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Ecological network

An ecological network is a graphical model representing the biotic interactions within an ecosystem, where nodes typically denote species, populations, or habitat patches, and links depict pairwise ecological relationships such as predation, mutualism, competition, or dispersal.^[1] These networks capture the structural and functional organization of communities, enabling analysis of how interconnected elements contribute to ecosystem dynamics across scales from local food webs to landscape-level connectivity.^[2] Originating from early concepts of food chains in the mid-20th century, the study of ecological networks has expanded since the 1990s to encompass diverse interaction types beyond trophic links, driven by advances in network theory and empirical data collection.^[1] Key properties of ecological networks include connectance, which measures the proportion of realized interactions relative to possible ones, and modularity, reflecting compartmentalized subgroups that enhance resilience.^[2] Networks can be directed (e.g., indicating predator-prey flow) or undirected, weighted by interaction strength, and bipartite (e.g., plant-pollinator systems separating two distinct node types).^[2] At the node level, metrics like degree (number of connections) and centrality identify keystone species whose removal could destabilize the system, while network-level analyses reveal patterns in biodiversity and stability.^[2] These structures are not static; in dynamic landscapes, they evolve through processes like species dispersal and environmental perturbations, influencing persistence and adaptation.^[3] Ecological networks serve as powerful tools for understanding ecosystem functioning, with applications in assessing stability against disturbances—such as how nested architectures buffer against extinctions—and predicting responses to global change like climate shifts or habitat fragmentation.^[4] In conservation, they inform strategies for enhancing connectivity, aligning with frameworks like the Kunming-Montreal Global Biodiversity Framework's targets for well-connected protected areas by 2030.^[4] Research highlights their role in modeling multilayer dynamics, where social, spatial, and trophic layers interact nonlinearly to shape community resilience, underscoring the need for integrated empirical studies to address metric proliferation and reproducibility challenges.^[2]

Definition and Fundamentals

Definition

An ecological network is a graph-based representation of interactions within an ecosystem, where nodes denote species, populations, or other biological entities, and edges signify biotic interactions such as predation, mutualism, competition, or parasitism.^[5] These models abstract complex community dynamics into structured frameworks, enabling the analysis of how species influence one another to maintain ecosystem function and biodiversity.^[6] Unlike networks focused on abiotic processes, such as nutrient cycling or energy flows through non-living components like soil and water, ecological networks emphasize relationships among living organisms, though abiotic factors can modulate these interactions indirectly.^[7]^[8] The foundational concepts draw from graph theory, where nodes (vertices) represent discrete units like species, and edges (links) capture pairwise relationships; edges may be undirected for symmetric interactions (e.g., mutualism benefiting both parties equally) or directed for asymmetric ones (e.g., predation with a clear consumer-resource flow).^[6] This bipartite or multipartite structure allows for the depiction of specialized roles, such as pollinators and plants in mutualistic webs. Historical origins trace to food web studies in the 1960s, with seminal contributions like Robert May's 1972 analysis sparking the complexity-stability debate by modeling random interaction matrices to explore ecosystem resilience.^[9] For instance, connectance—a basic measure of interaction density—emerged as a key property in these early frameworks.^[5]

