Theoretical Ecology

Humans are just another species on Earth, but modern telecoupled societies and their socioeconomies impose immense consumption demands on the biosphere, detaching from common ecological rules. Starting from a simple ecological consumer-resource model, with humans as the consumers and terrestrial organic carbon (i.e., the biosphere) as the resource, we assume that technology modulates both human carrying capacity,{nu} 0, and the rate of biosphere consumption, 0. Three different functional-relation scenarios were tested, modulated by parameter a. In all three scenarios, equilibria and stability directly depended on the relative role that technology played in the model parameters, or the compound technological impact ({epsilon} {equiv} 0{nu}0). Moreover, two of the three scenarios showed Hopf bifurcations and regions with no equilibrium. The models were parameterized and fitted to actual data using a trajectory of more than 150 years. These analyses suggest that we are currently in a stable oscillatory spiral with no immediate Hopf bifurcation threat, but within a trajectory that continuously depletes the biosphere and approaches a collapse in human population size if no changes are made in the relationship that technology has with growth (i.e.,{nu} 0) versus consumption (i.e., 0) dynamics. Because our predatory dynamics also appear to have shifted from regular predator- prey dynamics toward a supply-demand scenario, with persistently increasing values, the threat of a Hopf bifurcation is now present in our trajectory: changes in the stability of the coexistence equilibrium may arise. This simple model warns that we must pay closer attention to the predatory relations that our technologies are creating with bio-sphere dynamics, in a way that goes beyond population numbers and technological development alone.

Patterns in the vegetation across arid and semiarid regions may be explained as a form of self-organization driven by water scarcity, and are often modeled through reaction-diffusion dynamics. Recent work has shown that similar mathematical models generate patterns on networks. However, these studies have focused on idealized topologies with no reference to natural pattern-forming systems. Our study aims at bridging these two fields: we employ a physical reaction-diffusion vegetation model, and gradually modify the topology of the diffusion network by adding random shortcuts over a 2-dimensional grid, interpolating between a regular lattice and a random network. We found that network topology strongly shapes both the resulting vegetation patterns and the precipitation range that supports them. Three behavioral regimes emerge. On a regular lattice, high-regularity patterns develop reflecting local diffusion processes. On a random network, the system is dominated by global pressure towards homogenization yielding either a uniform state or a single patch. In the intermediate shortcut density range, as the network topology resembles a small world network, the interaction between the two scales of diffusion generates two kinds of disordered patterns: low-regularity patterns with a well-defined characteristic wavelength, and irregular patterns characterized by a broad patch size distribution. These disordered patterns resemble real-world observations and, in our model, they show different responses to changing precipitation. Although we focused on dryland vegetation, we suggest that network-mediated diffusion could lead to similar mechanisms in a wide variety of pattern-forming systems. HighlightsO_LIWe study vegetation pattern formation over different diffusion network topologies. C_LIO_LITwo kinds of stable disordered patterns states develop over small world topologies. C_LIO_LILow-regularity patterns with a well-defined characteristic wavelength. C_LIO_LIIrregular patterns characterized by a broad patch size distribution. C_LIO_LIThese different kinds of disordered states show different relations to precipitation. C_LI

Interaction networks, in which nodes represent species and edges represent direct interactions between species, have a long and impactful history in community ecology. However, co-occurrence networks, where edges represent statistical relationships among species presences or abundances, are often easier to construct from lab and field data. It is clear that co-occurrence edges often do not represent direct interactions, but frameworks for the interpretation of co-occurrence networks have not kept pace with their generation. It is therefore unclear when and how these networks can be used to gain insight into community dynamics. Here, we use a Generalized Lotka-Volterra-based model to explore the contexts in which emergent properties of species interaction networks are identifiable in their resulting co-occurrence networks. We find that, in spite of many differences in direct edges, key features of the true interaction network, such as unipartite modularity, high-degree nodes (hubs), and bipartite modularity and nestedness, can be preserved in co-occurrence networks. In contrast, node degree distributions are not preserved even in the most idealized scenarios. We propose that networks derived from large co-occurrence datasets could therefore be used in future empirical work to test existing hypotheses of how emergent network structures drive ecological community dynamics.

