions, centrality measures, and clustering coefficients, which provide quantitative descriptors of ecological network structure. For visualization, NetworkX integrates with matplotlib to create custom plots, such as node coloring by degree using colormaps [20]. This programmatic approach enables researchers to implement specialized analyses such as simulating species loss cascades, modeling interaction rewiring under environmental change, or calculating stability metrics from network topology.

Ecological network research requires both computational tools and conceptual frameworks to ensure scientifically robust outcomes. The following table catalogues essential methodological components referenced across the examined platforms:

Table 2: Essential Methodological Components for Ecological Network Research

Component	Function	Implementation Examples
Color Palettes	Encode categorical or continuous data in visualizations	ColorBrewer (sequential, divergent, qualitative) [23], Viridis [23]
Layout Algorithms	Determine node positioning for visual interpretation	Circular layout [20], Spring layout [19]
Network Metrics	Quantify structural properties of ecological networks	Degree centrality, connectivity, circuitry [22]
Statistical Mappings	Link data attributes to visual properties	Continuous mapping, discrete mapping, bypass overrides [17]
Ecological Indicators	Assess ecosystem structure and function	Habitat quality, soil retention, biodiversity indices [22]
Data Exchange Formats	Enable tool interoperability and data preservation	SIF, GML, XGMML (Cytoscape), Edge lists (NetworkX)

These methodological components form the essential conceptual infrastructure supporting ecological network research across domains. Color palettes and layout algorithms enable effective visual communication of complex relationships, while network metrics provide standardized quantitative descriptors for structural comparison. The integration of ecological indicators with network approaches represents a particularly promising direction for future methodological development, creating bridges between traditional ecology and network science.

The integrative use of Cytoscape, NetworkX, and BEFANA represents a powerful methodological framework for advancing ecological network research. Each platform brings complementary capabilities to the research process: Cytoscape provides sophisticated visualization and style mapping for interpreting complex networks [17]; NetworkX offers flexible programming interfaces for developing custom analyses and algorithms [18]; and BEFANA delivers specialized analytical workflows for linking biodiversity patterns to ecosystem functioning [16] [21]. This toolkit approach enables researchers to address fundamental questions about how ecological network structure influences ecosystem dynamics, stability, and responses to environmental change. As ecological challenges become increasingly complex and pressing, these computational tools will play an evermore critical role in generating insights that inform conservation prioritization, ecosystem management, and biodiversity policy. The continuing development and integration of these platforms will further strengthen our capacity to understand and protect ecological systems in an era of rapid global change.

Ecological networks (ENs) represent complex systems of interconnected habitats that maintain ecological integrity and biodiversity across landscapes. As human-induced habitat fragmentation intensifies globally, constructing ecological networks has emerged as a critical conservation strategy for mitigating ecosystem degradation [12]. The research framework for defining ecological network structure and function primarily follows two complementary technical routes: function-oriented strategies that emphasize ecosystem service assessment, and structure-oriented strategies that focus on the topological attributes and spatial configuration of the network [12]. This guide provides a comprehensive methodological framework for identifying ecological sources and corridors, integrating both functional and structural perspectives to ensure sustainable ecological network planning.

The fundamental premise of ecological network construction lies in its capacity to connect adjacent habitats (sources) through corridors, thereby maintaining the integrity and continuity of the entire landscape [12]. These networks serve as vital physical spaces for urban ecological systems, forming when multiple urban ecological patches connect to form corridors, which subsequently create interconnected networks [25]. Within the context of rapid urbanization, the precise identification of ecological sources and corridors has become increasingly crucial for balancing ecological conservation with developmental pressures.

Foundational Concepts and Definitions

Ecological Sources: Core habitat areas that serve as biodiversity reservoirs and provide significant ecosystem services. These natural resource patches constitute important habitats for species survival and migration while delivering various ecosystem benefits [12]. Contemporary selection of ecological sources has evolved from subjective selection of large landscape patches to quantitative evaluation using methods like Morphological Spatial Pattern Analysis (MSPA) and landscape connectivity assessment [26].

Ecological Corridors: Linear landscape elements that connect ecological sources, facilitating the movement of organisms and ecological flows between core habitats. Ecological corridors were initially designed to connect natural habitats for wildlife protection [26], with their conceptual foundation rooted in mitigating habitat fragmentation by connecting fragmented patches [26].

Ecological Networks: Integrated systems comprising ecological sources, corridors, and nodes that together maintain landscape connectivity and ecological processes. These complex networks connect core areas, nature reserves, and other landscape elements through ecological corridors and ecological nodes [26].

Data Acquisition and Preparation: Multi-Source Geospatial Data Integration

Constructing ecological networks requires integrating diverse geospatial datasets to accurately represent landscape characteristics and ecological processes. The table below summarizes the essential data requirements for ecological network identification.

Table 1: Essential Data Types for Ecological Network Construction

Data Category	Specific Data Types	Spatial Resolution	Primary Application
Land Use/Land Cover (LULC)	Forest, grassland, cropland, water body, built-up land, unused land [12]	1 km or finer [12]	Ecological source identification, resistance surface development
Climate Data	Annual mean temperature, annual precipitation [12]	Varies by GCM	Climate scenario construction
Topographic Data	Digital Elevation Model (DEM) [12] [26]	30m-250m [26]	Resistance surface factor
Infrastructure Data	Roads, railways [26]	Vector format	Anthropogenic resistance factor
Hydrological Data	Rivers, lakes, reservoirs [26]	Vector format	Ecological source identification
Vegetation Indices	NDVI, NPP [12]	Varies by sensor	Ecosystem service assessment
Human Impact Data	Human Footprint Index [12]	1 km	Resistance surface development

All datasets must be converted to a consistent projected coordinate system and resampled to a uniform spatial resolution (typically 1×1 km for regional analyses) to ensure analytical compatibility [12]. The integration of multi-source geospatial data, including remote sensing imagery and Points of Interest (POI) data, has become increasingly valuable for identifying urban functional areas and optimizing ecological networks [25].

Methodological Framework: A Step-by-Step Technical Protocol

Ecological sources form the foundation of ecological networks and can be identified through multiple complementary approaches:

Ecosystem Service Assessment Method: This function-oriented approach identifies areas crucial for providing key ecosystem services.

• Technical Implementation: Utilize geospatial models like InVEST, SolVES, or ARIES to evaluate ecosystem services such as habitat provision, soil conservation, and water retention [12]. These models effectively identify important natural resources and provide reliable references for EN construction.
• Analysis Workflow:
  • Select relevant ecosystem services based on regional characteristics
  • Run model simulations for each service
  • Overlay results to identify areas of high ecosystem service importance
  • Apply threshold criteria to delineate ecological sources

Spatial Pattern Analysis Method: This structure-oriented approach uses morphological characteristics to identify core habitat areas.

• Technical Implementation: Apply Morphological Spatial Pattern Analysis (MSPA) to classify landscape patterns into core, edge, bridge, and other morphological classes [26]. This method quantitatively evaluates the importance of ecological sources based on landscape connectivity.
• Analysis Workflow:
  • Preprocess land use data into binary maps (habitat vs. non-habitat)
  • Run MSPA classification using GUIDOS or similar tools
  • Extract core areas as potential ecological sources
  • Evaluate connectivity using Conefor2.6 or equivalent software

Step 2: Constructing Resistance Surfaces

Resistance surfaces represent the landscape's permeability to species movement and ecological flows, reflecting the cost or difficulty of movement through different areas [26].

Table 2: Typical Resistance Factors and Weighting Scheme

Resistance Factor	Sub-factors	Weight Range	Resistance Values
Land Use Type	Forest, grassland, water, cropland, built-up areas [26]	0.3-0.4	Low (forest) → High (built-up)
Topographic Conditions	Elevation, slope, aspect [26]	0.1-0.2	Varied by species requirements
Human Activity Intensity	Distance to roads, settlements, human footprint index [12]	0.2-0.3	Increasing with proximity
Infrastructure Density	Road density, building density [26]	0.1-0.2	Increasing with density

The resistance surface is constructed through weighted overlay analysis, with factor weights determined by expert judgment or analytical methods like Analytic Hierarchy Process (AHP). The general equation for resistance surface calculation is:

[ R = \sum{i=1}^{n} wi \times r_i ]

Where (R) is the total resistance, (wi) is the weight for factor (i), and (ri) is the resistance value for factor (i).

Step 3: Extracting Ecological Corridors and Nodes

Corridor Identification: The Minimal Cumulative Resistance (MCR) model is widely applied to identify potential ecological corridors [26]. The MCR model calculates the least-cost path between ecological sources, representing the route that minimizes movement resistance.

• Technical Implementation: Utilize Linkage Mapper software (https://linkagemapper.org/) to automatically generate least-cost paths between ecological sources [12] [26]. This toolbox calculates cost-weighted distances and identifies optimal connectivity pathways.
• Analytical Workflow:
  • Input ecological sources and resistance surface
  • Run cost-distance analysis
  • Generate least-cost paths between sources
  • Classify corridors by importance based on connectivity metrics

Node Identification: Ecological nodes are typically located at the convergence points of ecological corridors or in areas of functional weakness that connect scattered and isolated patches [26]. These nodes enhance ecological source connectivity and promote ecological flows through the network.

• Technical Implementation: Apply circuit theory models or pinchpoint analysis within Linkage Mapper to identify critical connectivity areas [26]. The ecological resistance surface model is widely used in extracting ecological nodes [26].

Methodological Integration Workflow

The following diagram illustrates the integrated methodological framework for identifying ecological sources and corridors:

Analytical Tools and Computational Approaches

Software Toolkit for Ecological Network Analysis

Table 3: Essential Software Tools for Ecological Network Construction

Software Tool	Primary Function	Application Context	Access
Linkage Mapper	Identifying ecological corridors and least-cost paths [12] [26]	Core corridor identification	https://linkagemapper.org/
Fragstats	Calculating landscape pattern metrics [26]	Landscape structure analysis	Commercial
Conefor	Assessing landscape connectivity [26]	Functional connectivity analysis	http://www.conefor.org/
NetworkX	Analyzing network structural stability [12]	Graph theory-based network analysis	Python library
InVEST	Evaluating ecosystem services [12]	Ecological source identification	https://naturalcapitalproject.stanford.edu/

Advanced Analytical Techniques

Structural Stability Assessment: Using NetworkX or similar graph analysis tools, researchers can calculate three key structural metrics to assess EN stability: maximum connectivity, transitivity, and efficiency [12]. This analysis involves systematically removing sources and corridors from the network and measuring the impact on overall connectivity.

Climate Scenario Integration: Constructing multiple future climate scenarios using Global Circulation Models (GCMs) of Shared Socioeconomic Pathways (SSPs) enables prospective assessment of EN sustainability [12]. This involves:

• Selecting relevant climate scenarios (e.g., SSP1-1.9, SSP2-4.5, SSP5-8.5)
• Integrating climate projections with land use change scenarios
• Assessing functional sustainability through range differences between current and future ecological sources

Citizen Experience Integration: Combining spatial analysis with public evaluation data from platforms like Dianping enables researchers to understand citizens' experiences and evaluations of urban ecological construction [25]. Sentiment analysis techniques can reveal issues with ecological corridors from multiple dimensions, enhancing public participation in corridor governance.

Case Study Applications: Methodological Implementation

Chongqing Mountainous Area Application

In the mountainous Chongqing region, researchers implemented a comprehensive ecological network identification process with the following outcomes [26]:

• Ecological Sources: 24 ecological sources were selected using MSPA and Conefor2.6 software
• Corridor Network: 87 potential ecological corridors and 35 ecological nodes were generated
• Network Metrics: Total network length of 2,524.34 km with average corridor length of 29.02 km
• Assessment Outcome: High overall complexity and network efficiency, but uneven spatial distribution, particularly in southwestern Chongqing

Xuchang Central Urban Area Application

In the central urban area of Xuchang, researchers employed multisource geospatial data to identify ecological corridors with specific results [25]:

• Spatial Pattern: Primary ecological corridor pattern situated in Weidu District
• Network Configuration: Precisely delineated 11 main ecological corridors in the central urban area
• Structural Analysis: Identification of Xudu Park as the ecological network hub, with West Lake Park and Luming Lake Park forming the core of the urban park system
• Methodological Innovation: Integration of POI data with public evaluation data to overcome limitations of remote sensing in urban environments

Yangtze River Delta Urban Agglomeration Application

This large-scale application demonstrated the integration of functional and structural assessment under climate change scenarios [12]:

• Climate Impact: 6.23% of current ecological sources projected to decline in ecosystem service provision by 2050 under nine future climate scenarios
• Structural Consequence: 33.55% decrease in EN structural stability resulting from functional degradations
• Spatial Pattern: Poor functional sustainable sources predominantly located in forests and water bodies with small average patch area, while high functional sustainable sources distributed in southwestern mountainous regions with larger average patch areas

Table 4: Essential Research Materials and Analytical Resources

Tool/Category	Specific Examples	Function/Application	Technical Specifications
Geospatial Data	LULC, DEM, Climate, HFP [12]	Landscape characterization	1km resolution, consistent projection
Connectivity Software	Linkage Mapper, Conefor [26]	Corridor identification, connectivity assessment	Cost-distance algorithms, graph theory
Ecosystem Service Models	InVEST, SolVES, ARIES [12]	Functional assessment of sources	Spatial explicit modeling
Landscape Metrics Tools	Fragstats, GUIDOS [26]	Structural pattern analysis	MSPA, patch-matrix analysis
Climate Projection Data	GCMs (EC-Earth3, GFDL-ESM4, MRI-ESM2-0) [12]	Future scenario construction	SSP pathways (1-1.9, 2-4.5, 5-8.5)
Social Data Sources	POI data, Dianping reviews [25]	Human experience integration	Text analysis, sentiment analysis

The methodological framework presented in this guide enables a comprehensive approach to ecological network identification that integrates both structural and functional dimensions. By following the step-by-step protocol of source identification, resistance surface development, and corridor extraction, researchers can create robust ecological networks that address both current conservation needs and future environmental challenges.

The integration of climate change scenarios and human experience data represents the cutting edge of ecological network research, moving beyond static structural assessments to dynamic, multi-dimensional evaluations. This integrated approach is particularly crucial for enhancing ecological strategies and ensuring landscape sustainability in the face of rapid urbanization and climate change [12].

Future methodological developments will likely focus on refining the integration of functional sustainability and structural stability assessments, enhancing the capacity of ecological networks to serve as effective spatial regulation strategies for biodiversity conservation and ecosystem benefit maintenance across changing environmental conditions.

The study of complex systems, from ecological communities to biomedical networks, requires analytical frameworks that can capture the multi-faceted nature of interactions within these systems. This technical guide introduces the Resource-Consumer-Function (RCF) tensor framework for multilayer network analysis, providing a mathematical foundation for integrating multiple interaction types into a unified model. Developed initially for ecological research, this framework demonstrates how multidimensional data structures can reveal hidden architectural patterns in complex networks, enabling the identification of keystone elements and their roles in system stability and function. The RCF tensor approach represents a paradigm shift from single-layer, unifunctional analyses toward a more holistic understanding of system complexity.

Traditional network analysis in ecology and bioinformatics has predominantly focused on single-layer representations of interactions, examining one relationship type at a time (e.g., pollination networks or protein-protein interactions). This approach overlooks the synergistic effects that emerge when multiple functions operate simultaneously within a system [27]. The challenge of integrating diverse interaction types with different units and measurement scales has previously limited our ability to model true system complexity [27].

The RCF tensor framework addresses these limitations by providing a mathematical structure that encapsulates multiple interaction types simultaneously. This approach enables researchers to move beyond a purely species-centric perspective to one that incorporates functional participation patterns, opening new avenues for understanding how system structure influences stability, resilience, and emergent properties [27] [28]. While developed in an ecological context, the framework's mathematical foundation makes it applicable across diverse domains including pharmaceutical research, systems biology, and social network analysis.

Theoretical Foundations of the RCF Tensor Framework

Mathematical Formulation

The core of this analytical framework is the RCF tensor, a rank-3 mathematical object that generalizes the concept of a matrix to three indices. Formally, the RCF tensor is defined as ( \mathcal{F} = {f{ix}^\alpha} ), where each element ( f{ix}^\alpha ) specifies the observed probability of co-occurrence between a resource ( i ) (e.g., plant species), a consumer ( x ) (e.g., animal or fungal species), and a specific ecological function ( \alpha ) (e.g., pollination, decomposition) [27].