Types of Interactions

Ecological networks are characterized by diverse biotic interactions that shape their architecture and functional dynamics. These interactions can be broadly categorized into trophic, mutualistic, competitive, and antagonistic types, each influencing the directionality, connectivity, and overall topology of the network.^[10] Trophic interactions primarily involve predation and herbivory, where one species consumes another, forming directed links from consumer to resource. These are commonly represented in food webs, which organize species into discrete trophic levels based on energy flow, such as producers at the base and top predators at the apex. This hierarchical structure promotes asymmetry in connectance, with basal species often linking to multiple consumers, thereby enhancing the network's directional flow and compartmentalization.^[10] Mutualistic interactions, such as pollination and seed dispersal, benefit both participating species and are typically modeled as undirected links. In pollination networks, for instance, plants provide nectar to pollinators like bees in exchange for pollen transfer, resulting in bipartite structures with high nestedness where generalist species connect to specialists, fostering robustness through redundant pathways. Symbiotic mutualisms, like mycorrhizal fungi aiding plant nutrient uptake, similarly create dense, reciprocal connections that increase overall network cohesion.^[11]^[12] Competitive interactions occur when species vie for shared resources, such as light or space, often leading to indirect negative effects within networks, while antagonistic interactions like parasitism impose direct harm on hosts without reciprocity. Host-parasite networks exemplify antagonism, featuring directed links from parasite to host, with parasites exhibiting broad host ranges that create modular clusters and lower overall connectance compared to mutualistic systems. These networks highlight exploitation-driven topologies, where specialist parasites target few hosts, contrasting with the generalized patterns in mutualisms.^[10] Interactions in ecological networks are frequently weighted by their strength, such as interaction frequency or biomass flow, which refines the representation of link importance beyond mere presence. For example, in food webs, weights based on consumption rates reveal scale-dependent effects that alter perceived centrality. Additionally, interactions can be signed to denote positive (mutualistic) or negative (antagonistic) outcomes, enabling analysis of balanced versus imbalanced configurations that influence network stability.^[13]^[10] Hybrid networks, or multiplex structures, integrate multiple interaction types within the same species set, such as combining pollination mutualisms with herbivory in plant-animal systems. This layering captures realistic complexity, where overlapping links can buffer perturbations, as seen in networks where mutualistic layers enhance persistence amid antagonistic ones. Such multiplex approaches underscore how combined interactions yield emergent structural properties distinct from single-type networks.^[14]^[15]

Structural Properties

Connectivity Measures

Connectivity measures quantify the extent and pattern of linkages among species in ecological networks, providing insights into overall network density and species interconnectivity. These metrics are fundamental for understanding network structure and are derived from graph theory applied to empirical data such as food webs and mutualistic interactions.^[16] Connectance represents the proportion of realized interactions relative to all possible ones, serving as a basic indicator of network sparsity or density. For undirected networks, it is calculated as C = \frac{L}{N(N-1)/2}, where L is the number of links and N is the number of nodes (species). In directed networks, such as food webs, the formula adjusts to C = \frac{L}{N(N-1)} to account for asymmetric interactions, though approximations like C = L / N^2 are common for large N. Empirical studies of natural networks, including 16 diverse food webs, report connectance values ranging from 0.026 to 0.315, with an average of 0.11; most fall between 0.05 and 0.3, reflecting sparse but functionally significant linkages.^[16]^[17] Degree distribution describes the frequency of nodes with varying numbers of connections, distinguishing in-degree (incoming links, e.g., number of prey or resources for a species) from out-degree (outgoing links, e.g., number of predators or consumers). In ecological networks, these distributions often follow non-random patterns, such as exponential or power-law tails, rather than uniform or Poisson forms expected in random graphs. For instance, analyses of marine food webs reveal exponential distributions in many cases, like Potter Cove, while polar and upwelling regions (e.g., Southern Ocean, Humboldt Current) show closer fits to power-law (scale-free) patterns due to hub species such as Antarctic krill, with fewer than 5% exhibiting strong scale-free properties overall. These patterns highlight heterogeneity, where a few species have disproportionately high degrees, influencing energy flow and resilience.^[16]^[18] The clustering coefficient measures local connectivity by assessing how often a node's neighbors are also connected, indicating the presence of tightly knit interaction groups. For a node i with degree k_i, the local clustering coefficient is CC_i = \frac{2T_i}{k_i (k_i - 1)}, where T_i is the number of triangles (closed triads) involving i; the network average is the mean over all nodes. High clustering coefficients can signal keystone species embedded in dense modules, as seen in microbial co-occurrence networks where species with elevated clustering, alongside high degree and centrality, are classified as keystones with 85% accuracy using discriminant analysis. In food webs, clustering ratios increase with network size, aiding identification of species critical for maintaining local stability.^[16]^[19]

Modularity and Nestedness

Modularity in ecological networks refers to the compartmentalization of the network into discrete modules, where species within a module interact more frequently with each other than with species in other modules, reflecting underlying organizational principles such as functional groups or geographic separation. This structure can buffer networks against perturbations by localizing interactions and limiting propagation of changes across the entire system. The seminal measure of modularity, introduced by Newman, quantifies the strength of division into communities using the formula