Minimum viable populations (MVPs) are population levels large enough to surmount risk from demographic, environmental, and genetic stochasticity. MVPs are estimated by biologists to guide conservation practices. However, MVPs are generally estimated for a target population without regard for how they interact with intra- and inter-species population dynamics in the broader ecological community. Thus, how and why population dynamics interact with MVPs imposed by conservation biologists remain unclear. When MVPs are imposed on a continuous population model, traditional analyses fail to capture the range of possible outcomes those MVPs create. Here, we describe viability space decomposition (VSD) as a mathematical tool to systematically analyze the potential crossing of MVPs during population dynamics. We demonstrate that different extinction and survival outcomes can be recovered from a model with imposed MVPs using three VSD concepts in junction with a traditional phase portrait: mortality manifolds which separate conditions that lead to different existential outcomes, ordering manifolds which determine the order of extinction events for multiple populations, and collapse manifolds which determine the survival or extinction of one species given the loss of another. We employ these methods with a standard consumer-resource model, and the methods can be scaled to systems with more species. VSD is a useful tool for conservation biologists and community ecologists concerned with boundary crossing problems in any dynamical system.

The phenology of organisms worldwide is shifting in response to changes in environmental conditions. There is growing concern that resulting timing mismatches among interacting species will negatively impact system-level properties, yet there is no general framework for evaluating community responses to changes in phenology. To address this gap, we developed a mathematical framework based on local stability analysis and used it to assess the resilience implications of phenological perturbations with a multi-year, highly time-resolved empirical dataset on subalpine plant-pollinator communities. The forecasted effects of phenological perturbations were largely independent of perturbations to species densities, indicating the potential for even small changes in phenology to disrupt the functioning of ecosystems that are otherwise highly stable.

Metacommunity theory explains how species distributions arise from local population dynamics and dispersal between habitat patches. Four conceptual paradigms--patch dynamics, species sorting, mass effects, and demographic stochasticity--have emerged as frameworks for understanding metacommunity structure and dynamics, but their integration remains an open problem. Here we introduce a probabilistic-stochastic-deterministic (PSD) modelling framework that unifies these paradigms within a single mathematical description. PSD approximates individual-based models (IBM) with computational efficiency comparable to ordinary differential equations (ODE) while capturing demographic stochasticity and permitting analytical treatment. Through validation against IBM simulations in single-patch communities and spatially explicit metacommunities with rock-paper-scissors dynamics, we demonstrate that PSD accurately reproduces IBM behaviour where ODE models fail, specifically when demographic stochasticity dominates during immigration. For metacommunities with long-distance dispersal, we analytically derive the period of a slow collective oscillations, revealing body-mass and dispersal-rate dependencies invisible to ODE theory. Our analysis shows that the four paradigms represent valid descriptions in different regions of parameter space, controlled by individual body-mass, immigration rate, and regional species richness. The PSD framework thus provides both a practical simulation tool and an analytical machinery for predicting metacommunity dynamics across ecological regimes.

Human activities are driving unprecedented environmental change, yet assessments of ecosystem resilience often overlook the rapid pace of change in the Anthropocene. Predator-prey systems are sensitive to the rate of environmental change and the whole system can collapse if predator population fail to promptly adjust to environmentally-driven shifts in resource population. Here, we investigate how different combinations of predator responsiveness and rates of environmental change influence the system vulnerability to critical transitions, explicitly addressing its interplay with magnitude of change. We found that, as predator responsiveness decreases, relatively slower rates and smaller magnitudes of environmental change leads to system collapse. Hence, even low and seemingly inoffensive total magnitudes of environmental change can be catastrophic if the rate of change is beyond a critical threshold. We propose considering predator responsiveness and current rates of environmental change as crucial factors in predicting the Anthropocenes impact on ecosystems.