This mathematical structure enables the integration of diverse interaction types into a unified model while maintaining the distinct identities of each functional dimension. The tensor can be visualized as a multilayer network where each layer represents a different ecological function, with connections between layers representing shared species participation [27].

Key Conceptual Advances

The RCF tensor framework introduces several conceptual advances over traditional network approaches:

• Multifunctional Integration: Unlike traditional single-function networks, the RCF tensor simultaneously captures multiple ecological functions within a single mathematical structure [27].

• Species-Function Duality: The framework enables dual perspectives, examining both how species participate in functions and how functions connect through shared species [27] [28].

• Quantitative Keystoneness: It extends the concept of keystone species to include multifunctional participation, quantifying both species' importance across functions and functions' roles in connecting species [27].

Table 1: Key Components of the RCF Tensor Framework

Component	Mathematical Representation	Ecological Interpretation
Resources	Index ( i )	Plant species providing resources
Consumers	Index ( x )	Animal/fungal species consuming resources
Functions	Index ( \alpha )	Ecological function mediating interaction
Interaction strength	Element ( f_{ix}^\alpha )	Probability of observed interaction

Experimental Implementation and Protocol

Data Collection and Standardization

The implementation of the RCF tensor framework requires systematic data collection across multiple functions. The protocol developed for the Na Redona case study exemplifies this approach [28]:

• Systematic Sampling Design: Conduct comprehensive surveys allocating equal effort to each interaction type, including pollination, herbivory, seed dispersal, decomposition, nutrient uptake, and fungal pathogenicity.

• Multi-Taxa Observation: Directly observe and record interactions between plants, animals, and fungi across all targeted functions.

• Laboratory Analysis: Process collected samples (e.g., pollen samples, droppings, root samples) for interaction identification.

• Data Normalization: Normalize raw interaction data by sampling effort to enable fair comparisons across different function types.

This protocol resulted in a comprehensive dataset of 1,537 weighted interactions between 691 species of plants, animals, and fungi across six ecological functions [27] [28].

Tensor Construction Workflow

The transformation of raw ecological data into an RCF tensor follows a structured workflow:

Key Analytical Transformations

The RCF tensor enables several key analytical transformations through mathematical operations:

• Resource-Function Matrix: By integrating out the consumer index ( x ), the RCF tensor reduces to a resource-function matrix ( M = {mi^\alpha} ) where ( mi^\alpha = \sumx f{ix}^\alpha ). This matrix encodes how plant species participate across different ecological functions [27].

• Network Projections: The resource-function matrix can be further projected to create:

  • Function-function networks based on shared plant species
  • Plant-plant networks based on shared functional participation [28]

• Nestedness Analysis: Statistical analysis of the resource-function matrix reveals non-random patterns in species-function participation [27].

Case Study: Na Redona Island Ecosystem

Experimental Setup and Data Collection

The RCF tensor framework was applied to a comprehensive study of the Na Redona island ecosystem in the Balearic Islands (Western Mediterranean Sea). The experimental design included [28]:

Table 2: Na Redona Case Study Experimental Parameters

Parameter	Specification
Location	Na Redona islet, Cabrera National Park, Spain
Sampling Period	Multiple field campaigns
Plant Species	16 systematically studied
Animal Species	46 identified and observed
Fungal ASVs	629 amplicon sequence variants
Interaction Functions	6 (pollination, herbivory, seed dispersal, decomposition, nutrient uptake, fungal pathogenicity)
Total Interactions	1,537 weighted interactions

Fieldwork presented significant challenges including difficult access to the uninhabited islet, adverse sea conditions, and the logistical complexity of simultaneous multi-taxa sampling [28]. The research team conducted initial assessments of resource availability (e.g., flowering species for pollinators, fruit-bearing plants for seed dispersers) before systematic sampling to allocate time efficiently across interaction types.

Structural Analysis Findings

Application of the RCF tensor framework to the Na Redona dataset revealed several key structural properties:

• Nested Architecture: The species-function network displayed a statistically significant nested structure, where generalist species participate in both specialist and generalist functions, while specialist species predominantly participate in generalist functions [27].

• Keystone Species Identification: Analysis identified a hierarchy of species importance, with the top six species in the "keystoneness" ranking all being woody shrubs [28].

• Function Centrality: Fungal decomposition emerged as a keystone function, playing a disproportionately important role in connecting different elements of the ecosystem [27].

Extinction Simulation Methodology

The framework incorporated an extinction analysis protocol to validate the importance of identified keystone elements:

• Ranked Removal: Species and functions were removed according to their keystoneness ranking derived from the RCF tensor analysis.

• Secondary Extinction Tracking: Researchers monitored subsequent species/function losses after each removal.

• Null Model Comparison: Results were compared against random removal sequences to establish statistical significance.

This analysis confirmed that removing species and functions in the order predicated by the RCF tensor rankings had a larger-than-random effect on secondary extinctions, validating the framework's ability to identify truly critical system elements [27].

The Scientist's Toolkit: Essential Research Reagents

Implementing the RCF tensor framework requires both computational tools and field research materials:

Table 3: Essential Research Reagents and Computational Tools

Tool/Reagent	Function/Purpose	Specifications
RCF Tensor Codebase	Mathematical implementation of tensor operations	Python/Matlab with tensor libraries
Field Data Sheets	Standardized recording of multi-taxa interactions	Customized for each function type
Pollen Sampling Kit	Collection and preservation of pollen samples	Includes slides, preservatives, microscopes
Root Sampling Equipment	Collection of root samples for fungal analysis	Sterile containers, coolers for transport
Interaction Database	Storage and management of observed interactions	Structured relational database
Null Model Algorithms	Statistical validation of network patterns	Custom implementation for ecological data

Implications for Ecological Network Research

The RCF tensor framework fundamentally reshapes how we conceptualize and analyze ecological networks in several crucial ways:

From Unifunctional to Multifunctional Analysis

Traditional ecological network research has been constrained by analyzing one function at a time (e.g., separate studies of pollination, herbivory, and seed dispersal). The RCF tensor framework enables truly multifunctional analysis, revealing how species participate across multiple functional domains simultaneously [27]. This approach has demonstrated that species' functional roles are highly heterogeneous, with some species acting as "multitaskers" while others maintain specialized participations [28].

Redefining Keystone Elements

The framework extends the classical concept of keystone species in two significant ways:

• Multifunctional Keystoneness: Quantifies how species contribute to multiple functions and connect different functional domains.

• Function Keystoneness: Introduces the novel concept that ecological functions themselves can have keystone properties in network architecture [28].

In the Na Redona study, this dual perspective revealed that woody shrubs with longer lifespans typically occupied higher positions in the keystoneness hierarchy, likely because their persistence enables connections with more diverse interaction partners across different functions [28].

Structural Patterns and System Stability

The discovery of nested architecture in species-function participation has important implications for ecosystem stability and resilience. Previous research has established that network structure significantly influences community persistence [8], though the relationship is environment-dependent. The nested pattern observed in the RCF tensor analysis suggests a structural organization that may enhance system robustness, though this requires further investigation across environmental gradients [8].

Future Directions and Applications

Methodological Extensions

The current RCF tensor framework opens numerous avenues for methodological development:

• Temporal Dynamics: Incorporating temporal dimensions to create RCFT (Resource-Consumer-Function-Time) tensors that capture seasonal and successional changes.

• Additional Interaction Types: Integrating competitive interactions, animal-animal relationships, and insect trajectory data.

• Abiotic Factors: Incorporating environmental parameters as additional tensor dimensions.

Cross-Domain Applications

While developed for ecological networks, the mathematical foundation of the RCF tensor framework makes it applicable to diverse domains:

• Pharmacogenomics: Modeling complex interactions between genes, drugs, and diseases in multilayer biological networks [29].

• Drug Discovery: Analyzing drug-target interactions across multiple similarity metrics and interaction types [30] [31].

• Systems Biology: Mapping functional relationships across molecular interaction layers [32].

Conservation and Management Implications

The ability to identify truly keystone species and functions through the RCF tensor framework provides valuable insights for ecosystem management and conservation prioritization. By understanding which elements play critical roles in maintaining multifunctional ecosystems, managers can make more informed decisions about protection and restoration strategies.

The RCF tensor framework represents a significant advancement in analytical methods for complex network analysis, providing a mathematically rigorous yet practical approach to modeling multidimensional interactions. By moving beyond single-layer network representations, this framework enables researchers to capture the true complexity of ecological systems and identify critical architectural features that would remain hidden in traditional analyses.

The case study of Na Redona island demonstrates how this approach reveals non-random patterns in species-function participation, identifies keystone elements through a multifaceted lens, and provides insights into the structural foundations of ecosystem stability. As network science continues to evolve across ecological, biological, and social domains, the RCF tensor framework offers a powerful tool for integrating multiple interaction types into a unified analytical paradigm.

The future development of this framework will undoubtedly enhance our understanding of complex systems across multiple domains, ultimately contributing to more effective conservation strategies, drug discovery pipelines, and management approaches for the complex networked systems that characterize our natural and engineered worlds.

The application of ecological network analysis to chaperone-client interactions represents a paradigm shift in how we conceptualize and investigate the complex molecular landscapes of cancer. This approach transposes methodologies developed for studying species interactions in ecosystems to the analysis of molecular interaction networks within tumors. Just as ecologists examine how environmental pressures reshape food webs and species relationships, cancer biologists can now investigate how the tumor microenvironment reshapes chaperone-client protein interactions. This perspective allows researchers to move beyond a static, single-gene view of cancer and toward a dynamic, systems-level understanding of tumor biology. The core premise is that cancer cells are not merely collections of autonomously functioning components, but complex adaptive systems where functional interdependencies and network topology dictate survival, proliferation, and therapeutic vulnerability [33].

At the heart of this approach are molecular chaperones, proteins that assist the conformational folding and stability of other proteins (clients) [34]. In cancer, chaperones are hijacked to support oncogenic processes, stabilizing mutated or overexpressed proteins that drive tumor progression. The chaperone-client interaction (CCI) networks they form are not static backbones but malleable structures that reorganize in response to cellular conditions. By applying ecological network analysis, researchers can quantify this plasticity, identify critical vulnerabilities, and predict the systemic consequences of targeting specific network nodes—a crucial consideration for developing cancer-specific therapeutic strategies [33].

Core Concepts and Definitions

Ecological Network Analysis

Ecological network analysis comprises a suite of quantitative tools developed to study the structure and dynamics of species interactions within ecosystems. When applied to cancer biology, these tools illuminate the organization and robustness of molecular interaction networks. Key concepts include:

• Nestedness: A non-random, hierarchical pattern of interaction where chaperones with specialized client sets interact with subsets of the clients of more generalized chaperones. This structure influences how perturbation spreads through the network [33].
• Specialization (Sc): The proportion of potential clients a chaperone actually interacts with across all cancer types. It reflects the inherent biophysical capacity of a chaperone [33].
• Realized Niche (Rcα): The proportion of its potential clients a chaperone actually interacts with within a specific cancer type α. This metric quantifies how the cancer environment modulates chaperone function [33].
• Robustness: The resistance of a network to functional collapse following the removal of nodes (chaperones). This is directly analogous to ecosystem resilience following species extinction [33].

Chaperones and Their Networks

Molecular chaperones are highly conserved proteins that facilitate the correct folding, assembly, and stabilization of other proteins, prevent aggregation, and target misfolded proteins for degradation [34] [35]. In cancer, their role is subverted to support the stability and function of oncoproteins. Several chaperone families are of particular importance:

• Hsp70: Aids in folding nascent polypeptide chains and prevents misfolding. It requires Hsp40 co-chaperones and ATP to function [34] [35].
• Hsp90: Stabilizes a specific set of "client" proteins, many of which are signal transduction proteins critical for cancer cell survival and proliferation [34].
• Chaperonins (Hsp60/Hsp10): Large, barrel-shaped complexes that provide an isolated environment for protein folding [34].
• Epichaperomes: Recently identified, stable oligomeric assemblies of chaperones and co-factors that form under chronic cellular stress. Unlike transient canonical chaperone complexes, epichaperomes act as scaffolding platforms that rewire protein-protein interaction networks to sustain pathological states in cancer and neurodegenerative diseases [36].

Table 1: Key Chaperone Families in Cancer Biology

Chaperone Family	Core Function	Role in Cancer	Example
Hsp70	Folding of nascent chains, prevention of aggregation	Supports oncoprotein folding, promotes cell survival	Hsp70, Hsc70 [34] [35]
Hsp90	Maturation and activation of specific client proteins	Stabilizes mutated/overexpressed oncogenes	Hsp90, GRP94 [34]
Hsp60/10	Provides isolated folding chamber	Supports mitochondrial protein homeostasis	GroEL/GroES (bacterial) [34]
Epichaperome	Scaffolding platform rewiring PPI networks	Drives pathological phenotypes by stabilizing disease networks	HSP90-containing stable assemblies [36]

A Foundational Case Study: Ecological Analysis of Mitochondrial CCI Networks

A seminal 2023 study published in Nature Communications provides a compelling proof-of-concept for applying ecological network analysis to chaperone biology across cancer types [33]. This study investigated interactions between 15 mitochondrial chaperones and 1,142 client proteins across 12 distinct cancer environments, with all chaperones and clients present in every network.

Key Quantitative Findings

The analysis revealed several critical patterns that demonstrate the power of an ecological perspective:

• Non-Random, Hierarchical Structure: Chaperone-client interactions displayed a significant weighted-nestedness pattern. This means chaperones interacting with a small proportion of their potential clients in a given cancer type were a subset of those interacting with a higher proportion, creating a hierarchy of interaction realization [33].
• Cancer-Dependent Realized Niches: The realized niche (Rcα) of individual chaperones varied substantially across cancer types. For instance, the chaperone SPG7 interacted with a high proportion of its potential clients in thyroid cancer (THCA) but a low proportion in breast cancer (BRCA) [33].
• Expression-Independent Patterns: Crucially, these patterns were not explained by variations in the expression levels of either chaperones or client proteins. This suggests that the network structure is governed by more complex, post-translational regulatory mechanisms and specific functional demands of each cancer type [33].

Table 2: Summary of Key Quantitative Findings from the Case Study [33]

Analysis Metric	Finding	Biological Interpretation
Specialization (Sc)	Ranged from 40% to 65% (Avg: 55.5% ± 8.1%)	Chaperones are inherently generalist but with varying degrees of specificity.
Realized Niche (Rcα)	Varied significantly by chaperone and cancer type (e.g., SPG7: high in THCA, low in BRCA)	The cancer microenvironment actively filters and shapes functional chaperone-client interactions.
Network Structure	Significant weighted-nestedness (p < 0.001 vs. 1000 randomized networks)	Creates a robust core-periphery structure, buffering the network against random failure.
Prediction Accuracy	High accuracy in predicting CCIs in one cancer based on another's structure	Underlying biophysical rules enable cross-cancer inference despite low network similarity.

Robustness Analysis and Therapeutic Implications

A central application of ecological network analysis is simulating system response to perturbation. The study simulated chaperone removal (inhibition) and found that network robustness was cancer-type specific, driven by the unique interaction redundancy and niche separation in each tumor environment. This finding has direct therapeutic implications: a chaperone inhibitor might cause widespread client protein misfolding and cell death in one cancer type where redundancy is low, but have minimal effect in another where other chaperones can compensate for its loss. This explains the variable efficacy of chaperone-targeting therapies observed in the clinic and underscores the need for cancer-specific CCI network mapping to guide patient stratification and combination therapy design [33].

Detailed Experimental Protocols and Workflows

Constructing Chaperone-Client Interaction Networks

The foundational step is the reconstruction of quantitative CCI networks from experimental data.