Q = \sum_i (e_{ii} - a_i^2),

where e_{ii} represents the fraction of all edges that lie within module i, and a_i is the fraction of edges that connect to module i; values of Q close to 1 indicate strong modularity. Detection typically involves optimization algorithms, such as simulated annealing or spectral methods, that maximize Q over possible partitions. In ecological contexts, modularity has been identified in mutualistic networks like plant-pollinator systems and antagonistic networks like host-parasite interactions, often revealing meso-scale structures critical for connectivity and resilience. Nestedness complements modularity by describing a hierarchical, asymmetric organization where the interaction partners of less connected (specialist) species form subsets of those of more connected (generalist) species, promoting robustness through redundancy among generalists. This pattern is particularly pronounced in bipartite mutualistic networks, such as seed-dispersal or pollination webs, where it facilitates coexistence by allowing specialists to rely on core generalists. A consistent and widely adopted metric for nestedness is NODF (Nestedness metric based on Overlap and Decreasing Fill), which evaluates the degree of overlap in row and column interactions when the adjacency matrix is sorted by decreasing connectivity, yielding scores from 0 (random) to 100 (perfectly nested). Almeida-Neto et al. developed NODF to address inconsistencies in earlier metrics, ensuring it aligns with the conceptual definition while being robust to network size and sampling biases. Network motifs, as recurrent subgraphs of three to five nodes, provide insights into the functional building blocks of ecological networks, appearing more frequently than in randomized equivalents and often conferring adaptive advantages. In trophic networks, motifs like three-species food chains (e.g., predator-prey-herbivore) facilitate energy transfer efficiency, while in mutualistic networks, feed-forward loops—where a generalist interacts with two specialists that also connect—enhance response speed to environmental changes, such as pollinator shifts in flowering phenology. Identification relies on enumeration algorithms that compare observed motif frequencies to null models preserving degree distributions, revealing overrepresentation; for instance, motifs combining competition and facilitation in plant communities predict coexistence patterns and biodiversity maintenance under stress. In-block nestedness integrates modularity and nestedness into a compound metric, characterizing networks where modular compartments exhibit internal nested hierarchies, thus capturing more nuanced topologies in bipartite systems like mutualisms. This structure allows for both compartmental isolation and within-module specialization, potentially optimizing stability. Flores et al. introduced methods to detect in-block nestedness by maximizing a score that rewards nested ordering within detected modules, benchmarking it against synthetic and real networks. Empirical evidence from ant-plant mutualistic networks, such as those in tropical forests, shows prevalent in-block nestedness, where modular divisions limit interaction spillover; furthermore, higher modularity in these networks reduces invasion risk by confining potential invasive species to specific compartments, preventing widespread disruption.

Dynamic Properties

Stability Analysis

The complexity-stability debate in ecological networks centers on whether increased structural complexity, such as higher species richness and connectance, promotes or undermines ecosystem persistence. In a seminal analysis, Robert May modeled ecological communities using random matrices to approximate the Jacobian of linearized Lotka-Volterra dynamics, revealing that high connectance typically leads to instability. Specifically, for a community matrix with zero mean interactions of variance \sigma^2 and connectance C (the fraction of realized interactions among possible ones) in a system of S species, asymptotic stability requires S C \sigma^2 < 1; beyond this threshold, the largest eigenvalue's real part becomes positive, indicating potential oscillatory divergence.^[20] This counterintuitive result challenged earlier intuitions that complexity fosters resilience, sparking decades of research into structural motifs that reconcile complexity with stability.^[21] Trophic coherence emerges as a key structural feature mitigating instability by organizing species into ordered trophic levels, reducing feedback loops that amplify perturbations. Trophic coherence is measured by T_c = 1/q, where q is the standard deviation of the trophic distances (absolute differences in trophic levels between predator and prey) across all links; higher T_c (lower q) reflects greater coherence and correlates with enhanced linear stability through minimized cycle lengths. Empirical analysis of 46 diverse food webs demonstrates that networks with elevated trophic coherence exhibit more negative leading eigenvalues in their community matrices, with trophic coherence and cannibalism together explaining over 80% of variation in stability across systems.^[22] This coherence promotes stability by aligning interactions hierarchically, akin to layered processing that dampens propagation of disturbances. Compartmentalization divides networks into weakly connected modules, limiting perturbation spread across subsystems; simulations of compartmentalized food webs show 5-15% higher persistence under species removal scenarios than fully connected equivalents, as disturbances remain contained within modules.^[23] Nestedness, where interaction matrices exhibit a core-periphery structure with specialists connected to subsets of generalists, enhances overall persistence by streamlining energy flow but heightens vulnerability to the loss of generalist species. In nested architectures, the removal of generalists—hubs linking multiple specialists—triggers cascading extinctions more severely than random losses. Meta-analyses confirm this duality: nestedness boosts baseline stability against random perturbations via efficient resource overlap, yet amplifies fragility to hub-specific threats like habitat loss affecting generalists. Optimization strategies to enhance stability, such as rewiring for reduced nestedness, are explored elsewhere.