How and why do species interactions produce unstable dynamics? In the simplest models, the answers are straightforward. In the Rosenzweig-MacArthur predator-prey model, resource self-facilitation due to predation mortality triggers oscillations; in Lotka-Volterra competition, positive feedback from stronger interspecific competition underlies alternative states. However, when unstable dynamics arise with three or more species, how and why answers become more opaque. We propose that dissection of feedback loops, chains of direct species interactions, can answer these questions in meso-scale models. To demonstrate, we disentangle instabilities in epidemics using three variations of a general yet mechanistic resource-host-parasite model. Resources introduce destabilizing self-facilitation but also positive interspecific direct effects on propagule production and transmission rate. Those direct effects then produce instabilities through feedback loops. First, we trace how resource self-facilitation catalyzes oscillations by weakening faster, shorter, lower levels of feedback relative to longer, slower feedback of the whole system. Then, we show how resource-dependent propagule yield introduces positive cascade fueling feedback, creating an Allee threshold inhibiting invasion of parasites. In a third variant, we traced how both resource-dependent components produced those unstable dynamics and more complex behaviors, including a period-doubling route to chaos to which we apply a form of loop tracing. Hence, we show how and why direct, positive effects of resources modulate feedbacks underlying oscillations, Allee effects, and more during epidemics. We propose that loop tracing, a generally applicable method, could empower ecologists to glean much deeper insight into dynamics of species interactions.

Global epistasis refers to the observation that the effect of a mutation or modification depends on the state of a biological system, not its detailed composition. Such patterns have been reported across biological scales, from proteins to organisms and ecosystems. In its simplest form, global epistasis appears as a linear relationship between the change in function or fitness due to a perturbation, and the background level of function or fitness. The mechanistic basis of global epistasis, particularly in ecological systems, remains unresolved. Here, we propose that in microbial communities, global epistasis describing the impact of adding a species to a community on function arises generically from constraints imposed by shared resource pools. We illustrate this mechanism in a single-species system growing on multiple substitutable resources, where global epistasis follows directly from nutrient limitation by an essential non-substitutable resource. We then extend this framework to multi-species communities competing for a single resource and show that the marginal effect of adding a species depends linearly on background community function, with a slope determined by the fraction of the resource claimed by the added species. We show that global epistasis persists in trophic cascades, but that facilitation and niche partitioning qualitatively break the linear dependence. This study provides a simple explanation for the appearance of global epistasis in ecosystems, and suggests that global epistasis should be a null expectation in ecosystems governed by competition. Our results propose that coupling between perturbations and shared resource pools might also help explain global epistasis at the organismal level.

1Although resources are typically distributed continuously in space, species distributions often organize into discrete clusters. In his seminal paper [36], Turing demonstrated that such clusters can spontaneously arise in population densities, even when populations evolve in environments with continuously varying conditions. This phenomenon is known as Turing instability. In this work, we focus on two models grounded in population dynamics: a one-dimensional model based on the nonlocal Fisher-KPP equation, and a two-dimensional model involving an environmental gradient. We show that phenotypic clusters (sometimes referred to as "species") emerge in these models. We prove that they do not emerge because of Turing instability, but because of stochasticity, and that they disappear when stochasticity is reduced. First, for both models, we start our simulations with initial populations uniformly distributed in the state space. We show that phenotypic clusters quickly emerge and that the distances between them depend on the population size, that is, on the degree of stochasticity. Next, we start from already clearly defined phenotypic clusters. We identify three regimes in the connection between population size, the initial distances between clusters, and the distances between clusters at equilibrium. Last, on the two-dimensional model, we relax the hypothesis of complete clonality by varying the effective recombination rate, explore its effect on phenotypic clustering, and show that phenotypic clustering decays drastically with slight recombination.