Protocol: Inferring CCIs from Co-Expression Data

• Data Collection: Obtain transcriptomic (RNA-Seq) and proteomic data for the cancer type(s) of interest from matched tumor samples. Public resources like The Cancer Genome Atlas (TCGA) are typical starting points.
• Data Preprocessing: Normalize expression data and control for batch effects. Ensure sample size is consistent across cancer types when making comparisons to avoid sampling bias [33].
• Interaction Scoring: Calculate a connectivity score between each chaperone and potential client protein. While correlation was used in the foundational study [33], other advanced methods are available:
  • Pearson Correlation: A basic measure of linear association.
  • Partial Least Squares (PLS) Regression: A robust method that models the expression of a chaperone as a function of all other genes, effectively capturing multivariate influences and suitable for high-dimensional data where the number of genes exceeds the number of samples [37].
• Network Assembly: For each cancer type, construct a bipartite network where nodes are chaperones and clients, and weighted edges represent the statistically significant interaction scores.

Diagram 1: CCI Network Construction Workflow

Quantifying Ecological Network Metrics

Once networks are constructed, their architectural properties can be quantified.

Protocol: Calculating Specialization and Realized Niche

• Potential Interactions (Pc): For a chaperone c, define Pc as the union of all clients it interacts with in any of the cancer types studied.
• Specialization Index (Sc): Calculate as Sc = Pc / Total Number of Potential Clients. A value of 1 indicates a perfect generalist.
• Cancer-Specific Links (Lcα): Count the number of clients a chaperone c interacts with in a specific cancer type α.
• Realized Niche (Rcα): Calculate as Rcα = Lcα / Pc. This is a proportion reflecting how much of its potential the chaperone realizes in a given environment [33].

Protocol: Testing for Nestedness

• Matrix Construction: Create a matrix where rows are chaperones, columns are cancer types, and values are either Rcα or Lcα.
• Null Model Generation: Use permutation tests (e.g., 1000 randomizations) to shuffle interactions within the network while preserving row and column totals, creating a distribution of expected nestedness values under randomness.
• Significance Testing: Compare the observed nestedness value of the real network to the null distribution. A p-value < 0.05 indicates a significantly nested structure not explainable by chance [33].

Simulating Network Robustness

A key goal is predicting how the network responds to therapeutic intervention.

Protocol: Simulating Chaperone Removal

• Node Removal: Simulate the removal (inhibition) of a specific chaperone from the network.
• Impact Assessment: Quantify the downstream effect by calculating the number of client proteins that lose all their chaperone interactions ("collapse") or the reduction in global network connectivity.
• Iterative Simulation: Repeat the removal for each chaperone, and for combinations of chaperones, in a systematic manner.
• Robustness Curve: Plot the proportion of intact clients remaining versus the proportion of chaperones removed. The area under this curve is a metric of overall network robustness, allowing comparison across cancer types [33].

Diagram 2: Chaperone Removal Simulation

Successfully applying ecological network analysis to chaperone biology requires a combination of computational tools, data resources, and chemical probes.

Table 3: Research Reagent Solutions for CCI Network Analysis

Resource Category	Specific Tool/Reagent	Function in Research	Example Use Case
Data Resources	TCGA (The Cancer Genome Atlas)	Source of multi-omics (genome, transcriptome) data from thousands of tumor samples.	Obtain RNA-Seq data for co-expression analysis across 33 cancer types [38].
Pathway Databases	KEGG, Reactome, HumanCyc	Curated databases of biological pathways and interactions.	Visualization of enriched pathways and overlay of genomic data [39].
Network Analysis Software	Cytoscape (with Enrichment Map)	Open-source platform for network visualization and analysis.	Visualize CCI networks and identify functional themes in large pathway lists [39].
Differential Network Analysis	dna R Package (CRAN)	Statistical toolkit for performing differential network analysis.	Test for differences in network connectivity between two cancer types or conditions [37].
Structural Network Tools	NetFlow3D	A unified framework integrating 3D protein structure with PPI network topology.	Map the multiscale effects of mutations from atomic to network levels [38].
Chemical Probes	PU-H71 (Zelavespib)	Small molecule that selectively binds and disrupts epichaperomes, not canonical HSP90 complexes.	Functionally validate epichaperome-dependent cancers and probe network fragility [36].

Advanced Applications: From Epichaperomes to Differential Network Analysis

Targeting the Epichaperome

The ecological network perspective finds a powerful application in understanding epichaperomes. Unlike dynamic canonical chaperones, epichaperomes are stable, pathological scaffolds that rewire protein-protein interaction (PPI) networks to sustain disease states. They represent a distinct, maladaptive network configuration. The small molecule PU-H71 (zelavespib) exemplifies a network-specific therapeutic; it does not broadly inhibit HSP90, but rather selectively targets and disrupts the HSP90 incorporated into epichaperomes. Tumor sensitivity to PU-H71 directly correlates with epichaperome abundance, not total HSP90 levels, demonstrating the principle of targeting a specific network state rather than a single protein [36].

Differential Network Analysis

This statistical framework formalizes the comparison of network topologies under different conditions. It asks: How does the CCI network differ between a normal and cancerous state, or between two cancer subtypes? Key tests include [37]:

• Differential Connectivity of a Single Gene: Assessing if a specific chaperone has significantly more or fewer interactions in one condition versus another.
• Differential Connectivity of a Gene Set: Testing if a predefined group of chaperones shows coordinated changes in connectivity.
• Differential Modular Structure: Determining if the overall community structure of the network is altered between conditions.

These methods, implemented in tools like the dna R package, allow researchers to move from descriptive network maps to statistically rigorous comparisons of network rewiring in cancer [37].

Applying ecological network analysis to chaperone-client interactions provides a sophisticated, quantitative framework for redefining how we study structure and function in cancer biology. It shifts the focus from isolated molecular entities to the dynamic web of interactions that underpin tumorigenesis. The key takeaways are that CCI networks are (1) structured in a non-random, hierarchical way, (2) plastic and reshaped by the cancer environment, and (3) predictive of therapeutic vulnerability. This approach offers a mechanistic bridge between genetic alterations and the emergent pathological phenotypes of cancer. By defining cancer as a system of ecological interactions, we can better identify critical leverage points for therapy, anticipate mechanisms of resistance, and ultimately design more effective and personalized network-based treatment strategies.

Navigating Challenges: Strategies for Robust and Sustainable Network Design

Understanding the stability and fragility of complex systems is a cornerstone of ecological research. Ecological networks, representing species as nodes and their interactions as links, provide a powerful framework for investigating how system structure dictates function and response to disturbance [40]. The accelerating rate of species population declines has made predicting the consequences of species loss increasingly relevant, moving this research from theoretical exercise to urgent necessity [40]. Robustness, defined as the ability of a network to maintain its connectivity and functionality despite the removal of nodes (species) or links (interactions), is a critical metric for ecosystem stability [41]. Assessing robustness to node removal and various perturbation scenarios allows researchers to diagnose systemic fragility, identify keystone species, and anticipate catastrophic collapse, thereby informing effective conservation and restoration strategies [40] [42]. This guide details the core methodologies, metrics, and tools for diagnosing network fragility within the broader context of ecological network structure and function research.

Theoretical Foundations of Network Robustness

The robustness of an ecological network is not an intrinsic property but emerges from its topological architecture and the dynamic constraints of its constituent interactions. Different theoretical frameworks have been established to understand this phenomenon.

The Multilayer Network Perspective

Historically, ecological network analysis focused on single interaction types (e.g., food webs). However, species in nature are connected via multiple interaction types simultaneously (e.g., pollination and herbivory), forming 'multilayer' networks [40]. Tripartite networks, composed of two layers of bipartite interactions (see Figure 1), reveal that the overall robustness of a community is a combination of the robustness of its individual, interacting networks [40]. The interdependence of robustness between these layers is affected by how they are connected, particularly by connector nodes (shared species that have interactions in both layers) [40]. Studies of 44 tripartite networks showed that the proportion of connector nodes and how their links are split between layers differ significantly between network types (e.g., mutualism-mutualism vs. antagonism-antagonistic), influencing systemic fragility [40].

The Historical Contingency of Robustness

Network robustness is deeply shaped by evolutionary history. Ecosystems evolve complexity that is robust to historical extinction pressures but can be fragile under novel conditions [43]. Research on digital host-parasite networks and empirical data reveals that consumers (e.g., parasites) tend to specialize on "dependable" hosts—those that have been less vulnerable to extinction in the past [43]. This adaptation means that networks are far more robust to historical species loss sequences than to random or novel sequences, the latter being a proxy for the unpredictable pressures of global change [43]. This historical contingency creates a trade-off; stability in a past environment can predispose the network to collapse under future environmental changes [43].

Key Metrics and Quantitative Benchmarks

Robustness is quantified through simulation and the calculation of specific metrics. The table below summarizes key metrics used in robustness assessments.

Table 1: Key Metrics for Assessing Network Robustness to Node Removal

Metric	Description	Interpretation
Robustness (R)	Area under the curve of the fraction of surviving species (often animal sets) vs. the fraction of removed plants [40].	A higher R-value indicates a more robust network. A value of 1 indicates no secondary extinctions; 0 indicates immediate collapse.
Connectivity Robustness	The ability of a network to maintain its original connectivity after node removal [41].	A key indicator for the stability of Ecological Networks (ENs), abstracting patches and corridors into nodes and links.
Participation Coefficient of Connector Nodes (PCC)	Measures how evenly the links of a connector node are split between two interaction layers in a multilayer network [40].	High PCC (~0.89) indicates links are equally split, as seen in antagonistic-antagonistic networks. Lower PCC (~0.59) indicates lopsided connections.
Area Under the Disassembly Curve (AUC)	Quantifies parasite assemblage robustness during sequential host removal [43].	Used to compare robustness across different removal sequences (historical, random, worst-case).

Quantitative benchmarks from large-scale studies provide context for these metrics. For instance, analysis of 44 tripartite networks revealed that only ~10% of shared species acted as connector nodes in mutualistic-mutualistic networks, compared to ~35% in antagonistic-antagonistic networks [40]. In a study on the Yellow River Basin, optimized ecological networks showed a 43.84%–62.86% increase in dynamic patch connectivity and an 18.84%–52.94% increase in dynamic inter-patch connectivity after model optimization, directly enhancing robustness [44].

Experimental Protocols for Robustness Assessment

A standard approach for assessing robustness involves in-silico simulations of node removal, tracking the cascade of secondary extinctions. The following provides a detailed protocol.

Primary Protocol: Sequential Node Removal and Robustness Calculation

This protocol is widely used for evaluating robustness in mutualistic, antagonistic, and multilayer ecological networks [40] [43].

1. Network Representation:

• Abstract the ecological community into a network. Species are represented as nodes. Trophic, mutualistic, or parasitic interactions are represented as links or edges [40].
• For multilayer networks, clearly define the different interaction layers and the set of species (connector nodes) shared between them [40].

2. Define Removal Sequence: Sequentially remove nodes (e.g., plant species) according to a specific sequence. Critical sequences include:

• Random Removal: Non-strategic removal as a null model [40] [42].
• Historical Removal: Removal based on historical vulnerability to extinction (e.g., from population time series in digital evolution or intrinsic vulnerability in fishes) [43].
• Novel/Condition-Based Removal: Removal based on current or projected vulnerability (e.g., IUCN threat status) [43].
• Generalist-Preferred Removal: Probability of removal is proportional to the number of interactions (degree) [42].
• Specialist-Preferred Removal: Probability of removal is inversely proportional to the number of interactions [42].
• Worst-Case/Best-Case Removal: Removal ordered to minimize or maximize the persistence of dependent species [43].

3. Simulate Secondary Extinctions: After each primary removal, assess the network for secondary extinctions. The most conservative hypothesis, which provides a lower bound on damage, is that a secondary extinction occurs only when a consumer (animal) species loses all its resource links [40].

• Example: In a plant-pollinator-herbivore network, removing a plant species may lead to the secondary extinction of a pollinator if that plant was its only food source [40].

4. Calculate Robustness:

• Let ( p ) be the proportion of removed primary nodes (e.g., plants).
• Let ( s(p) ) be the proportion of dependent nodes (e.g., animal species) that remain extant.
• Plot ( s(p) ) against ( p ) for the entire removal sequence.
• The robustness value ( R ) is the area under this curve [40]. A larger area indicates a higher robustness.

5. Analyze Interdependence (for Multilayer Networks):

• Calculate the robustness of each animal species set (e.g., pollinators and herbivores) separately.
• Investigate the correlation between these robustness values. A high correlation indicates that the same plants are important for the persistence of both animal sets, creating higher systemic interdependence and potential fragility [40].

Protocol for Evaluating Connectivity Robustness in Landscape Networks

This protocol applies complex network theory to spatial ecological networks, where patches are nodes and corridors are links [41].

1. Network Identification:

• Identify ecological patches using methods like Morphological Spatial Pattern Analysis (MSPA).
• Construct a comprehensive resistance surface based on natural and anthropogenic factors.
• Identify ecological corridors using the Minimum Cumulative Resistance (MCR) model or circuit theory [41].

2. Abstract to Complex Network:

• Abstract the landscape network into a complex network format, where ecological patches are nodes and ecological corridors are links [41].

3. Simulate Network Attacks:

• Random Attack: Randomly remove nodes (patches) and recalculate network connectivity after each removal.
• Deliberate Attack: Remove nodes in a specific order of importance (e.g., based on degree centrality or betweenness centrality) and recalculate connectivity [41].

4. Evaluate Connectivity Robustness:

• The connectivity robustness is characterized by the ability of the network to maintain connectivity under the different attack modes. The rate of connectivity loss is tracked as a function of nodes removed [41].

Table 2: Reagent Solutions for Network Robustness Research

Research Reagent / Tool	Function in Analysis
igraph Library	A core collection of network analysis tools for R, Python, and C/C++. Used for calculating network metrics, simulating node removal, and generating network layouts [45] [46].
Null Models	Statistical models used to generate random networks for comparison. Helps determine if a network's observed robustness is significantly different from expectation, given specific constraints [40].
Centrality Measures (Degree, Betweenness, Closeness)	Topological metrics used to rank species (nodes) for deliberate attack sequences or to identify keystone species. Degree (number of links) is often a strong, simple predictor of importance [42].
Future Land Use Simulation (FLUS) Model	A cellular automata model used to predict future land use changes under different scenarios (e.g., Business-as-Usual, Ecological Security). Provides the spatial data for projecting future ecological networks and their robustness [41].
Morphological Spatial Pattern Analysis (MSPA)	An image processing technique that identifies and classifies ecological patches within a landscape based on their morphological shape and connectivity. Used to define nodes in spatial ecological networks [44] [41].

Visualization of Methodologies

The following diagram illustrates the core experimental workflow for assessing network robustness through sequential node removal, integrating the protocols described above.

Figure 1: Node Removal Robustness Assessment Workflow. The process involves iteratively removing nodes based on a defined sequence, checking for secondary extinctions, and finally calculating a robustness metric from the resulting data.

The next diagram conceptualizes a tripartite ecological network, highlighting the connector nodes that link different layers of interaction, a critical feature for understanding robustness in multilayer systems.

Figure 2: Tripartite Ecological Network with Connector Node. This structure shows two interaction layers (e.g., pollination and herbivory) sharing a set of plant species. The 'Plant Connector' node, highlighted with a bold border, interacts across both layers, influencing the interdependence and overall robustness of the community.

Discussion and Research Outlook

The methodologies outlined provide a robust framework for diagnosing fragility, but several frontiers demand attention. A primary challenge is the move from static to dynamic network models that can incorporate species' demographic and evolutionary responses to perturbations [42]. Furthermore, the integration of machine learning with network theory, as seen in frameworks for optimizing ecological networks in arid regions, presents a promising avenue for predicting network behavior and designing effective restoration strategies under deep uncertainty [44]. Finally, as global change creates novel environments, the disconnect between historical network robustness and future fragility underscores the need for preemptive research that tests networks against projected, non-historical extinction sequences [43]. The ultimate goal of this research is to evolve from diagnosing fragility to proactively engineering resilience, ensuring the persistence of critical ecosystem functions and services.

Ecological network (EN) research is a critical conservation strategy for mitigating habitat fragmentation and ecosystem degradation, forming a system of nested networks that connect adjacent habitats through corridors to maintain landscape integrity and continuity [12]. In arid and semi-arid regions, this research takes on heightened importance as these areas face acute challenges from water scarcity, fragile ecosystems, and disproportionate vulnerability to land degradation and climate change impacts [47]. The core focus of ecological network structure and function research lies in understanding and optimizing the interactions between landscape patterns and ecological processes to enhance ecosystem stability and service delivery.