Optimization Strategies

Rewiring algorithms in ecological networks involve adaptive reorganization of interactions to enhance stability, particularly by optimizing link placement to minimize the dominant eigenvalue of the system's Jacobian matrix, which serves as a key metric for local asymptotic stability. In simulations of three-guild networks (pollinators, plants, herbivores), adaptive rewiring increased resilience by balancing mutualistic and antagonistic interactions, with stability measured as the negative real part of the largest eigenvalue (- \operatorname{Re}(\lambda_{\max})), showing optimal performance at moderate competition strengths (\Omega_c = 0.05) where resilience values exceeded those of static networks by up to 20%. These algorithms prioritize rewiring toward more efficient connections, such as generalist-specialist pairings, to reduce perturbation propagation while maintaining biomass productivity across guilds.^[24] Trade-offs in ecological networks often arise between connectance levels, where higher connectance boosts short-term resilience to disturbances by increasing resource redundancy but can reduce long-term efficiency through over-specialization or invasion vulnerability. For instance, in model food webs, connectance above 0.2 enhances resistance to random invasions yet heightens brittleness under targeted attacks on high-degree nodes, illustrating a stability-efficiency dilemma. Persistence under extinctions can be quantified differently for random versus targeted scenarios; for random extinctions, community persistence P_M decays gradually as P_M = \langle P(M_i = M_j, t \mid M_i = M_j, t_0) \rangle, maintaining viability until ~60% species loss in bipartite networks, whereas targeted removal of generalists causes abrupt collapse at ~35% loss due to cascading co-extinctions. These dynamics highlight the need to balance connectance (e.g., 0.15–0.25) for resilience without sacrificing energetic efficiency in resource flows.^[25] Keystone species management in ecological networks relies on centrality measures to identify and protect hubs that disproportionately influence stability, with betweenness centrality quantifying a species' role as a bridge between network modules. Species with high betweenness (e.g., values >0.1 in normalized scales) act as critical connectors, and their targeted protection via conservation corridors can prevent fragmentation, as seen in plant-pollinator systems where removing such hubs reduces overall controllability by 15–20%. This approach prioritizes generalist species, whose centrality correlates with structural controllability (\phi \approx 1), enabling proactive interventions to sustain network persistence amid perturbations.^[26] Recent post-2020 simulations of climate-impacted urban green networks demonstrate that optimal modularity thresholds around 0.4–0.5 enhance disturbance resistance by compartmentalizing effects, with networks in Beijing-Tianjin-Hebei showing 25% improved robustness to node removal after optimization, buffering against climate-driven habitat loss.^[27] As of 2025, emerging studies integrate machine learning to predict dynamic network responses to ongoing climate perturbations, further refining optimization for resilience.^[28]