Understanding the drivers of biodiversity in the worlds rivers, which are known to be hyperdiverse relative to their coverage area, has been an enduring goal in ecology. While regression-based empirical studies have identified a suite of environmental factors that are correlated with riverine fish biodiversity, these insights are often system-specific and inconsistent across regions. In contrast, a more limited body of studies have suggested that network connectivity of rivers affects fish biodiversity by limiting dispersal, and basin shape may modulate these relationships. The few theoretical papers that have explored basin morphology effects have tended to use extreme network shapes and inconsistent methods, thus limiting general insights. Here, we build on these results to demonstrate that river basin morphology, as measured by log aspect ratio, can alter both network connectivity and biodiversity in simulated, all-else-equal scenarios. First, we quantify variation in log aspect ratio across the worlds 100 largest rivers and use this empirical range of shape variation to guide synthetic experiments. In particular, we use Optimal Channel Networks (OCNs) constrained to basins with log aspect ratios within realistic range to study how shape alters connectivity profiles when node number and basin area are held constant. By coupling OCNs with dendritic neutral models, we demonstrate that variation in aspect ratio and concomitant changes in connectivity lead to substantial changes in simulated biodiversity. Finally, we use Earth Movers Distance to establish that basin-shape-induced changes in node-level connectivity distributions are predictive of transformations in node-level distributions of and {beta} diversity. Overall, elongated basins such as the Mekong River feature lower species richness (-diversity), higher turnover ({beta}-diversity), and less variable distributions of both quantities relative to a square reference basin. Furthermore, approximately one third of the worlds largest rivers are elongated enough to potentially feature statistically-detectable, shape-mediated variation in connectivity and biodiversity.

Habitat complexity (HC) in part determines the diversity, stability, and behavior of food webs and can influence predation according to a wide variety of functional relationships. Many aquatic species provide habitat complexity and are also consumed by other species (e.g., macrophytes, corals, mussels). However, food web theory does not readily account for these species that act as edible habitat complexity (EHC). Here, we combine existing theory on predator-prey interactions, HC, and prey switching to describe the role of EHC in benthic food web models. We dissect feedback loops in each model to demonstrate how self-regulation of the prey species, mediated by species densities and HC, drives that food webs behavior. HC can stabilize predator-prey interactions by coupling prey self-regulation with HC self-regulation. EHC can further stabilize predator-prey interactions across a wide variety of "HC functions" that relate HC to predation rates. Significance StatementHabitat complexity (HC) plays a critical role in trophic interactions, population dynamics, and food web stability. However, little theory exists to describe edible habitat complexity (EHC), where a species is both consumed and confers habitat complexity for other species. We provide a series of models demonstrating how HC and EHC alter the population dynamics and stability of simple aquatic food webs. HC is strongly stabilizing in food webs by providing safety in rarity for prey. EHC provides safety in rarity for both prey and the EHC species because their predators are omnivorous. Given the prevalence of EHC species in aquatic systems (e.g., macrophytes, corals, mussels), our models demonstrate the importance of maintaining EHC species in aquatic systems for stable food webs.

Haptotaxis is an understudied form of directed cell migration in which movements are biased by gradients of immobilized ligands. For example, fibroblasts and other mesenchymal cells sense and respond to gradients of extracellular matrix (ECM) composition, which is relevant during tissue morphogenesis and repair. As a step towards understanding how haptotactic gradients spatially bias cell adhesion, intracellular signal transduction, and cytoskeletal dynamics, we formulated a phase field model of whole-cell migration, in which the occupancy of potential adhesion sites changes stochastically with time. With careful assignment of parameter values, the model predicts significant haptotactic bias for adhesion-site gradient steepness of a few percent across the cell. We then used the model to predict how the cells removal of surface-bound ECM ligand (as observed in experiment) and/or the presence of a competing, chemotactic gradient influence(s) haptotactic fidelity. An emergent principle is that gains in directional persistence naturally offset losses of directional bias, at the cost of greater cell-to-cell heterogeneity of the response. In the case of orthogonally oriented gradients, this offset manifests as a remarkable robustness of the multi-cue response.

Elucidating how habitat degradation facilitates extinction is critical for effective conservation efforts. Here, we propose integrating physiologically-structured population models into stochastic population viability analyses to assess how differing consequences of habitat degradation interact to drive extinction dynamics in a focal population. Using the isolated spectacled caiman Caiman crocodilus population/ecomorph from the Apaporis River as a case study, we find that threatening the resource base, which individuals increasingly rely upon, to outgrow vulnerable size ranges and mature accelerates extinction. We also found that when habitat degradation impacts both the primary adult and juvenile resource bases, this can have marked synergistic effects on threatening population viability. By contrast, destroying nesting sites has only a small effect on accelerating the impact of deteriorating prey availability. Through integrating community-level feedback between habitat degradation/change and population dynamics/structure, our approach provides a comparative framework for assessing the relative importance of distinct mechanisms through which habitat degradation ultimately drives extinction risk.