The structure of an EN refers to its physical configuration—the spatial arrangement of ecological sources (core habitats) and corridors (connecting pathways) that facilitate ecological flows [12]. The function encompasses the ecological processes and services the network supports, including biodiversity conservation, habitat provision, and maintenance of ecological connectivity [12]. Research in this field increasingly recognizes that sustainable EN management requires integrated assessment of both functional sustainability (the capacity to consistently maintain ecosystem services) and structural stability (the ability to maintain overall connectivity when components are disrupted) [12].

Quantitative Assessment of Ecological Network Degradation

Comprehensive analysis of ecological network changes in arid regions reveals significant degradation trends that directly impact ecosystem functionality. The data presented below summarizes key findings from empirical studies conducted in vulnerable ecosystems.

Table 1: Spatiotemporal Changes in Ecological Network Components (1990-2020)

Network Component	Change Metric	Magnitude of Change	Ecological Implications
Core Ecological Sources	Area decrease	-10,300 km² (core)-23,300 km² (secondary core)	Reduced habitat availability and quality [44]
Vegetation Cover	Proportion of high/extraordinarily high cover	-4.7% decrease	Diminished carbon sequestration and habitat function [44]
Drought Stress	Area of highly arid regions	+2.3% increase	Enhanced water stress on vegetation [44]
Landscape Resistance	High resistance area	+26,438 km² increase	Impaired species movement and genetic flow [44]
Ecological Corridors	Total length	+743 km increase	Potential for improved connectivity [44]

Table 2: Threshold Effects of Vegetation Under Drought Stress

Parameter	Critical Change Interval	Biological Significance
Temperature-Vegetation Dryness Index (TVDI)	0.35-0.6	Critical moisture stress range triggering vegetation response [44]
Normalized Difference Vegetation Index (NDVI)	0.1-0.35	Threshold for significant vegetation degradation [44]

The data demonstrates concerning trends, particularly the substantial loss of core ecological sources—critical habitats that serve as the foundation for ecological networks. This degradation is compounded by increasing drought stress, with vegetation showing significant threshold effects that must inform restoration strategies [44].

Methodological Framework for Ecological Network Analysis

Integrated Technical Workflow

The following Graphviz diagram illustrates the comprehensive methodological framework for analyzing and optimizing ecological networks in vulnerable regions:

Diagram Title: Ecological Network Assessment Workflow

Experimental Protocol: Climate Scenario Integration

Objective: To assess EN sustainability under multiple future climate scenarios by integrating functional and structural analyses [12].

Materials and Input Data:

• Land use/land cover (LULC) data (2020-2050 projections)
• Climate data: Three Global Circulation Models (GCMs) - EC-Earth3, GFDL-ESM4, MRI-ESM2-0
• Human Footprint (HFP) index
• Geographic auxiliary data: PET, DEM, NDVI, NPP, road networks [12]

Methodology:

• Scenario Construction: Develop ten scenarios including one current (2020) and nine future scenarios (2030, 2040, 2050 under SSP1-1.9, SSP2-4.5, and SSP5-8.5) [12].
• Ecological Source Delineation: Identify ecological sources based on ecosystem service importance using geospatial models (InVEST, SolVES, ARIES) [12].
• Network Development: Construct ecological networks using Linkage Mapper toolbox, identifying potential ecological corridors [12].
• Functional Sustainability Assessment: Calculate range differences between current and future ecological sources to quantify functional degradation [12].
• Structural Stability Analysis: Use NetworkX to compute three topological metrics:
  • Maximum connectivity
  • Transitivity
  • Efficiency [12]

Optimization Strategies for Arid Region Ecological Networks

Technical Interventions and Restoration Approaches

Table 3: Optimization Strategies for Ecological Networks in Arid Regions

Strategy Category	Specific Interventions	Expected Outcomes
Corridor Optimization	Introducing buffer zonesPlanting drought-resistant species [44]	Improved connectivity with 43.84%-62.86% increase in dynamic patch connectivity [44]
Key Area Restoration	Restoring forests and wetlandsEstablishing desert shelter forests [44]	Enhanced core habitat function and desertification prevention
Water Management	Constructing artificial wetlandsImplementing water-efficient irrigation	Mitigation of water stress in highly arid regions
Technology Integration	AI-powered resource managementIoT-based sensors for land management [47]	Precision conservation and adaptive management

Technological Solutions Framework

The following Graphviz diagram illustrates the key technological solutions for ecological network optimization in arid regions:

Diagram Title: Technological Solutions for Arid Region Networks

Table 4: Research Reagent Solutions for Ecological Network Analysis

Tool/Category	Specific Function	Application Context
Geospatial Analysis Tools
Linkage Mapper Toolbox	Identifying ecological corridors and least-cost paths	EN construction and corridor optimization [12]
InVEST Model Suite	Evaluating ecosystem services	Ecological source identification [12]
Morphological Spatial Pattern Analysis (MSPA)	Analyzing spatial pattern of landscapes	Core habitat identification and fragmentation assessment [44]
Network Analysis Libraries
NetworkX	Computing topological metrics (connectivity, transitivity, efficiency)	EN structural stability assessment [12]
Circuit Theory Models	Modeling landscape connectivity and movement pathways	Predicting species migration routes and corridor effectiveness [44]
Data Processing Resources
The Lens Platform	Analyzing scientific publications and patents (400,000+ publications, 300,000+ patents)	Technology foresight and innovation tracking [47]
Tracxn	Market size analysis and growth projection (15,000+ companies, 150+ countries)	Technology market assessment [47]

The integration of functional sustainability and structural stability assessments provides a comprehensive framework for ecological network optimization in arid regions facing habitat loss. By implementing the detailed methodologies and optimization strategies outlined in this technical guide—including corridor optimization with drought-resistant species, keystone area restoration, and advanced technology integration—researchers and practitioners can significantly enhance ecological network resilience. The projected outcomes, including 43.84%-62.86% improvements in patch connectivity and enhanced resistance to vegetation degradation thresholds, demonstrate the efficacy of these approaches [44].

Future research must continue to integrate climate scenario projections with ecological network planning, particularly through methodologies that assess range differences between current and future ecological sources [12]. This proactive assessment is crucial for developing ecological strategies that can withstand the pressures of climate change and human activity while maintaining the ecosystem services vital for landscape sustainability in arid and hyper-arid regions.

This technical guide provides a comprehensive framework for integrating climate projections into the functional sustainability assessment of ecological networks. As climate change introduces systemic threats to network structure and function, a proactive, scenario-based approach becomes essential for maintaining ecological security and ecosystem services. This whitepaper synthesizes advanced methodologies from contemporary research, establishing a standardized protocol for assessing how networks respond to combined climate and land use stressors. Designed for researchers, scientists, and environmental professionals, this document bridges the critical gap between theoretical network ecology and applied climate adaptation strategies.

Ecological networks (ENs) are fundamental for safeguarding regional ecological security by connecting habitats and maintaining ecological flows. However, under the multiple pressures of urbanization and climate change, their structural and functional integrity faces systemic threats [48]. Climate change is known to abruptly shift ecosystem functions in drylands worldwide, and its impact on global belowground ecosystem multifunctionality portends significant degradation of ecosystem services [49]. While most previous studies have explored ENs based on ecosystem service evaluation and structure construction, the functions and structures of EN have rarely been integrally assessed under climate change scenarios [12]. This gap is particularly critical given that future climate change is projected to result in a 20.8% loss of global belowground ecosystem multifunctionality (BEMF) under SSP585 by 2100 [49]. The sustainability of EN requires the integrated evaluation of both function and structure, as incomplete evaluations may lead to an overestimation of the EN's ability to resist external disturbances caused by climate change [12].

Theoretical Foundation: Structure-Function-Resilience Dynamics

A robust framework for future-proofing ecological networks requires understanding the interrelationships between structural characteristics, functional performance, and resilience dynamics. This structure-function-resilience framework systematically analyzes the spatiotemporal evolution of ENs under disturbance regimes [48].

• Structural Integrity refers to the physical configuration of the network, including ecological sources, corridors, and their spatial connectivity. Key metrics include landscape aggregation, patch size distribution, connectivity indices, and fragmentation levels.
• Functional Performance encompasses the ecosystem processes and services maintained by the network, such as nutrient cycling, habitat provision, species migration, and carbon sequestration. This is quantified through indicators of ecosystem multifunctionality.
• Resilience Dynamics represent the network's capacity to maintain its structure and function when subjected to disturbances such as climate stressors or habitat fragmentation. This includes both resistance to change and recovery capacity after disturbance.

The coupling mechanism linking these dimensions is critical: structural damage typically triggers functional decline, which in turn leads to resilience loss, creating a cascade effect that compromises overall network sustainability [48].

Climate Scenarios and Projection Frameworks

Integrating climate projections begins with selecting appropriate climate scenarios from the Coupled Model Intercomparison Project Phase 6 (CMIP6) and the Shared Socioeconomic Pathways (SSPs) framework. These scenarios represent different trajectories of greenhouse gas concentrations and socioeconomic development.

Table 1: Climate Scenario Framework for Network Sustainability Assessment

Scenario	Radiative Forcing (W/m²)	Key Characteristics	Projected Global Temperature Increase	Relevance to Network Assessment
SSP1-1.9	1.9	Low challenges to mitigation and adaptation	~1.5°C by 2100	Sustainability and stabilization scenario
SSP1-2.6	2.6	Low challenges to adaptation	<2.0°C by 2100	Best-case for network preservation
SSP2-4.5	4.5	Intermediate pathway	~2.7°C by 2100	Middle-of-the-road scenario
SSP5-8.5	8.5	High challenges to mitigation	>4.0°C by 2100	High-risk scenario for severe degradation

Based on [49] [12]

The selection of scenarios should be guided by the assessment objectives. SSP126 (aligned with SSP1-2.6) maintains relatively stable ecological sources and higher resilience, while SSP585 (aligned with SSP5-8.5) projects continued source decline, increased fragmentation, and significantly reduced resilience [48]. For a comprehensive assessment, studies typically include a current baseline scenario (e.g., 2020) and multiple future time slices (2030, 2040, 2050) under selected SSPs [12].

Methodological Framework: Integrated Assessment Protocol

Workflow for Climate-Integrated Assessment

The following diagram illustrates the comprehensive workflow for integrating climate projections into ecological network sustainability assessments.

Ecological Source Identification and Network Construction

Ecological sources are derived from the importance of ecosystem services using geospatial models. Key processes include:

• Ecosystem Service Evaluation: Utilize models like InVEST, SolVES, or ARIES to assess key services: habitat provision, soil conservation, water retention, and carbon sequestration [12].
• Importance Zonation: Apply spatial analysis to identify areas of high ecosystem service importance, which are designated as ecological sources.
• Corridor Delineation: Use the Linkage Mapper toolbox or similar circuit theory approaches to model potential ecological corridors between sources based on landscape resistance [12].

Functional Sustainability Assessment

Functional sustainability evaluates whether the current EN can consistently maintain ecosystem services under future climate conditions. The methodology involves:

• Climate-Niche Modeling: Project future distribution of ecological sources using species distribution models (e.g., MaxEnt) or empirical relationships between climate variables and ecosystem function.
• Range Difference Analysis: Quantify the spatial overlap and difference between current and future ecological sources [12].
• Threshold Identification: Determine critical climate thresholds for ecosystem function. Research has identified an abrupt shift in global belowground ecosystem multifunctionality at a mean annual temperature threshold of approximately 16.4°C [49].

Table 2: Key Ecosystem Function Indicators for Multifunctionality Assessment

Function Category	Specific Indicators	Measurement Approach
Productivity	Belowground Net Primary Productivity	Remote sensing, field measurements
Carbon Storage	Belowground Biomass Carbon Stock Density	Soil sampling, allometric equations
Nutrient Pools	Soil Organic Carbon, Total Nitrogen, Total Phosphorus	Laboratory analysis of soil samples
Nutrient Cycling	Gross Nitrogen Mineralization & Immobilization Rates	Incubation experiments, isotopic tracing
Soil Biology	Microbial Biomass Carbon, Nitrogen, Phosphorus	Chloroform fumigation extraction

Based on [49]

Structural Stability Assessment

Structural stability assesses the EN's ability to maintain overall connectivity when components are disrupted. Using graph theory and complex network analysis through tools like NetworkX:

• Node Removal Simulation: Systematically remove sources and their connected corridors from the network, simulating functional degradation [12].
• Topological Metric Calculation:
  • Maximum Connectivity: Measures the size of the largest connected component.
  • Transitivity: Quantifies the probability that adjacent nodes are connected (clustering).
  • Efficiency: Evaluates how efficiently information is exchanged across the network.
• Resilience Testing: Implement four disturbance strategies to quantitatively assess impacts [48]:
  • Random: Random node/link failure
  • Climate-stress: Targeted removal of climate-vulnerable components
  • Source-degradation: Removal of ecologically degraded sources
  • Corridor-fragmentation: Simulating barrier effects on corridors

Integrated Sustainability Assessment

The final phase integrates functional and structural assessments to determine overall network sustainability:

• Impact Quantification: Calculate the percentage decline in structural stability resulting from functional degradation of ecological sources [12].
• Spatial Pattern Analysis: Identify geographical areas where sources transition from high to low functional sustainability.
• Scenario Comparison: Evaluate sustainability outcomes across different climate scenarios to identify robust conservation priorities.

Essential Research Toolkit

Table 3: Key Research Reagents and Computational Tools for Network Assessment

Tool/Platform	Type	Primary Function	Application Context
Linkage Mapper	GIS Toolbox	Identifies corridors and least-cost paths	Ecological network construction & corridor modeling
NetworkX	Python Library	Complex network analysis and metrics	Graph theory analysis of network structure & stability
InVEST	Model Suite	Evaluates ecosystem services & natural capital	Ecological source identification & functional assessment
CLUE-S	Land Use Model	Simulates land use change under scenarios	Projecting future landscape patterns under climate change
D3.js	JavaScript Library	Creates interactive data visualizations	Network visualization & result communication

Based on [48] [12]

Key Findings and Climate Impact Projections

Empirical applications of this framework reveal critical patterns for network sustainability:

• Urban Expansion Dominance: Urban expansion has been a key driver of ecological source degradation in rapidly developing regions. For future scenarios, SSP126 maintains stable ecological sources, while SSP585 projects continued source decline [48].
• Structural Degradation: Historical EN landscape patterns were highly aggregated with large, connected patches, but future scenarios exhibit increasing fragmentation. SSP126 shows high diversity but severe fragmentation, and SSP585 displays low diversity and poor connectivity [48].
• Resilience Decline: Historical resilience was highest initially but declined later, with source degradation causing the most severe disruption. Future resilience is projected to decrease overall, particularly under SSP585, which exhibits heightened sensitivity to combined land use and climate stress [48].
• Functional Thresholds: Research identifies abrupt shifts in ecosystem multifunctionality along climate gradients. Belowground ecosystem multifunctionality shows a critical threshold at a mean annual temperature of 16.4°C, with different driving factors dominating below and above this threshold [49].

Management Implications and Adaptation Strategies

The prospective assessment provided by this framework enables targeted interventions:

• Prioritization: Identify and reinforce poorly sustainable sources, typically smaller forest and water body patches in central regions, while protecting high-sustainability sources in less vulnerable areas like southwestern mountainous regions [12].
• Corridor Reinforcement: Strengthen critical corridors connecting climate-stable areas, particularly those that maintain connectivity under multiple future scenarios.
• Land Use Planning: Implement strict protection for ecological sources and corridors in regional development plans, particularly in urbanizing regions where expansion threatens network integrity [48].
• Climate-Smart Design: Promote "climate-smart" green infrastructure design, including selecting drought-tolerant species and optimizing green corridor orientation for climate resilience [50].

Integrating climate projections into functional sustainability assessments provides an essential evidence base for future-proofing ecological networks. The structure-function-resilience framework enables researchers and practitioners to move beyond static conservation planning toward dynamic, climate-adaptive management. By quantifying how functional changes trigger structural reorganization and resilience loss, this approach offers actionable insights for safeguarding ecosystem services and strengthening regional ecological security in an era of rapid environmental change. As climate impacts intensify, this integrated methodology will become increasingly vital for developing effective ecological strategies that maintain network functionality across uncertain future conditions.