Modeling Approaches

Graph-Theoretic Frameworks

Ecological networks are commonly represented using graph theory, where species or populations serve as nodes and interactions such as predation or mutualism as edges. The adjacency matrix A provides a fundamental representation, defined as an n \times n matrix where n is the number of nodes, and the entry A_{ij} = 1 if an interaction exists from node i to node j, and 0 otherwise.^[29]^[30] In undirected graphs, typical for symmetric interactions like mutualism, the matrix is symmetric (A_{ij} = A_{ji}), whereas directed graphs, common in trophic networks like food webs, allow asymmetric interactions to reflect energy flow or dependency direction.^[31]^[32] Centrality metrics quantify the importance of nodes within these networks, aiding in the identification of influential species such as keystone predators or pollinators. Degree centrality measures the number of direct connections to a node, indicating local influence; for instance, high-degree nodes in food webs often represent generalist consumers.^[33] Closeness centrality assesses how close a node is to all others, calculated as the inverse of the sum of shortest path lengths, highlighting efficient information or energy propagators in mutualistic networks.^[34] Eigenvector centrality extends this by weighting connections to highly connected nodes, revealing nodes embedded in dense substructures, as seen in eigenvector analyses of green space ecological networks where central hubs facilitate biodiversity flow.^[33]^[34] Null models enable statistical assessment of whether observed network patterns deviate from randomness, preserving key constraints like degree distributions to test for non-random structure. Randomization tests reshuffle interactions while maintaining marginal totals, such as row and column sums in bipartite networks, to generate ensembles for comparison.^[35] The configuration model, a prominent null approach, rewires edges to match the observed degree sequence, with the expected number of edges between nodes i and j given by:

p_{ij} = \frac{k_i k_j}{2m}

where k_i and k_j are the degrees of nodes i and j, and m is the total number of edges; this probability helps evaluate if empirical connectance exceeds random expectations in ecological datasets.^[36]^[37] Implementation of these frameworks relies on software libraries tailored for graph analysis. NetworkX, a Python package, supports adjacency matrix construction, centrality computations, and null model simulations for ecological data.^[38] Similarly, igraph provides efficient tools in R and Python for handling large-scale networks, including randomization routines applicable to food web adjacency matrices.^[39] These tools facilitated a historical shift in the 1990s from qualitative descriptions of food webs—often limited to presence-absence links—to quantitative graph-based analyses incorporating weighted interactions and statistical rigor.^[1]^[40] Such frameworks underpin conservation efforts by pinpointing critical nodes for protection.^[41]

Advanced Dynamic Models

Advanced dynamic models extend traditional ecological network frameworks by incorporating temporal variability and multiple interaction layers, enabling a more realistic representation of dynamic ecological processes such as seasonal shifts, disturbances, and multifaceted species interactions. These models build on static baselines by allowing edges to vary over time or across interaction types, facilitating analyses of resilience, propagation of effects, and evolutionary dynamics in complex systems.^[42] Temporal networks capture changes in ecological interactions over time, where edges representing connections like predation or pollination fluctuate due to seasonal variations or disturbances such as fires or climate events. For instance, in plant-pollinator systems, network structure shifts markedly between seasons, with turnover in species participation and interaction strengths altering connectivity patterns. Key metrics in these models include temporal motifs, which identify recurring short sequences of interactions within a time window, revealing patterns like sequential foraging behaviors in animal movement networks. Path diversity, another critical measure, quantifies the variety of temporal paths between nodes, assessing how multiple routes for energy or information flow evolve over time and contribute to system robustness against disruptions. These approaches have been applied to long-term datasets, such as a 12-year study of a butterfly-plant visitation network, demonstrating significant temporal restructuring—including species turnover and link rewiring—that influences overall network stability.^[43]^[44]^[45]^[46] Multiplex networks address multi-faceted interactions by structuring ecological systems as layered graphs, where each layer represents a distinct interaction type, such as trophic (predator-prey) or mutualistic (pollination) relationships, with shared nodes across layers. Interlayer connectivity analysis examines how species or resources link these layers, for example, through overlapping roles in food webs and symbiosis networks, revealing emergent properties like enhanced modularity or vulnerability to cascading failures. In a study of 104 species across trophic and non-trophic layers, multiplex structures uncovered non-random edge distributions that static models overlook, improving predictions of community dynamics. Tools like multilayer modularity (e.g., Q_B ≈ 0.77 in host-parasite systems) quantify interlayer dependencies, aiding assessments of how perturbations in one layer propagate.^[47]^[48] Integration with stochastic processes further advances these models by embedding population dynamics directly onto network topologies, such as through generalized Lotka-Volterra equations adapted for graph structures. In this framework, species abundances evolve via \dot{x}_i = x_i (r_i + \sum_j A_{ij} x_j), where A_{ij} reflects network interactions, and stochastic noise from environmental variability or demographic fluctuations is incorporated via random matrix theory or stochastic differential equations. This allows simulation of coexistence thresholds, where noise levels (\sigma > \sqrt{N}) determine persistence in large networks (N species), as seen in analyses of random interaction matrices that predict stability boundaries. Such models have illuminated how network motifs influence invasion resistance in mutualistic communities.^[49]^[50] Recent advances from 2020 to 2025 leverage artificial intelligence and machine learning, particularly graph neural networks (GNNs), to infer hidden links in sparse ecological data. GNNs process bipartite structures like plant-pollinator networks, using node features (e.g., species traits) and edge probabilities to predict unobserved interactions, achieving high accuracy (AUROC 85.4%) even with imperfect detection in datasets covering hundreds of species. This inductive approach uncovers missing trophic links, enhancing model completeness for dynamic predictions in under-sampled systems.^[51]^[52]