Mathematical modelling is essential for understanding how complex biological systems respond to genetic, physiological, and environmental changes. Existing approaches, however, often require trade-offs between mechanistic detail, model size, parameter uncertainty, and interpretability. Ordinary differential equation (ODE) models capture biochemical processes with quantitative precision but can demand extensive parameterisation. In contrast, large statistical and machine-learning models rely on substantial datasets and frequently lack mechanistic transparency. Qualitative approaches such as Boolean networks improve scalability but may oversimplify biological behaviour. To address some of these limitations, we present PSoup, an R package that automatically converts knowledge graphs into transparent, parameter-free, qualitative models. PSoup uses algebraic update rules designed around a fixed, biologically interpretable baseline, enabling predictions of relative change across diverse perturbations without requiring kinetic parameters. This design allows PSoup to integrate information across biological scales and from heterogeneous experimental sources. We evaluated PSoup using the well-studied shoot branching network of Bertheloot et al. (2019), which ncorporates hormonal (auxin, strigolactone, cytokinin) and metabolic (sucrose) regulation. Across 78 experimental conditions, PSoup correctly predicted 88.5% of perturbation outcomes, including 89.5% accuracy for unique, biologically consistent comparisons. We further demonstrate how PSoup can distinguish among alternative plausible network topologies, revealing how structural differences influence emergent system behaviour. PSoup offers an intuitive, accessible, and mathematically transparent framework for exploring biological networks. Its capacity to integrate diverse knowledge and test alternative hypotheses positions it as a powerful tool for biological discovery and a valuable complement to existing modelling approaches.

Spatial heterogeneity of abiotic resources is essential for species coexistence. Ecological theory often assumes predefined heterogeneity of resources that constrains community dynamics, but the recent developments of meta-ecosystem ecology and zoogeochemistry highlight nutrient patterns could result from the interactions between the activities and movements of organisms and their abiotic environment. Here we investigate the mechanisms by which biotic-abiotic feedbacks could generate nutrient spatial heterogeneity in a simple plant-herbivore occupancy model where populations forage, recycle, and disperse in a homogenous landscape. By systematically varying organisms ranges of foraging and dispersal, and recycling levels, we found that limited dispersal of plants plays a key role on the emergence of nutrient patchiness by favoring small clusters of vegetation that shape their environment through consumption and recycling. However, herbivores could also create nutrient spatial heterogeneity when large foraging and dispersal ranges, and high recycling, allow them to efficiently track plant hot spots and to increase population persistence. Unexpectedly, strong aggregation of herbivore populations did not necessarily result in nutrient clustering. Rather than via recycling, herbivores mainly affected nutrient distribution indirectly, through their top-down impact on plant distribution. When evenly spread in the landscape, herbivore populations with large foraging ranges created areas of strong herbivory pressure unfavorable to plant colonization where nutrient can accumulate. These results can help understand the dynamical feedback between biota and abiotic resources. In a context where human activities alter both nutrient distribution and species abundances, a better understanding of this biotic-abiotic feedback will be key to anticipate the response of ecosystems to current perturbations.

O_LIStage-dependent interactions, in which different life cycle stages (e.g., juveniles, adults) exert different per-capita competitive effects, are widespread across ecological communities. However, whether explicitly accounting for such ontogenetic variation improves forecasts of stochastic community dynamics remains unclear. We tested how the strength of stage dependence and species life-history strategy influence the predictive accuracy of community models that either include or ignore stage-specific interactions. C_LIO_LIWe constructed stochastic two-species competition models using stage-structured matrix population models spanning five virtual life histories along the fast-slow continuum. Density dependence was imposed separately on juvenile survival, adult survival, progression, retrogression, or fertility, and the strength of stage dependence varied from adult-driven to juvenile-driven competition. We then fitted deterministic projection models with and without stage-dependent interaction terms to simulated time series and quantified predictive performance over 100 time-step forecasts using mean absolute percentage error (MAPE). C_LIO_LIIncreasing stage dependence consistently reduced the predictive accuracy of models that ignored stage structure. However, absolute prediction errors remained small across all scenarios (MAPE < 0.7%), even under strong stage dependence. The influence of life-history strategy depended on which vital rate was density dependent: when juvenile survival was density dependent, faster life histories showed larger errors; when progression, retrogression, or fertility were density dependent, slower life histories exhibited greater errors; and when adult survival was density dependent, no consistent life-history effect emerged. Across simulations, temporal variation in population structure was low (coefficient of variation < 0.036), and prediction error was strongly associated with the magnitude of structural fluctuations rather than life-history pace per se. C_LIO_LISynthesis. Stage-dependent interactions can, in principle, alter stochastic competitive dynamics, but their practical importance for ecological forecasting depends on the extent to which population stage structure fluctuates through time. When environmental stochasticity dominates and stage structure remains near equilibrium, simpler models that ignore stage dependence provide robust approximations of community dynamics. Our results identify conditions under which demographic detail is necessary for forecasting and highlight the central role of structural variability in linking life-history strategy to community-level dynamics. C_LI