The "Keystone Paradox" emerges from the critical challenge in conservation ecology of identifying which elements within a complex ecological network are most vital to its overall sustainability and should therefore be the primary targets for intervention. This whitepaper posits that resolving this paradox requires an integrated methodology that simultaneously assesses the functional sustainability and structural stability of ecological networks under dynamic environmental conditions [12]. Moving beyond traditional, static structural analysis, the framework detailed herein leverages prospective climate scenarios and complex network theory to quantify how projected functional degradations of ecological sources propagate through network topology to diminish its overall persistence [12] [8]. The provided technical guide outlines standardized protocols for this integrated assessment, designed to provide researchers and policymakers with actionable insights for long-term ecological management and the enhancement of landscape sustainability.

The study of ecological networks has historically branched into two complementary yet often disconnected technical routes: one focused on ecosystem functions and the other on network structures [12]. Function-oriented research quantifies the provision of ecosystem services—such as habitat quality, carbon sequestration, and water purification—often utilizing geospatial models like InVEST, SolVES, and ARIES [12]. In contrast, structure-oriented research characterizes the topological attributes of networks—including connectivity, nestedness, and modularity—using graph theory and landscape metrics to understand the spatial configuration of patches and corridors [12] [8].

The Keystone Paradox arises at the intersection of these two approaches. A network component might be identified as critical based on its structural position (e.g., a highly connected node) but may be functionally vulnerable to future environmental change. Conversely, a component that is currently a high-functioning source of ecosystem services might occupy a structurally redundant position, making its protection a less efficient investment for sustaining the entire network [8]. Consequently, defining ecological network research must involve the synthesis of these perspectives. The core thesis of this whitepaper is that prioritization is fundamentally a function of both the projected functional sustainability of network components and their role in maintaining structural stability, a relationship that is environment-dependent [8].

Methodological Framework: An Integrated Protocol

This section provides a detailed, step-by-step experimental protocol for assessing the Keystone Paradox, adaptable to most regional contexts. The workflow integrates geospatial analysis, climate projection, and network modeling.

Scenario Construction and Data Preprocessing

Objective: To model the future environmental context in which the current ecological network must function.

• Step 1: Select Climate Models and Scenarios

  • Utilize a minimum of three Global Circulation Models (GCMs) from the Coupled Model Intercomparison Project (CMIP) to capture a range of climate uncertainties [12]. Recommended models include EC-Earth3, GFDL-ESM4, and MRI-ESM2-0.
  • Adopt multiple Shared Socioeconomic Pathways (SSPs)—such as SSP1-1.9, SSP2-4.5, and SSP5-8.5—to represent different trajectories of radiative forcing and socioeconomic development [12].
  • Combine GCMs and SSPs to construct a matrix of future scenarios (e.g., for years 2030, 2040, 2050), with the present day (e.g., 2020) as the baseline scenario [12].

• Step 2: Data Collection and Standardization

  • Gather datasets for current and projected future Land Use/Land Cover (LULC), annual mean temperature, annual precipitation, and human footprint index [12].
  • Collect geographic auxiliary data, including Potential Evapotranspiration (PET), Digital Elevation Model (DEM), Normalized Difference Vegetation Index (NDVI), and Net Primary Production (NPP) [12].
  • Preprocess all raster datasets to a consistent spatial resolution (e.g., 1 km²) and projected coordinate system to ensure analytical compatibility [12].

Objective: To delineate the core components of the current ecological network.

• Step 1: Map Ecosystem Service Importance

  • Employ geospatial models (e.g., InVEST) to evaluate key ecosystem services such as habitat quality, water yield, and soil conservation [12].
  • Spatially overlay the results of multiple ecosystem service evaluations to identify areas of high combined importance. These areas are designated as ecological sources [12].

• Step 2: Delineate Ecological Corridors

  • Use a linkage identification tool, such as the Linkage Mapper toolbox, to model potential corridors between ecological sources [12].
  • The analysis typically relies on a resistance surface derived from LULC data, where higher resistance values are assigned to anthropogenic land uses like built-up areas [12].
  • The output is a mapped ecological network (EN) for the current scenario, consisting of nodes (sources) and edges (corridors).

Quantifying Functional Sustainability

Objective: To measure the capacity of current ecological sources to maintain their ecosystem service provision under future climate scenarios.

• Step 1: Project Future Ecological Sources

  • Repeat the ecosystem service importance analysis (Section 2.2, Step 1) for each future climate and LULC scenario [12].
  • Identify the spatial distribution and capacity of ecological sources for each future time slice.

• Step 2: Calculate Functional Sustainability Index

  • For each current ecological source, calculate the change in its ecosystem service capacity or the spatial overlap between its current range and its future projected range [12].
  • Classify the functional sustainability of each source. For example:
    • High: Minimal loss or gain in service-providing capacity/range.
    • Medium: Moderate loss.
    • Low/Poor: Significant degradation or complete loss of function [12].

Assessing Structural Stability

Objective: To evaluate the robustness of the ecological network's topology to the functional degradation of its components.

• Step 1: Model the Network Topology

  • Translate the current ecological network (sources and corridors) into a graph object using a library such as NetworkX [12].
  • Each ecological source is a node, and each corridor is an edge.

• Step 2: Simulate Node Failure and Calculate Metrics

  • Simulate the failure or degradation of network components by sequentially removing ecological sources that have been classified as having low or poor functional sustainability, along with their connected corridors [12].
  • After each removal, calculate key topological metrics that serve as proxies for structural stability [12]:
    • Maximum Connectivity (Component Size): The size of the largest remaining connected subgraph. A rapid decline indicates fragmentation.
    • Transitivity (Clustering Coefficient): The probability that adjacent nodes of a node are connected. Measures the redundancy of connections.
    • Efficiency: The inverse of the average shortest path length between all nodes. Measures the ease of movement or ecological flow across the network.
  • Repeat the simulation process until all sources have been removed to understand the cumulative impact on stability [12].

• Step 3: Integrate Function and Structure

  • The final output is a quantitative assessment of how the projected functional decline of specific sources under climate change translates into a loss of structural stability for the entire network [12]. This integrated result directly addresses the Keystone Paradox by identifying which sources are both functionally vulnerable and structurally critical.

Quantitative Assessment: Data Integration and Analysis

The following tables summarize the key quantitative metrics and data types involved in the integrated assessment protocol.

Table 1: Key Structural Metrics for Assessing Network Stability

Metric	Definition	Interpretation in EN Context	Tool for Calculation
Maximum Connectivity	The number of nodes in the largest connected component of the network.	Indicates the risk of network fragmentation; a large drop signifies low robustness [12].	NetworkX
Transitivity	The ratio of triangles to triplets in the network.	Measures local redundancy; higher values suggest alternative pathways exist if a node is lost [12].	NetworkX
Global Efficiency	The average inverse shortest path length between all node pairs.	Quantifies the ease of movement or gene flow across the entire network; higher is better [12].	NetworkX

Table 2: Core Data Requirements for Integrated EN Assessment

Data Category	Specific Variables	Source Examples	Role in Protocol
Land Use/Land Cover (LULC)	Forest, grassland, cropland, water, built-up land [12].	National land cover maps, ESA CCI-LC.	Create resistance surface; identify sources from ecosystem services.
Climate	Annual mean temperature, annual precipitation [12].	WorldClim, CMIP6 GCMs.	Drive future ecosystem service models.
Topography & Productivity	DEM, NDVI, NPP [12].	SRTM, MODIS, Copernicus.	Auxiliary variables for ecosystem service modeling.
Anthropogenic Pressure	Human Footprint Index (HFP), road networks [12].	Venter et al. HFP, OSM.	Refine resistance surface and identify conflict areas.

Visualization of Workflows and Signaling Pathways

The following diagram, generated using Graphviz, illustrates the core logical workflow and data integration process for addressing the Keystone Paradox.

Integrated Assessment Workflow for the Keystone Paradox

The Scientist's Toolkit: Research Reagent Solutions

This section details the essential computational tools, models, and data sources required to implement the proposed methodology.

Table 3: Essential Research Tools for Integrated EN Analysis

Tool/Solution	Type	Primary Function	Application in Protocol
InVEST Suite	Geospatial Software Model	Evaluates and maps ecosystem services [12].	Quantifying habitat quality, water yield, etc., to identify ecological sources.
Linkage Mapper	GIS Toolbox	Identifies and maps wildlife corridors and ecological networks [12].	Delineating least-cost-path corridors between ecological sources.
NetworkX	Python Library	Creates, manipulates, and studies the structure of complex networks [12].	Modeling the EN as a graph and calculating topological metrics (connectivity, efficiency).
CMIP6 GCM Data	Climate Projection Data	Provides future projections of temperature, precipitation, and other variables [12].	Constructing future scenarios to assess climate change impacts on ecosystem functions.
R (with igraph) / MATLAB	Programming Environment	Alternative platforms for advanced statistical analysis and network modeling.	Complementary analysis, data processing, and custom metric development.

Ensuring Efficacy: Validating, Comparing, and Scaling Network Models

Ecological networks, representing the complex web of species interactions, are foundational to understanding ecosystem structure and function. Defining and quantifying this structure requires robust analytical frameworks that can distinguish biologically significant patterns from random assemblages. Benchmarking performance through null models and extinction analysis has emerged as a critical methodology for validating ecological network research, allowing scientists to test hypotheses, quantify resilience, and forecast ecosystem responses to anthropogenic change. This approach provides the statistical rigor needed to advance beyond mere description of networks to predictive science that can inform conservation priorities [51].

The integration of these methods addresses a fundamental challenge in ecology: ecosystems are complex adaptive systems where overall behavior depends on interactions between participating agents and cannot be predicted by knowing individual agent behaviors in isolation [52]. Within a broader thesis on ecological network structure and function research, benchmarking serves as the essential link between theoretical network ecology and applied conservation science, creating a framework for assessing network resilience and identifying keystone species and critical functions that maintain ecosystem stability [27] [53].

Theoretical Foundations of Validation Methods

Null Models: Establishing Statistical Baselines

Null models provide a statistical framework for testing whether observed network patterns differ significantly from what would be expected by chance. These models generate randomized versions of ecological networks while preserving specific constraints, creating a distribution of possible networks against which the observed network can be compared. The core principle is to distinguish significant ecological structure from random assembly processes, thereby identifying non-random patterns of species interactions [27].

The application of null models has revealed that ecological networks exhibit statistically significant non-random structure across multiple dimensions. Research on multilayer ecological networks has demonstrated nested participation patterns in species-function relationships, where specialist species interact with subsets of the partners that generalist species interact with [27]. This nested structure has profound implications for ecosystem resilience, as it suggests certain species play disproportionate roles in maintaining multiple ecological functions simultaneously.

Extinction Analysis: Quantifying Network Resilience

Extinction analysis represents a complementary approach that tests network robustness by simulating species loss and tracking subsequent secondary extinctions. Also referred to as "extinction cascades," this methodology examines how the loss of biological interactions following the extinction of a species leads to additional species extinctions, thereby quantifying network resilience landscapes defined by link-loss sensitivity and rewiring probability thresholds [51].

The theoretical foundation of extinction analysis rests on niche theory and its application to species interactions. The concept of interaction niches describes the identity and functional properties of the partners with which a species can interact [53]. The size of a species' interaction niche indicates the breadth of biotic conditions the species can tolerate, with species possessing larger interaction niches generally being more resilient to disturbances. Extinction analysis operationalizes this theoretical framework by simulating how network structure collapses under different scenarios of species loss.

Experimental Protocols and Methodologies

Protocol 1: Constructing and Implementing Null Models

Objective: To test whether observed network structure differs significantly from random expectation for a specific network property.

Step-by-Step Procedure:

• Network Characterization: Quantify the observed network using relevant metrics (e.g., connectance, nestedness, modularity, degree distribution).
• Null Model Selection: Choose an appropriate null model that randomizes the observed network while preserving key characteristics. Common approaches include:
  • Permutation Models: Randomly shuffle interactions while preserving the number of interactions per species (fixed row and column sums).
  • Probabilistic Models: Generate networks based on probability distributions derived from species traits or abundances.
• Random Network Generation: Create a large number (typically ≥1000) of randomized networks using the selected null model algorithm.
• Metric Calculation: Compute the same network metrics for each randomized network as were calculated for the observed network.
• Statistical Comparison: Compare the observed metric value against the distribution of values from randomized networks to calculate a p-value and effect size.

Applications and Interpretation: This protocol allows researchers to identify whether specific network properties represent significant ecological structure. For instance, the study of multilayer networks in the Na Redona islet ecosystem applied this approach to demonstrate a non-random, nested structure in how plant species participate across different ecological functions [27]. The resulting p-values indicate whether observed patterns are statistically significant, while effect sizes quantify the magnitude of deviation from null expectations.

Protocol 2: Performing Extinction Analysis

Objective: To quantify network robustness by simulating species loss and tracking secondary extinctions under different scenarios.

Step-by-Step Procedure:

• Network Preparation: Format the ecological network with nodes representing species and edges representing interactions.
• Extinction Scenario Definition: Establish the sequence of primary species removals. Common approaches include:
  • Random removal: Species are removed in random order to simulate stochastic extinction.
  • Trait-based removal: Species are removed based on vulnerability traits (e.g., specialization, rarity).
  • Topological removal: Species are removed based on network properties (e.g., highest to lowest degree).
• Secondary Extinction Rules: Define criteria for secondary extinctions following primary removals:
  • Topological cascades: A species goes secondarily extinct if it loses all interaction partners.
  • Interaction strength thresholds: A species goes secondarily extinct if it loses a critical proportion of its total interaction strength.
  • Rewiring potential: Incorporate the ability for species to form new interactions using the concepts of "rewiring capacity" and "rewiring potential" [53].
• Iterative Simulation: For each primary removal, apply secondary extinction rules and update the network structure until no further extinctions occur.
• Robustness Metric Calculation: Compute robustness (R) as the proportion of species remaining in the network after the extinction cascade relative to the initial number.

Implementation Tools: The NetworkExtinction R package provides a flexible implementation of this protocol, enabling simulations of extinction cascades across both trophic and mutualistic networks with varying levels of link-importance and realization of potential interactions [51].

Table 1: Key Metrics for Benchmarking Network Performance

Metric Category	Specific Metric	Ecological Interpretation	Application Context
Structural Metrics	Connectance	Proportion of possible interactions that are realized	Network complexity assessment
	Nestedness	Pattern where specialists interact with subsets of generalists' partners	Mutualistic network resilience
	Modularity	Degree to which network forms distinct subgroups	Food web compartmentalization
Resilience Metrics	Robustness (R)	Proportion of species remaining after extinction cascade	Ecosystem stability assessment
	Rewiring Capacity	Multidimensional trait space of potential interaction partners [53]	Species' adaptive potential
	Secondary Extinction Rate	Number of species lost per primary extinction	Vulnerability to co-extinction
Functional Metrics	Functional Redundancy	Number of species performing similar ecological roles	Buffer against species loss
	Multifunctional Hub Status	Species disproportionately participating across functions [27]	Keystone species identification

Integration of Machine Learning in Network Prediction and Validation

Predictive Modeling of Species Interactions

Machine learning approaches, particularly neural networks, are increasingly employed to predict species interactions and generate networks for benchmarking. The fundamental challenge these methods address is the difficulty of comprehensively sampling all possible interactions in diverse ecological communities [54]. A proof-of-concept implementation involves:

• Feature Extraction: Using techniques like probabilistic principal component analysis (PCA) on species co-occurrence data to create feature vectors for each species.
• Network Architecture: Implementing feed-forward neural network layers with RELU and sigmoid activation functions to predict interaction probabilities between species pairs.
• Model Training: Dividing data into training and testing sets (typically 80-20 split) while implementing strategies to counter sampling biases, such as inflating datasets with positive interactions [54].

These predictive models create hypothesized networks that can be validated against empirical observations using the null model and extinction analysis frameworks described previously. The integration of machine learning represents a paradigm shift from purely statistical to predictive approaches in network ecology.