Applications

Conservation and Restoration

Network-based reserve design leverages graph-theoretic properties of ecological networks to select protected areas that preserve connectivity and structural integrity. By prioritizing sites within modular or nested network configurations, conservation efforts can maintain functional links between habitats, reducing fragmentation and enhancing resilience to disturbances. For instance, in metapopulation models, reserves are chosen to protect high-connectivity nodes, ensuring gene flow and species dispersal across landscapes. This approach, applied to fragmented ecosystems, has shown that safeguarding modular compartments limits the spread of local collapses to the broader network.^[53] Simulations of species loss in ecological networks reveal the potential for cascading extinctions, where primary removals trigger secondary losses through disrupted interactions. In food web and mutualistic models, secondary extinctions occur when a species' in-degree falls to zero, meaning it loses all resource or partner connections. The extent of these cascades depends on targeting strategy; removing high-degree species (e.g., generalists) amplifies secondary extinctions compared to random removal, as measured by network robustness R = \frac{\sum y(x)}{\max(x)}, where x is the proportion of primary extinctions and y(x) is the proportion of surviving species. Such simulations underscore the vulnerability of low-connectivity networks to even modest species losses.^[54] Restoration techniques in ecological networks emphasize reintroducing keystone species to rebuild structural properties like nestedness, which organizes interactions hierarchically to promote stability. Keystone species, identified by high centrality metrics such as degree or betweenness, disproportionately influence network topology; their reintroduction enhances overall connectivity and persistence, with betweenness-guided strategies being optimal in over 90% of simulations for maximizing persistence in plant-pollinator networks. Prioritizing reintroductions based on total connections (degree) maximizes biodiversity rebound, particularly in nested structures where generalist species facilitate specialist integration. This strategy outperforms random reintroductions by restoring asymmetric dependencies critical for community assembly.^[55]^[26] Case studies from coral reef networks post-2010 bleaching events demonstrate how network metrics predict recovery trajectories. In the Great Barrier Reef, connectivity strength and destination metrics (incoming larval links) identify source reefs for restoration, with high-connectivity sites supplying larvae to damaged areas and accelerating cover rebound after events like the 2016-2017 bleaching. Simulations integrating these metrics with climate projections under RCP 4.5 and 8.5 scenarios forecast persistent declines without intervention. However, the 2023-2025 global mass bleaching event, which impacted over 84% of the world's coral reefs, led to the largest recorded annual decline in Great Barrier Reef coral cover as of August 2025. In the Coral Triangle, network analyses project relatively higher cover retention compared to other regions, though the same 2023-2025 bleaching intensified risks and underscored the need for targeted larval enhancement.^[56]^[57]^[58]^[59]