The Biodiversity-Ecosystem Functioning (BEF) literature has shown species diversity to be essential for ecosystem functioning and services. Yet although acquiring information through interspecific networks can impact ecosystem functioning, it is unclear how it is modulated by species diversity. Eliciting vocal responses using predator models across a latitudinal gradient, we first show that the species diversity of birds increases public information about predation both in the low-cost system of mobbing and in the higher-cost system of alarm calls. A similar result was also found across a fragment area gradient for mobbing; this system was then used to test how species diversity affects interspecific information flow in mobbing communities. We set up two BEF playback experiments, manipulating the species richness level of the playback sound files by varying the number of species producing mobbing calls (one, two, four, eight species). In an experiment in which the call rate across treatments was held constant, and only heterospecific responses were counted, increasing species richness of the sound files increased the number of species and individuals responding, the number of calls produced and their frequency range, and decreased latency to call. An experiment in which call rate increased with the addition of species in each treatment showed a similar, but stronger pattern. There was little evidence that the signals of one particular species changed responses. This supports the hypothesis that the species diversity of a community is a key component influencing the quantity and quality of information flow inside it.

Parasites play an outsized role in mediating the persistence and stability of host populations. Flour beetles (Tribolium spp.) have long served as classic examples of population dynamics under both disease-free and infected conditions, with elegant combinations of theory and experiments demonstrating, for example, that cannibalism rates can push populations from stability to chaos. As with most organisms in nature, however, flour beetles rarely face just one parasite species, and co-infecting parasites can antagonize or facilitate each other through resources and immunity. To test the prediction that non-neutral interactions would qualitatively alter population stability, we first raised flour beetles (Tribolium castaneum) in infection-free, single-infection, or coinfection microcosms and quantified relative prevalence and parasite intensity. Next, we reworked a classic stage-structured discrete-time model to include single and multiple infections and performed sensitivity and bifurcation analyses to identify the most important (co)infection-associated parameters for population stability. The model predicts that stability is highly sensitive to parasite transmission mode regardless of infection multiplicity, but facilitation among parasites rapidly drives populations into oscillations and chaos under realistic conditions. This study identifies an important mechanism for explaining population variability and highlights the importance of within-host mechanisms for driving dynamics at higher levels of biological organization.

Natural populations are often nonlinear and exhibit substantial variability. A central question is how stochasticity interacts with density-dependent regulation to shape population stability. We address this using four long-term time series of Trinidadian guppies and find that their dynamics are well described by a stochastic logistic model with multiplicative environmental noise. The model predicts that stochasticity does not merely add fluctuations around deterministic carrying capacity, but alters the equilibrium structure. Using stochastic bifurcation theory, we show that increasing noise shifts the most-probable population size below the deterministic equilibrium and can push populations closer to a noise-induced bifurcation, even when mean growth rates remain positive. The effects of stochasticity across populations align with known ecological differences among streams, particularly the effects of light level and seasonality. The analysis also identifies populations most sensitive to perturbations, which are not detected by standard early warning indicators. Temporal and spectral analyses further show that intrinsic growth rate governs local recovery, while seasonal variation interacts with density-dependence to shape longer-term population fluctuations. Together, our results show that stochasticity can alter resilience and vulnerability by reshaping ecological stability landscapes.