Addressing Inference Consistency Challenges

A significant consideration in benchmarking predicted networks is the consistency, or lack thereof, between different interaction inference approaches. Research has demonstrated little consistency between networks inferred using different methodologies (COOCCUR, NETASSOC, HMSC, and NDD-RIM) across ecologically relevant skills [51]. This highlights the critical importance of robust validation frameworks and suggests that different inference methods may capture complementary aspects of network structure.

To address this challenge, researchers have developed demographic simulation frameworks that create realistic populations of interacting species across time and space, establishing guidelines for assessing ecological network inference performance [51]. These simulated datasets provide known "ground truth" networks against which inference methods can be rigorously benchmarked.

Table 2: Research Reagent Solutions for Ecological Network Analysis

Research Reagent	Type	Primary Function	Application Example
KrigR R Package [51]	Climate Data Tool	Access, aggregate, and process state-of-the-art climate data	Linking environmental gradients to network structure
NetworkExtinction R Package [51]	Analysis Tool	Simulate extinction cascades with varying parameters	Quantifying network resilience to species loss
Multilayer Network Framework [27]	Mathematical Framework	Integrate multiple interaction types into unified model	Analyzing species' roles across ecological functions
Rewiring Capacity Metrics [53]	Analytical Metric	Quantify species' potential to form new interactions	Assessing adaptive potential under global change
Tensor Decomposition Methods [27]	Mathematical Approach	Reduce complexity of multidimensional interaction data	Identifying patterns in species-function relationships
Neural Network Architectures [54]	Predictive Model	Predict unobserved species interactions	Completing partial network data

Visualization of Methodological Workflows

The following diagrams illustrate key methodological workflows for implementing null models and extinction analysis in ecological network research.

Figure 1: Null Model Validation Workflow

Figure 2: Extinction Analysis Methodology

Application to Ecological Network Research

Case Study: Multifunctional Network Analysis

The application of these benchmarking approaches to the Na Redona islet ecosystem exemplifies their utility in identifying keystone elements in ecological networks. By constructing a resource-consumer-function (RCF) tensor encompassing 1537 interactions across six ecological functions, researchers applied null model analysis to demonstrate a non-random, nested structure in how plant species participate across different functions [27].

Subsequent extinction analysis enabled ranking of both species and functions by importance, identifying woody shrubs and fungal decomposition as keystone actors whose removal had larger-than-random effects on secondary extinctions [27]. This integrated approach provides a template for identifying critical conservation targets in complex ecosystems.

Assessing Network Resilience to Global Change

Benchmarking methodologies are particularly valuable for forecasting ecological responses to anthropogenic pressures. The concepts of rewiring capacity (the multidimensional trait space of all potential interaction partners for a species within a region) and rewiring potential (the total trait space covered by interaction partners of species at a target trophic level locally) provide quantitative metrics for assessing network adaptability [53].

Application of these concepts to plant-hummingbird networks across the Americas has enabled mapping of how ecological networks may respond to global change, identifying regions and network types with greater inherent resilience to species turnover and interaction rewiring [53]. This represents a significant advance beyond static network descriptions toward predictive frameworks for ecosystem management.

Benchmarking performance through null models and extinction analysis provides an essential statistical foundation for ecological network research, transforming pattern description into hypothesis testing and prediction. These methodologies enable researchers to distinguish biologically significant network architecture from random assemblages, quantify resilience to species loss, and identify keystone elements that maintain ecosystem functions.

As ecological networks face increasing pressure from anthropogenic change, these benchmarking approaches will play a crucial role in forecasting ecosystem responses and guiding conservation priorities. The integration of machine learning, multilayer network frameworks, and trait-based approaches with traditional validation methods represents an emerging frontier that will enhance our ability to predict and preserve ecological complexity in an era of global change.

Network analysis provides a powerful framework for examining relationships between different entities, from molecular interactions within a cell to the broad ecological connections across a landscape [55]. In biological sciences, this approach allows researchers to study complex systems as interconnected networks of mutually interacting entities, where each component affects the overall function [56]. The universal language of graph theory—comprising nodes (representing entities) and edges (representing interactions)—enables cross-system comparisons that reveal fundamental organizational principles across different scales of biological organization [56] [57]. This whitepaper examines the structural, functional, and analytical parallels between molecular, cellular, and ecological networks, providing researchers with methodological frameworks for investigating network architecture and dynamics within the context of ecological network structure and function research.

The core premise of network biology is that biological systems can be meaningfully represented as graphs where nodes correspond to biological entities and edges depict interactions between them [56]. This representation applies consistently whether studying protein-protein interactions, gene regulatory networks, cellular coordination networks, or ecological habitat networks [56] [3] [58]. The cross-scale applicability of network analysis creates a unified approach for understanding how complex biological systems organize, function, and maintain resilience against disturbances—a fundamental pursuit in ecological network research that now extends to biomedical applications including drug development [56].

Network Types and Structural Properties

Molecular Interaction Networks

Molecular interaction networks form the foundational layer of cellular organization, governing fundamental biological processes through precise interaction patterns [56]. These networks include:

• Protein-Protein Interaction (PPI) Networks: These represent specific molecular contacts between proteins with defined binding regions and biological functions [56]. PPIs are essential to virtually every cellular process and play increasingly important roles in drug development, as they help researchers understand complex disease disorders, assign functions to uncharacterized proteins, and elucidate detailed signaling pathways [56]. Key resources for PPI information include BioGRID and STRING databases [56].

• Gene Regulatory Networks (GRNs): These represent the complex mechanisms regulating gene expression at transcriptional, translational, and splicing levels [56]. In GRNs, proteins serve dual roles as both products and controllers of gene expression, creating complex feedback loops that determine cellular states and fate decisions [56].

• Metabolic Networks: These consist of chemical reactions involving the catalytic conversion of small biomolecules (metabolites) through enzymatic reactions [56]. Metabolic networks can be represented with metabolites as nodes and reactions as edges, or alternatively as reaction adjacency graphs where nodes represent reactions and edges connect reactions where the product of one serves as the substrate for another [56].

Cellular Networks and Coordination Modules

At the cellular level, networks describe how different cell types coordinate within tissues to achieve cohesive functioning. Recent single-cell transcriptomic advances have enabled the identification of coordinated cellular modules (CMs)—groups of cell types that consistently co-occur across tissues and function as integrated units [58]. These multicellular coordination networks represent a higher organizational level than molecular networks, revealing how diverse cell types organize within tissue niches for coordinated physiological functions [58].

The identification of these cross-tissue cellular modules demonstrates that functionally related organs share similar functional modules, such as mucosal immunity present in both the small intestine and colon [58]. This modular organization represents a fundamental principle of tissue-level organization, with different cellular modules exhibiting specific preferences for particular human body systems and performing distinct physiological functions [58].

Ecological Networks

Ecological networks (ENs) represent the structural and functional connections between landscape elements that collectively safeguard regional ecological security [3]. These networks include ecological sources (core habitat areas), ecological corridors (connecting pathways between sources), and other landscape elements that together form a cohesive ecological infrastructure [3]. Unlike molecular and cellular networks, ecological networks operate at landscape scales and face distinct pressures from urbanization and climate change that threaten their structural and functional integrity [3].

The structure-function-resilience framework provides a comprehensive approach for analyzing ecological networks, enabling researchers to systematically examine the spatiotemporal evolution of EN structure, their ecosystem functions, and their resilience to various disturbance regimes [3]. This framework allows for quantitative assessment of how different disturbance strategies—random, climate-stress, source-degradation, and corridor-fragmentation—impact both structural and functional resilience of ecological networks [3].

Table 1: Comparative Analysis of Network Types Across Biological Scales

Network Attribute	Molecular Networks	Cellular Networks	Ecological Networks
Representative Nodes	Genes, proteins, metabolites	Cell types, cell states	Habitat patches, ecological sources
Representative Edges	Physical interactions, regulatory relationships	Cellular co-occurrence, communication	Landscape connectivity, species movement
Primary Functions	Cellular processes, metabolic pathways, information processing	Tissue organization, multicellular coordination	Biodiversity maintenance, ecosystem service provision
Characteristic Structure	Scale-free, modular	Tissue-specific compositions, cross-tissue modules	Spatial networks, patch-matrix systems
Perturbation Responses	Mutation, expression changes	Inflammation, aging, disease	Urbanization, climate change, fragmentation
Analysis Methods	Centrality measures, motif analysis	Covariance analysis, NMF, clustering	Landscape metrics, connectivity modeling

Analytical Methods and Metrics

Network Construction and Feature Detection

The methodologies for constructing and analyzing networks vary significantly across biological scales, yet share common mathematical foundations in graph theory:

Molecular Network Construction: Molecular interaction networks are typically built from high-throughput experimental data (e.g., yeast two-hybrid systems for PPIs) or computational predictions, often integrated from multiple databases [56]. Feature detection in these networks employs centrality measures to identify critical nodes, modularity analysis to detect functional units, and motif discovery to identify recurrent network patterns [56].

Cellular Module Identification: The CoVarNet computational framework identifies coordinated cellular modules by leveraging covariance in cell subset frequencies across samples [58]. This approach uses non-negative matrix factorization (NMF) to identify co-occurring cell subsets and determines specifically correlated subset pairs to construct CM networks [58]. Topological and statistical evaluations then validate these networks, revealing multicellular ecosystems with distinct tissue preferences and functional specializations [58].

Ecological Network Mapping: Ecological networks are constructed using landscape data, including land use/cover maps, species distribution data, and connectivity models [3]. The random forest regression model can be employed to explore the driving effects of land use and cover change (LUCC) on the evolution of EN structure and function, revealing coupling mechanisms between structural, functional, and resilience properties [3].

Key Network Metrics and Their Interpretations

Several graph-theoretical metrics provide universal analytical tools across network types, though their biological interpretations vary by scale:

• Degree Centrality: Measures the number of connections a node has [57]. In molecular networks, high-degree "hub" proteins are often essential for survival; in cellular networks, highly connected cell types may serve integrative functions; in ecological networks, well-connected habitats support higher biodiversity [56] [57].

• Betweenness Centrality: Quantifies how frequently a node lies on the shortest path between other nodes [57]. Nodes with high betweenness serve as critical bridges or bottlenecks across all network types—whether controlling information flow in molecular networks, mediating interactions in cellular networks, or serving as stepping stones in ecological networks [57].

• Clustering Coefficient: Measures the tendency of nodes to form tightly connected groups [57]. High clustering indicates modular organization, which may represent functional modules in molecular networks, specialized tissue niches in cellular networks, or distinct habitat complexes in ecological networks [57].

• Path Length: Calculates the average number of edges between node pairs [57]. Short path lengths facilitate rapid information transfer in molecular networks, efficient coordination in cellular networks, and effective dispersal in ecological networks [57].

Table 2: Cross-Scale Analytical Methods in Network Biology

Method Category	Specific Techniques	Molecular Applications	Cellular Applications	Ecological Applications
Network Construction	High-throughput screening, Database integration, Covariance analysis	PPI mapping, GRN inference	Cellular module identification from scRNA-seq	Landscape mapping, Connectivity modeling
Topological Analysis	Centrality measures, Community detection, Motif analysis	Essential gene identification, Functional module detection	Key cell type identification, Tissue niche characterization	Critical habitat identification, Conservation prioritization
Dynamics Modeling	Differential equations, Boolean networks, Agent-based models	Signaling dynamics, Metabolic flux analysis	Cellular differentiation trajectories, Multicellular coordination	Species movement simulations, Landscape genetic processes
Perturbation Analysis	Node/edge removal, Sensitivity analysis, Robustness testing	Drug target identification, Disease mechanism elucidation	Aging, disease progression studies	Climate change impact assessment, Urbanization scenario planning
Integration Methods	Multi-omics integration, Machine learning, Graph neural networks	Pathway mapping across data types	Cross-tissue atlas integration	Multi-species, multi-habitat network modeling

Experimental and Computational Protocols

Single-Cell RNA Sequencing for Cellular Network Analysis

The emergence of single-cell RNA sequencing (scRNA-seq) has revolutionized our ability to map cellular networks and identify coordinated cellular modules. The following protocol outlines the key steps for generating data suitable for cellular network analysis:

Cell Preparation and Sequencing:

• Use the Microwell-seq process with bead sizes adapted to target cells (20μm and 28μm beads with 25μm and 32μm microwells) [59].
• Employ different bead sequences optimized for different species (beads 2.0 for mice, beads 3.0 for zebrafish and Drosophila) [59].
• Process includes cell and bead collection, reverse transcription, exonuclease I treatment, second-strand synthesis, and cDNA amplification to generate barcoded single-cell libraries [59].
• Sequence libraries on Illumina HiSeq or MGI DNBSEQ-T7 sequencer with 150bp read length for both reads [59].

Data Processing and Quality Control:

• Align reads to appropriate reference genomes using STAR aligner [59].
• Obtain digital gene expression matrices using modified Dropseq tools [59].
• Filter cells detecting <500 transcripts and 200 genes, excluding cells with high mitochondrial gene content [59].
• Detect and remove potential doublets using DoubletFinder (approximately 5% of cells typically removed as doublets) [59].
• Use Seurat and Scanpy for dimension reduction, clustering, and differential gene expression analysis [59].

Cellular Module Identification:

• Apply the CoVarNet framework, which uses non-negative matrix factorization (NMF) to identify factors prioritizing cell subsets based on weights [58].
• Determine specifically correlated subset pairs as potential edges in CM networks [58].
• Construct multiple CM networks by connecting co-occurring nodes through potential edges [58].
• Perform topological and statistical evaluations to validate identified modules [58].

Ecological Network Resilience Assessment

For ecological networks, assessing resilience under different disturbance scenarios provides critical insights for conservation planning:

Network Construction and Scenario Development:

• Construct ecological networks for multiple time points (e.g., 1990-2060) using land cover data and species distribution models [3].
• Develop future scenarios based on Shared Socioeconomic Pathways (e.g., SSP126 and SSP585) to project different climate and urbanization trajectories [3].

Disturbance Strategy Implementation:

• Implement four distinct disturbance strategies: random, climate-stress, source-degradation, and corridor-fragmentation [3].
• Quantitatively assess impacts of each disturbance strategy on both structural and functional resilience [3].
• Use random forest regression models to explore driving effects of land use and cover change on EN structure and function evolution [3].

Resilience Metric Calculation:

• Calculate historical and projected future resilience metrics under different scenarios [3].
• Analyze structural connectivity (probability of connectivity index), node importance (betweenness centrality), and functional capacity under various disturbance regimes [3].
• Identify chain reactions of "structural damage → functional decline → resilience loss" triggered by different disturbance types [3].

Network Analysis Workflow: Cellular Modules

Visualization and Data Integration Techniques

Network Visualization Approaches

Effective visualization is crucial for interpreting complex network relationships across biological scales. Key considerations include:

Layout Algorithms: Selecting appropriate graph layout algorithms significantly enhances interpretability [57]. Force-directed layouts simulate physical forces to achieve aesthetically pleasing arrangements, with repulsive forces pushing nodes apart and attractive forces pulling connected nodes together [57]. These are particularly effective for visualizing community structures and clusters. Circular layouts arrange nodes in circular patterns, suitable for cyclic or periodic relationships, while hierarchical layouts organize nodes in layers based on hierarchical relationships or importance [57].

Visual Encoding Techniques: Proper visual encoding ensures clear communication of network properties [57]. Varying node size can represent quantitative attributes like degree centrality or importance, while node color can encode categorical or continuous variables [57]. Similarly, edge thickness can represent connection strength or weight, and different line styles can distinguish edge types or categories [57]. In directed networks, arrowheads clearly indicate relationship directionality [57].

Accessibility Considerations: Accessible design practices ensure visualizations are usable for all audiences, including people with disabilities [60] [61]. This includes ensuring sufficient color contrast between text and background (at least 4.5:1 for body text), avoiding reliance on color alone to convey meaning, and providing alternative text for charts and images [60] [62] [61]. These considerations are particularly important when presenting complex network diagrams to diverse scientific audiences.