Broader Ecological and Human Contexts

Ecological networks provide a framework for understanding disease transmission in natural systems, where species interactions serve as pathways for pathogen spread analogous to contact networks in human epidemiology. The susceptible-infected-recovered (SIR) model, originally developed for human populations, has been adapted to ecological graphs to simulate how diseases propagate through food webs or host-parasite interactions, revealing that network topology—such as degree distribution—influences outbreak thresholds and persistence.^[60] For instance, in plant-pathogen networks, modular structures can contain epidemics by limiting spread across compartments, while heterogeneous networks accelerate transmission due to superspreader nodes.^[61] Anthropogenic disruptions significantly alter the structure and function of ecological networks, with habitat fragmentation reducing overall connectance by isolating patches and diminishing inter-species interactions. This fragmentation, driven by land-use changes like urbanization and agriculture, decreases network density and increases edge effects, leading to biodiversity loss and impaired ecosystem services such as pollination.^[62] Pollution further modifies interaction strengths within these networks; for example, chemical contaminants weaken mutualistic links in aquatic food webs by affecting foraging behavior and survival rates, thereby shifting network stability toward collapse.^[63] In lake ecosystems, combined pollution and overexploitation have been shown to reorganize trophic interactions, reducing resilience to perturbations.^[63] In coevolutionary and spatial ecology, metapopulation networks model how subpopulations connected by dispersal corridors maintain species viability amid environmental variability, with network connectivity determining recolonization rates post-extinction events. These frameworks highlight how spatial structure influences evolutionary dynamics, such as adaptation to heterogeneous habitats.^[64] For invasive species, metapopulation dynamics drive rapid spread across fragmented landscapes; lionfish invasions in coral reefs exemplify how high dispersal along network edges amplifies establishment and outcompetes natives, underscoring the need for targeted control at source populations.^[65] Recent models integrating stochastic spread in one-dimensional metapopulations demonstrate that optimal management minimizes costs by prioritizing high-connectance links.^[66] Studies from the 2020s on urban ecosystems have utilized multiplex networks—layered graphs capturing multiple interaction types—to uncover patterns in human-wildlife conflicts, revealing how overlapping social and ecological layers exacerbate encounters like coyote incursions in residential areas. These analyses show that multiplex structures highlight conflict hotspots where human infrastructure intersects wildlife corridors, informing mitigation strategies.^[67] Regarding climate change, recent projections address modeling gaps in ecological networks by incorporating dynamic interaction shifts, such as altered trophic links under warming scenarios; for instance, simulations predict that increased temperatures will weaken mutualisms in lake networks, amplifying vulnerability unless adaptive dispersal is enhanced.^[63] Such advancements bridge earlier limitations in static models, projecting up to 20-30% declines in network robustness by mid-century without intervention.^[63]

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igraph – Network analysis software
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Another way to represent an ecological network is the adjacency matrix, that is a square matrix whose rows and columns run over all the species name in the ...<|control11|><|separator|>
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Applying network theory to animal movements to identify properties ...
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Network ecology in dynamic landscapes - Journals
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Temporal variation in plant–pollinator networks from seasonal ...
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Analysis of temporal patterns in animal movement networks
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Strong, Long-Term Temporal Dynamics of an Ecological Network
Nature is organized into complex, dynamical networks of species and their interactions, which may influence diversity and stability.Missing: seasonal motifs<|separator|>
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[PDF] Ecological Multilayer Networks - UCLA Department of Mathematics
Nov 13, 2015 · Networks provide a powerful approach to address myriad phenomena across ecology. Ecological systems are inherently 'multilayered'.
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a guided tour with large Lotka–Volterra models and random matrices
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Motif profile dynamics and transient species in a Boolean model of ...
Mar 26, 2015 · ... temporal motifs capture the nature of species–species interactions ... Mutualistic ecological networks provide a rich context in which ...
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Imperfect Detection in Heterogeneous Complex Ecological Network
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[PDF] Graph neural networks for modeling ecological networks and food ...
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Science | AAAS
**Summary:**
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An ecological network approach to predict ecosystem service ...
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Network-based restoration strategies maximize ecosystem recovery
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The spectral underpinnings of pathogen spread on animal networks
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Disruption of ecological networks in lakes by climate change and ...
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Invasive species control in a one-dimensional metapopulation network
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A single changing hypernetwork to represent (social-)ecological ...
Oct 24, 2024 · We illustrate in a simple example that any ecosystem can be represented by a single hypergraph, here called the ecosystem hypernetwork.Missing: seminal | Show results with:seminal