Tools for Network Analysis and Visualization

Various specialized tools facilitate network analysis and visualization across biological domains:

• Gephi: A free, open-source desktop visualization tool specializing in network visualization and analysis [55].
• Cytoscape: Provides powerful tools for biological network analysis and visualization, particularly strong for molecular interaction networks [57].
• VOSViewer: Focuses on bibliometric network visualization and analysis, but also applicable to other network types [55].
• NodeXL: An add-on to Microsoft Excel that enables creation of node-link diagrams using spreadsheet data (Windows only) [55].
• R packages: igraph provides comprehensive network analysis capabilities; ggraph extends the grammar of graphics to network visualization; visNetwork creates interactive network visualizations using the vis.js library [57].
• Python libraries: NetworkX offers wide-ranging network analysis and visualization functions; Plotly enables creation of interactive network visualizations in Python [57].

Network Types Hierarchy

Research Reagent Solutions and Computational Tools

Table 3: Essential Research Reagents and Tools for Network Biology

Category	Specific Tool/Reagent	Application Purpose	Key Features
Sequencing Technologies	Microwell-seq	Single-cell RNA sequencing for cellular network analysis	Adaptable bead sizes (20μm, 28μm) for different cell types, species-specific bead sequences [59]
Data Integration Tools	BBKNN	Batch correction in single-cell data integration	Top-performing integration tool for harmonizing extensive datasets across tissues and conditions [58]
Network Analysis Software	Gephi	Network visualization and analysis	Free, open-source desktop tool specializing in network visualization [55]
Network Analysis Software	Cytoscape	Biological network analysis and visualization	Powerful platform for molecular interaction networks with extensive plugin ecosystem [57]
Network Analysis Software	NetworkX (Python)	Network analysis and visualization	Comprehensive library for creating, analyzing, and visualizing complex networks [57]
Network Analysis Software	igraph (R)	Network analysis and visualization	Comprehensive network analysis capabilities with statistical focus [57]
Computational Frameworks	CoVarNet	Cellular module identification	Leverages covariance in cell subset frequencies using NMF and correlation analysis [58]
Spatial Validation	Immunofluorescence staining	Spatial validation of cellular networks	Confocal microscopy imaging of tissue sections to verify spatial relationships [59]
Database Resources	BioGRID, STRING	Protein-protein interaction data	Curated molecular interaction data for network construction [56]

Discussion and Future Perspectives

The comparative analysis of networks across molecular, cellular, and ecological scales reveals fundamental organizational principles that transcend biological hierarchies. Structural similarities—such as modular architecture, hub-and-spoke configurations, and scale-free properties—suggest evolutionary conservation of efficient network designs [56] [58]. Functional parallels in information processing, resource allocation, and response coordination further highlight universal principles of biological organization [56] [3].

The cross-tissue cellular modules identified through single-cell transcriptomics represent a crucial intermediate level of biological organization between molecular networks and ecological systems [58]. These modules demonstrate how multicellular coordination enables emergent tissue-level functions, similar to how species interactions enable ecosystem functions [58]. This parallel suggests that the structure-function-resilience framework developed for ecological networks [3] may be productively applied to understanding cellular networks in health and disease.

Future research directions should focus on multi-scale network integration, developing computational frameworks that explicitly link molecular, cellular, and ecological networks [56] [3]. Such integration would enable researchers to predict how perturbations at one scale propagate through others—for example, how genetic mutations affect cellular organization and ultimately ecosystem function. Machine learning and artificial intelligence approaches are increasingly being integrated with network biology to tackle these complex multi-scale challenges [56].

The emerging landscape of network biology points toward a more unified understanding of biological systems across scales, with potential applications in drug development, conservation biology, and synthetic biology [56] [3]. As network-based approaches continue to evolve, they will provide increasingly powerful frameworks for understanding the fundamental principles governing biological organization from molecules to ecosystems.

Ecological networks (ENs) form the foundational architecture of functioning ecosystems, safeguarding regional ecological security from an overall perspective [3]. The structural stability of these networks—comprising ecological sources, nodes, and corridors—is intrinsically linked to their capacity to deliver essential ecosystem services. However, under the multiple pressures of urbanization and climate change, their structural and functional integrity faces systemic threats [3]. This technical guide establishes a comprehensive framework for conducting sustainability audits that quantitatively correlate structural stability metrics with ecosystem service delivery outcomes. Designed for researchers and scientists, this whitepaper provides methodological protocols, analytical frameworks, and visualization tools to advance ecological network structure and function research. By integrating recent findings from diverse ecosystems—from the West African drylands to the highly urbanized Guangdong-Hong Kong-Macao Greater Bay Area (GBA)—this guide addresses critical gaps in assessing how ENs maintain functional integrity under simultaneous climatic and anthropogenic stressors [63] [3].

Conceptual Framework: Structure-Function-Resilience Dynamics

The relationship between structural stability and ecosystem service delivery operates through a cascading framework where structural integrity enables functional performance, which collectively determines systemic resilience. This structure-function-resilience framework provides a systematic approach for analyzing the spatiotemporal evolution of ENs [3].

• Structural Dimension: This comprises the physical configuration of ENs, including ecological sources (core habitats), nodes (stepping-stone habitats), and corridors (connectivity pathways). Structural metrics include landscape aggregation, patch connectivity, and fragmentation indices [3].

• Functional Dimension: This encompasses the ecosystem processes and services supported by the network structure, including biodiversity maintenance, carbon sequestration, climate regulation, and water purification [63]. Functionality depends on structural integrity for service delivery.

• Resilience Dimension: This represents the capacity of ENs to maintain structural and functional attributes despite disturbances from climate stressors or anthropogenic pressures [3]. Resilience emerges from the interaction between structure and function.

The socio-ecological systems (SES) approach further enriches this framework by emphasizing the interlinked dimensions of governance institutions, stakeholder networks, and community engagement processes that enable or constrain Nature-based Solution (NbS) implementation [63]. When structural components degrade—through source degradation or corridor fragmentation—a chain reaction triggers functional decline and ultimately reduces resilience, creating a feedback loop that accelerates systemic collapse [3].

Methodological Protocols for Sustainability Auditing

Ecological Network Mapping and Structural Analysis

Objective: Quantify the structural composition and configuration of ecological networks to establish baseline metrics for correlation with service delivery.

Protocol:

• Land Classification: Utilize satellite imagery (Landsat, Sentinel) to classify land use/cover change (LUCC) categories with random forest algorithms [3].
• Source Identification: Delineate ecological sources based on patch size, ecosystem type, and biodiversity value using spatial analysis software (ArcGIS, QGIS).
• Corridor Delineation: Apply circuit theory or least-cost path models to map potential connectivity corridors between ecological sources.
• Structural Metrics Calculation:
  • Patch Cohesion Index: Measures physical connectivity between patches
  • Corridor Connectivity Index: Quantifies linkage effectiveness between core habitats
  • Node Importance Value: Ranks stepping-stone habitats by their contribution to network connectivity

Data Requirements: Multi-temporal remote sensing imagery (1990-2020+), species distribution data, topographic maps, and land use planning documents [3].

Ecosystem Service Assessment

Objective: Quantify ecosystem service delivery across the ecological network to establish functional performance metrics.

Protocol:

• Carbon Sequestration: Model carbon storage using InVEST's Carbon Model with aboveground, belowground, soil, and dead organic matter carbon pools.
• Climate Regulation: Measure urban heat island mitigation through land surface temperature analysis using thermal infrared data.
• Biodiversity Maintenance: Conduct field surveys of species richness and abundance, complemented with acoustic monitoring and camera trapping.
• Habitat Quality: Apply InVEST's Habitat Quality module incorporating threat sources (urban areas, roads), sensitivity of habitat types to threats, and distance from threats.

Validation: Ground-truth through field surveys, vegetation sampling, and soil carbon measurements [63].

Resilience Assessment Under Disturbance Scenarios

Objective: Evaluate structural and functional resilience of ENs under different disturbance regimes.

Protocol:

• Disturbance Simulation: Develop four disturbance strategies to quantitatively assess impacts [3]:
  • Random Disturbance: Random removal of network nodes
  • Climate-Stress Disturbance: Simulating climate impacts like drought on vegetation
  • Source-Degradation Disturbance: Targeted degradation of core habitats
  • Corridor-Fragmentation Disturbance: Simulating barrier effects from infrastructure
• Resilience Metrics: Calculate pre- and post-disturbance structural connectivity and ecosystem service capacity.
• Scenario Analysis: Project future conditions under climate scenarios (SSP126, SSP585) and urban expansion trends [3].

Table 1: Key Structural, Functional, and Resilience Metrics for Sustainability Auditing

Dimension	Metric	Measurement Approach	Interpretation
Structural	Patch Cohesion Index	Spatial analysis of land cover maps	Higher values indicate better physical connectivity
	Corridor Connectivity Index	Circuit theory modeling	Measures functional connectivity between core habitats
	Node Importance Value	Network centrality analysis	Identifies critical stepping-stone habitats
Functional	Carbon Sequestration Rate	InVEST Carbon Model	Tons C/ha/year stored
	Biodiversity Capacity	Mean Species Abundance (MSA) model	Percentage of original species richness maintained
	Habitat Quality Index	InVEST Habitat Quality module	0-1 scale reflecting habitat condition
Resilience	Resistance Capacity	Pre-/post-disturbance function comparison	Ability to maintain function under stress
	Recovery Potential	Time series analysis after disturbance	Rate of return to pre-disturbance state
	Adaptive Capacity	Response diversity to multiple stressors	Ability to reorganize while maintaining function

Case Study Applications

Bontioli Natural Reserve, Burkina Faso: NbS Interventions

The Bontioli Natural Reserve (BNR) in Burkina Faso's West African drylands exemplifies vegetation decline driven by combined climate and anthropogenic pressures. Research documented a consistent vegetation decline at a rate of 0.051 ± 0.043/year, driven by rising temperatures and declining rainfall, exacerbated by anthropogenic land use pressure since 2000 [63]. Strong correlations were observed between human population growth and cropland expansion (R² = 0.903) and vegetation loss (R² = 0.793) [63]. Consequently, 53.85% of species populations are declining, with 30.77% classified as endangered or vulnerable [63].

NbS Protocol Implementation:

• Participatory Governance Framework: Engage local communities in co-management processes through structured stakeholder workshops [63].
• Vegetation Dynamics Analysis: Apply generalized additive modeling (GAM) to assess long-term vegetation response to climate stressors [63].
• Functional Restoration: Implement reforestation, agroforestry, and ecological corridors to restore structural connectivity [63].
• Structural Rehabilitation: Establish buffer zones to reduce edge effects and create habitat stepping stones [63].

Table 2: Bontioli Reserve Sustainability Audit Findings

Parameter	Historical Baseline	Current Status	Trend	Primary Driver
Vegetation Cover	89% (1957)	62% (2025)	Decline: 0.051/year	Climate + Anthropogenic
Cropland Area	12% (2000)	34% (2025)	Expansion: R²=0.903 with population	Anthropogenic
Species Status	92% stable (1980)	53.85% declining (2025)	30.77% endangered/vulnerable	Habitat loss
Carbon Sequestration	High (1990)	Moderate-declining (2025)	Correlated with vegetation loss	Climate + Land use

Guangdong-Hong Kong-Macao Greater Bay Area: Urbanization Impacts

The highly urbanized GBA represents a contrasting case where urban expansion rather than agricultural pressure drives ecological network degradation. Research analyzing the period 1990-2060 reveals that urban expansion has been a key driver of ecological source degradation [3]. Future scenarios project continued decline under SSP585, while SSP126 maintains relatively stable ecological sources [3].

Key Findings:

• Historical EN landscape patterns were highly aggregated with large, connected patches, but future scenarios exhibit increasing fragmentation [3].
• SSP126 shows high diversity but severe fragmentation, while SSP585 displays low diversity and poor connectivity [3].
• Historical resilience was highest initially but declined later, with source degradation causing the most severe disruption [3].
• Beneficial land conversions (e.g., cropland to forest) enhance connectivity and node importance, improving structural integrity [3].
• Urban expansion-dominated destructive conversions fragment landscapes, disrupt corridors, isolate key nodes, and trigger the chain reaction of "structural damage → functional decline → resilience loss" [3].

Experimental Workflow and Signaling Pathways

The research methodology for sustainability auditing follows a systematic workflow that integrates data collection, analysis, and visualization. The diagram below illustrates this experimental pathway:

Ecological Network Sustainability Audit Workflow

The conceptual framework for structure-function relationships in ecological networks can be visualized through the following signaling pathway:

Structure-Function-Relationship Pathway in Ecological Networks

The Scientist's Toolkit: Research Reagent Solutions

Table 3: Essential Research Tools and Methods for Ecological Network Sustainability Auditing

Tool/Platform	Primary Function	Application Context	Technical Specification
Random Forest Regression	Predictive modeling of LUCC drivers	Analyzing factors driving ecological network evolution [3]	R package 'randomForest' with 500+ trees
InVEST Suite	Ecosystem service modeling	Quantifying carbon storage, habitat quality, water purification [63]	Python-based with GIS integration
Geographically and Temporally Weighted Regression (GTWR)	Spatiotemporal analysis	Modeling non-stationary relationships in ecosystem services [3]	MATLAB or Python implementation
Circuit Theory Models	Connectivity analysis	Mapping ecological corridors and pinch points [3]	Circuitscape or Linkage Mapper
Generalized Additive Models (GAM)	Non-linear trend analysis	Assessing vegetation response to climate stressors [63]	R package 'mgcv' with spline smoothing
SSP-RCP Scenarios	Future projections	Modeling climate and development pathways [3]	IPCC framework integration

Sustainability auditing through the correlation of structural stability with ecosystem service delivery provides a robust framework for assessing ecological network health under global change pressures. The integrated methodologies presented in this technical guide enable researchers to quantify the cascading effects of structural degradation on functional capacity and resilience dynamics. Findings from diverse ecosystems consistently demonstrate that beneficial land conversions enhance connectivity and node importance, thereby improving structural integrity, while urban expansion and climate stressors trigger a destructive chain reaction of structural damage leading to functional decline and ultimately resilience loss [3].

The protocols outlined—particularly the disturbance-based resilience testing and structure-function-resilience framework—offer actionable insights for land use planning and conservation prioritization. For dryland ecosystems like Bontioli Reserve, NbS implementations represent cost-effective strategies to restore ecological function and strengthen community-based conservation [63]. In highly urbanized regions like the GBA, strategic protection of critical corridors and nodes maintains functional connectivity despite development pressures [3]. Future research should focus on refining threshold indicators that signal imminent state transitions in ecological networks, enabling proactive intervention before systemic collapse occurs.

Ecological networks (ENs) are fundamental spatial constructs for maintaining biodiversity, ecosystem resilience, and sustainable landscape management. Defining their structure and function requires integrative approaches that operate across multiple spatial and functional scales. This whitepaper synthesizes methodologies and findings from two contrasting case studies: the large-scale, rapidly urbanizing Pearl River Delta (PRD) region in China and the small, isolated Na Redona Islet in the Balearic Islands. The PRD case exemplifies the dynamics of landscape-scale ecological networks under intense anthropogenic pressure, while Na Redona provides a groundbreaking model for quantifying multifunctional species-interaction networks. Together, they offer a complementary framework for advancing ecological network research, highlighting that effective conservation depends on both preserving large-scale spatial connectivity and safeguarding the complex web of species interactions that underpin ecosystem functioning.

Large-Scale Landscape Networks: The Pearl River Delta (PRD) Urban Agglomeration

The PRD, one of China's most dynamic urban agglomerations, has served as a living laboratory for analyzing long-term changes in landscape ecological networks from 2000 to 2020. Research here focuses on the spatial configuration of ecological components—sources, corridors, and resistance surfaces—and their relationship with anthropogenic ecological risk (ER).

Quantitative Dynamics of the PRD Ecological Network (2000-2020)

Long-term studies reveal significant changes in the structural integrity of the PRD's ecological network, driven by rapid urbanization. The data below summarizes the core changes over two decades [11].

Table 1: Spatiotemporal Dynamics of the PRD Ecological Network (2000-2020)

Metric	2000	2020	Change (2000-2020)
Area of High Ecological Risk Zones	Baseline	-	Increased by 116.38%
Area of Ecological Sources	Baseline	-	Decreased by 4.48%
Flow Resistance in Corridors	Baseline	-	Increased
Spatial Correlation (Moran's I) between EN and ER	-	-	-0.6 (p < 0.01)

Experimental Protocol: Constructing a Landscape Ecological Network

The following established protocol details the steps for constructing and analyzing a landscape ecological network, as applied in the PRD [11] [64].

Step 1: Identification of Ecological Sources Ecological sources are large patches with high habitat quality and low ecosystem degradation, crucial for maintaining regional ecological security.

• Data Inputs: Land use/cover data, vegetation indices (NDVI), ecosystem service values.
• Methodology:
  • Calculate habitat suitability based on ecosystem degradation and landscape connectivity.
  • Classify the resulting suitability map into levels using the Natural Breaks method.
  • Select the highest suitability level as candidate ecological source patches.
  • Apply an area threshold (e.g., 45 hectares in the PRD) to exclude small, fragmented patches and ensure spatial continuity and ecological functionality.

Step 2: Construction of Ecological Resistance Surfaces Resistance surfaces represent the landscape's impedance to ecological flows, such as species movement.

• Data Inputs: Stable factors (e.g., slope, elevation/DEM) and dynamic factors (e.g., land use type, distance from roads, nighttime light data, vegetation coverage).
• Methodology:
  • Standardize all factor rasters.
  • Determine the weight of each factor using Spatial Principal Component Analysis (SPCA).
  • Create a comprehensive resistance surface using the weighted sum formula: ( RS = \sum{i=1}^{m} F{ij} w_{j} ) where RS is the resistance surface, F_ij is the j-th factor of the i-th grid, and w_j is the assigned weight [11].

Step 3: Delineation of Ecological Corridors and Networks Corridors connect ecological sources and facilitate material and energy exchange.

• Primary Tool: Minimum Cumulative Resistance (MCR) Model. This model identifies the path of least resistance between ecological sources, which are defined as potential corridors [64].
• Alternative Tool: Circuit Theory. This theory can be used to simulate ecological flows more robustly, identifying not only optimal corridors but also areas of high movement probability (pinch points) and barriers [11].
• Validation & Analysis: Use tools like Linkage Mapper to model the network and gravity models to assess interaction strength between patches. The final network is a system of ecological sources (nodes) and corridors (links).

Small-Scale Multilayer Networks: The Na Redona Islet Ecosystem

In contrast to the landscape approach, research on Na Redona pioneered a mathematical framework to analyze multiple ecological functions within a single, integrated model. This shifts the focus from a purely species-centric view to a species-function perspective [27] [28].

Experimental Protocol: Building a Resource-Consumer-Function (RCF) Tensor

This protocol outlines the procedure for constructing a multilayer ecological network from empirical field data [27] [28].

Step 1: Systematic Field Sampling and Data Collection The goal is to gather comprehensive interaction data across multiple ecological functions.

• Defined Functions: Pre-define the ecological functions to be studied (e.g., pollination, herbivory, seed dispersal, decomposition, nutrient uptake, pathogenicity).
• Direct Observation: Conduct field campaigns to directly observe and record interactions between species (e.g., plant-pollinator, plant-herbivore).
• Sample Collection: Collect physical samples (e.g., droppings for seed dispersal analysis, root samples for fungal association, pollen samples) for later laboratory identification.
• Effort Normalization: Allocate equal sampling effort to each targeted interaction type to minimize observational bias.

Step 2: Laboratory Processing and Interaction Identification

• Taxonomic Identification: Use morphological and genetic methods (e.g., Amplicon Sequence Variants - ASVs for fungi) to identify species from collected samples.
• Data Cleansing and Normalization: Clean raw data and normalize interaction frequencies based on sampling effort. Convert raw counts into probabilities of co-occurrence to allow for comparison across different functions and units.

Step 3: Construction of the RCF Tensor and Projected Networks

• Tensor Formulation: Encode the complete dataset into a rank-3 Resource-Consumer-Function (RCF) tensor ( \mathcal{F} = {f{ix}^{\alpha}} ), where ({f}{ix}^{\alpha}) is the observed probability of co-occurrence between a resource (plant) species i, a consumer (animal/fungi) species x, via an interaction of function α [27].
• Integration: Mathematically integrate out the consumer index to obtain a 2D Resource-Function matrix. This bipartite network encodes how plant species and functions are intertwined.
• Further Projection: This matrix can be projected to create 1) a Function-Function network (where functions are linked if they share plant species) and 2) a Plant-Plant network (where plants are linked if they share functions).

Key Findings from the Na Redona Case Study

Application of the RCF tensor framework to the Na Redona dataset (1537 interactions between 691 plants, animals, and fungi across 6 functions) yielded critical insights [27] [28]:

• Nested Structure: The Resource-Function matrix exhibited a statistically significant nested architecture, indicating that specialist plant species participate in a subset of the functions that generalist plants participate in.
• Keystone Multitaskers: The concept of keystone species was extended to "multifunctional keystoneness." The top six species in the keystoneness hierarchy were all woody shrubs, suggesting their disproportionate role in connecting multiple functions due to longer lifespans and broader interaction niches.
• Hub Function: Interactions related to fungal decomposition emerged as a "hub function," playing a critical role in connecting species within the multifunctional network.

The Scientist's Toolkit: Essential Reagents and Materials

Table 2: Key Research Reagents and Solutions for Ecological Network Studies

Item	Function/Application	Relevance
Gaofen-1 / Landsat Satellite Imagery	Provides land use/cover classification and vegetation indices (NDVI).	Fundamental for identifying ecological sources and land use change in landscape-scale studies (PRD) [11] [64].
Digital Elevation Model (DEM)	Provides topographical data (elevation, slope).	A key stable factor in constructing ecological resistance surfaces [11].
Morphological Spatial Pattern Analysis (MSPA)	A image processing technique to identify spatially structured landscape elements (e.g., cores, bridges).	Used for precise, geometry-based identification of potential ecological sources from land cover data [64].
Amplicon Sequence Variants (ASVs)	High-resolution genetic markers for identifying fungal and bacterial taxa.	Crucial for characterizing below-ground interactions and identifying consumers in multilayer network studies (Na Redona) [27].
Linkage Mapper Toolbox	A GIS toolset for modelling landscape connectivity and mapping corridors.	Implements the MCR model and circuit theory to construct and map ecological networks [65].
R / Python (igraph, Tensorly)	Programming environments for statistical computing, network analysis, and tensor algebra.	Essential for analyzing network topology, calculating centrality metrics, and implementing the RCF tensor framework [27].

The juxtaposition of the PRD and Na Redona case studies provides a powerful, multi-scale lens through which to define ecological network structure and function.

• The PRD Lesson: At the landscape scale, the spatial configuration of ecological components is paramount. The PRD demonstrates that urbanization creates a spatial mismatch between ecological networks and ecological risk, leading to a concentric segregation where high-ER clusters dominate the urban core (within 50 km) and EN hotspots are pushed to the urban periphery (100-150 km) [11]. Effective governance must therefore involve adaptive, multi-scale EN planning that proactively addresses these spatiotemporal dynamics.

• The Na Redona Lesson: At the species-interaction scale, multifunctionality is the key to understanding ecosystem complexity. The nested structure of the species-function network reveals that biodiversity is not just about the number of species, but about how they are interlinked through multiple ecological roles [27] [28]. Conservation efforts must prioritize multifunctional "keystone" species and the critical functions that bind the community.

In conclusion, a holistic definition of ecological network research must integrate both the spatial-explicit, landscape approach exemplified by the PRD and the multilayer, species-interaction approach pioneered on Na Redona. The former provides the macro-scale physical blueprint for connectivity, while the latter reveals the micro-scale functional interactions that animate the system. Future research and conservation policy must leverage frameworks from both perspectives to build ecosystems that are resilient in both structure and function.

Conclusion

Defining ecological network structure and function provides a powerful, unifying framework for understanding complexity across biological scales, from landscapes to molecular systems. The cross-disciplinary application of these principles, particularly the analysis of nestedness, robustness, and keystone elements, offers transformative potential for biomedical research. It enables a systems-level view of human disease, revealing how cellular interaction networks influence therapeutic outcomes. Future efforts should focus on refining multilayer network models to better capture the dynamism of biological systems, integrating real-time data for predictive analytics in drug development. This approach promises to move beyond single-target strategies towards network pharmacology, ultimately enhancing the resilience and efficacy of therapeutic interventions.

References

• 1. Linking experimental results, biological networks and ... [https://pubmed.ncbi.nlm.nih.gov/15972003/]
• 2. Network-based approaches for analysis of complex ... [https://www.sciencedirect.com/science/article/abs/pii/S095816691630115X]
• 3. Structural, functional, and resilience dynamics of ecological ... [https://pubmed.ncbi.nlm.nih.gov/40850253/]
• 4. What Is Network Visualization? A Guide to Seeing Your ... [https://resources.l-p.com/knowledge-center/what-is-network-visualization-understanding-data-connections]
• 5. Complexity and stability of ecological networks: a review ... [https://link.springer.com/article/10.1007/s10144-018-0628-3]
• 6. Uncovering the Structures In Ecological Networks [https://scholarcommons.sc.edu/etd/2567/]
• 7. Constructing an effective ecological network structure to ... [https://open.library.ubc.ca/soa/cIRcle/collections/ubctheses/24/items/1.0438568]
• 8. Rethinking the importance of the structure of ecological ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC6065350/]
• 9. 5 pitfalls to avoid when working with color in data ... [https://flourish.studio/blog/color-in-data-visualization/]
• 10. Principles of Ecology Revisited: Integrating Information and ... [https://www.frontiersin.org/journals/ecology-and-evolution/articles/10.3389/fevo.2019.00219/full]
• 11. Effectiveness analysis of ecological networks in ... [https://www.nature.com/articles/s41598-025-18588-5]
• 12. Integrating the functions and structures to assess ... [https://link.springer.com/article/10.1007/s10980-024-01799-y]
• 13. Types & Examples of Quantitative Data [https://www.fullstory.com/blog/quantitative-data-examples-types/]
• 14. Ten simple rules to create biological network figures for ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC6762067/]
• 15. Structure Data for Analysis [https://help.tableau.com/current/pro/desktop/en-us/data_structure_for_analysis.htm]
• 16. BEFANA: A tool for biodiversity-ecosystem functioning ... [https://www.eudaphobase.eu/news/befana-a-tool-for-biodiversity-ecosystem-functioning-assessment-by-network-analysis/]
• 17. 12. Styles — Cytoscape User Manual 3.10.4 documentation [https://manual.cytoscape.org/en/stable/Styles.html]
• 18. Tutorial — NetworkX 3.5 documentation [https://networkx.org/documentation/stable/tutorial.html]
• 19. Labels And Colors — NetworkX 3.5 documentation [https://networkx.org/documentation/stable/auto_examples/drawing/plot_labels_and_colors.html]
• 20. Node Colormap — NetworkX 3.5 documentation [https://networkx.org/documentation/stable/auto_examples/drawing/plot_node_colormap.html]
• 21. BEFANA: A tool for biodiversity-ecosystem functioning ... [https://www.sciencedirect.com/science/article/pii/S0304380022001739]
• 22. Optimization of the Ecological Network Structure Based on ... [https://www.mdpi.com/2072-4292/14/20/5245]
• 23. Advanced Visualization: Working with Palettes [https://cytoscape.org/cytoscape-tutorials/protocols/advanced-palettes/]
• 24. Color Cast [https://apps.cytoscape.org/apps/colorcast]
• 25. Identification and Analysis of Ecological Corridors in the ... [https://www.mdpi.com/2220-9964/13/9/322]
• 26. Identifying Ecological Corridors and Networks in Mountainous ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC8124316/]
• 27. On the structure of species-function participation in ... [https://www.nature.com/articles/s41467-024-53001-1]
• 28. On the structure of species-function participation in ... [https://communities.springernature.com/posts/on-the-structure-of-species-function-participation-in-multilayer-ecological-networks]
• 29. An Exploratory Application of Multilayer Networks and ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC10606656/]
• 30. Multi-layer graph attention neural networks for accurate ... [https://www.nature.com/articles/s41598-024-75742-1]
• 31. Network-based multi-omics integrative analysis methods in ... [https://biodatamining.biomedcentral.com/articles/10.1186/s13040-025-00442-z]
• 32. Application of Multilayer Network Models in Bioinformatics [https://www.frontiersin.org/journals/genetics/articles/10.3389/fgene.2021.664860/full]
• 33. Ecological network analysis reveals cancer-dependent ... [https://www.nature.com/articles/s41467-023-41906-2]
• 34. Chaperone (protein) [https://en.wikipedia.org/wiki/Chaperone_(protein)]
• 35. Chaperone - an overview | ScienceDirect Topics [https://www.sciencedirect.com/topics/pharmacology-toxicology-and-pharmaceutical-science/chaperone]
• 36. Epichaperomes: redefining chaperone biology and ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC11933791/]
• 37. Differential Network Analysis in Human Cancer Research [https://pmc.ncbi.nlm.nih.gov/articles/PMC4868626/]
• 38. A multiscale functional map of somatic mutations in cancer ... [https://www.nature.com/articles/s41467-024-54176-3]
• 39. Pathway and Network Analysis of Cancer Genomes - PMC [https://pmc.ncbi.nlm.nih.gov/articles/PMC4717906/]
• 40. The structure and robustness of ecological networks with two ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC10830016/]
• 41. Ecological network identification and connectivity ... [https://www.sciencedirect.com/science/article/abs/pii/S0304380023001151]
• 42. Network-based restoration strategies maximize ecosystem ... [https://www.nature.com/articles/s42003-023-05622-3]
• 43. Environmental change makes robust ecological networks ... [https://www.nature.com/articles/ncomms12462]
• 44. Research on the evolution and optimization of ecological ... [https://www.sciencedirect.com/science/article/pii/S266597272500251X]
• 45. igraph – Network analysis software [https://igraph.org/]
• 46. Networks in R and Python - Network Analysis [https://infoguides.gmu.edu/networkanalysis/rpython]
• 47. Pioneering a sustainable future for hyper-arid regions [https://www.adlittle.com/en/insights/viewpoints/pioneering-sustainable-future-hyper-arid-regions]
• 48. Structural, functional, and resilience dynamics of ecological ... [https://www.sciencedirect.com/science/article/pii/S0301479725029664]
• 49. Climate change is predicted to reduce global belowground ... [https://www.nature.com/articles/s41467-025-64453-4]
• 50. Urban Green Infrastructure and Urban Landscape Ecology [https://www.mdpi.com/1999-4907/16/11/1627]
• 51. A Macroecological Perspective to Ecological Networks [https://www.erikkusch.com/project/phd-packages/]
• 52. Investigating the use of network analysis metrics to ... [https://www.sciencedirect.com/science/article/abs/pii/S0959652624025277]
• 53. Fundamental Interaction Niches: Towards a Functional ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC12123259/]
• 54. A roadmap towards predicting species interaction networks ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC8450634/]
• 55. Guide to Data Visualization: Networks - Research Guides [https://libguides.utk.edu/data_viz/networks]
• 56. Emerging landscape of molecular interaction networks [https://pmc.ncbi.nlm.nih.gov/articles/PMC9018971/]
• 57. 6.5 Network and graph visualizations [https://fiveable.me/reproducible-and-collaborative-statistical-data-science/unit-6/network-graph-visualizations/study-guide/l7ZZ7oTCKSJp7IEp]
• 58. Cross-tissue multicellular coordination and its rewiring in ... [https://www.nature.com/articles/s41586-025-09053-4]
• 59. Construction of a cross-species cell landscape at single- ... [https://pmc.ncbi.nlm.nih.gov/articles/PMC9881150/]
• 60. Color contrast - Accessibility - MDN Web Docs - Mozilla [https://developer.mozilla.org/en-US/docs/Web/Accessibility/Guides/Understanding_WCAG/Perceivable/Color_contrast]
• 61. Elements must meet minimum color contrast ratio thresholds [https://dequeuniversity.com/rules/axe/4.8/color-contrast]
• 62. Understanding Success Criterion 1.4.3: Contrast (Minimum) [https://www.w3.org/WAI/WCAG21/Understanding/contrast-minimum.html]
• 63. Strengthening Ecosystem Sustainability and Climate ... [https://www.mdpi.com/2673-4834/6/3/111]
• 64. Analysis on Ecological Network Pattern Changes in the ... [https://www.mdpi.com/2072-4292/16/20/3800]
• 65. A framework for the construction of effective landscape ... [https://www.sciencedirect.com/science/article/abs/pii/S0301479725004852]