Theoretical Ecology

Multiple global-change forces, from habitat alterations to warming, are altering food webs and trophic interaction strengths. Such changes in trophic interactions have important implications, as it is a tenet of ecology that trophic interactions are linked to the functioning and stability of ecosystems. For example, changes in the presence or strength of intraguild predation (IGP), the consumption of a predator by another predator that competes for shared prey, can have cascading effects on the biomasses of species and trophic levels. For this reason, IGP can affect key ecosystem functions at the base of the food web and is of special interest to practitioners of biological pest control. However, the relationship between IGP and ecosystem stability is not yet well understood, especially whether and how IGP might affect the stability of non-adjacent lower trophic levels including primary producers. In this study we simulate the dynamics of a six-species, four-trophic-level food web plus a limiting nutrient to explore the relationship between IGP strength and the temporal variability of species- and trophic group-biomass. By varying the IGP rate given the abundance of the eaten predator, we find that the model food web abruptly shifts between equilibria in which all species maintain either constant biomass or stable limit cycles where all trophic levels exhibit sustained and significant oscillations. While complex feedback in the model creates a divergence between the IGP functional response and the resulting realized IGP strength, both stronger IGP functional responses and stronger realized IGP are associated with a higher likelihood of oscillations. Furthermore, analyses indicate that the strongest consumptive interaction induces the oscillating behavior in an indirect effect initiated by the change in IGP. Overall, these results suggest that as food web structure changes in ecosystems worldwide, strengthening IGP runs the risk of inducing destabilizing effects that extend to the base of food webs, while weakening IGP could confer stability to ecosystem functions such as primary production. Finally, we discuss relevance to management, including the implication that IGP among biological control agents should be minimized to maintain stable crop production.

Environmental variability can strongly alter coexistence among competing species and their extinction risk, particularly when population dynamics are shaped by behavioral interactions, such as fear. In this work, we develop a novel stochastic differential equation competition model that incorporates both non-consumptive fear effects and environmental variability to investigate how behavioral interactions influence species coexistence under random fluctuations. Our result reveals that environmental stochasticity can drive species to extinction even when the corresponding deterministic system admits coexistence. In particular, under an explicit stability condition on the fear and competition parameters and sufficiently strong averaged noise intensities, we prove that both competing species become extinct exponentially almost surely. Conversely, we derive a stochastic persistence criterion in terms of fear, competition, and noise-induced suppression parameters for the fearful species. We further demonstrate that environmental noise may reverse classical competition-exclusion outcomes, leading to qualitatively different long-term dynamics from those predicted deterministically. These results provide rigorous thresholds separating stochastic extinction from persistence and highlight the critical role of environmental variability in fear-mediated competitive ecosystems. From an applied perspective, these results provide insight into how behavioral interactions and environmental variability influence species survival, with potential applications in ecological management and conservation.

Humans are efficient and deadly predators, yet they may also interact with wildlife in non-lethal ways. This study explores how interactions with lethal and non-lethal human "superpredators" alter predator-prey dynamics using an agent-based modelling approach. Our model incorporates both the consumptive (lethal) and non-consumptive (behavioural) effects of humans, as well as of predators on prey. We explored how the replacement of apex predators by humans affects mesopredator-prey dynamics, with particular emphasis on trophic targeting and differences between lethal and non-lethal interactions. We found that human superpredators have a greater effect on model outcomes than apex predators. When superpredators consume mesopredators alone or with prey, the probability of mesopredator-prey coexistence increases to a greater extent than when apex predators consume mesopredators. In contrast, superpredators consuming only prey slightly increases overall extinction risks and reduces coexistence. Non-lethal superpredators, despite eliciting anti-predator responses in mesopredators and prey, had a negligible effect on population dynamics. Our findings demonstrate that human superpredators may functionally replace apex predators when they are lethal. However, non-lethal interactions with humans may not be as ecologically significant as lethal interactions, even when humans induce anti-predator responses.

1.Partial Rank Correlation Coefficient (PRCC), usually performed following Latin Hyper-cube Sampling (LHS), is a global sensitivity analysis that quantifies the monotonic relationship between model parameters and the desired output. To carry out this analysis, a range of acceptable parameter values must be known or estimated. However, within a biological context, approximating these values may be difficult. Parameter values and ranges can be taken from different organisms or systems or be estimated to produce qualitative phenomena in the model. Using a mathematical model of the epithelial mesenchymal transition (EMT) as a test case, this work examines how the parameter ranges chosen prior to analysis can influence LHS-PRCC results and shape subsequent analysis interpretations. Previous LHS-PRCC analysis of this model restricted parameters to {+/-}10% of their original value, which limits the scope and interpretability of parameter influence. Such a small range assumes, in the biological sense, that parameters are well-measured with little variability. Here, this work extends the previous analysis and explores several parameter ranges ({+/-}25%, {+/-}50% of the original value). This work also tests whether, within the {+/-}10%, {+/-}25% and {+/-}50% parameter ranges, the bistable switch present in the original model are maintained. Ultimately, this work showcases how a choice made prior to analysis, such as the accepted parameter ranges for biological rates and values in complex dynamical systems can influence sensitivity analysis results and interpretability. Additionally, these choices can have hidden consequences, such as the loss of phenomenological behavior. Thus, explicit prior knowledge about the appropriate parameter values is needed before using analysis to guide future experiments and model development.

Theory predicts that strong species interactions drive ecological instability, but strong interactions are common in ecosystems while strong instability appears rare. This discrepancy motivates enduring interest in ecological mechanisms that limit or counteract instability. Dormancy - reversible metabolic suppression - may be one. Dormancy is a ubiquitous life history trait found in organisms ranging from bacteria to trees. Dormant individuals form "seed banks" that are temporarily disengaged from demographic processes and species interactions, creating a memory of past ecological dynamics. Seed banks can stabilize predator-prey interactions, but whether, when, and how they affect the stability of larger ecological networks is uncertain. We show that dormancy stabilizes oscillatory dynamics in a minimal mathematical model and illustrate how dormancy converts high oscillation frequency into strong restoring force. We find that dormancy can have qualitative stabilizing effects in structured food webs that undergo Hopf bifurcations and exhibit oscillatory instability, but not in unstructured networks or those dominated by competitive or mutualistic interactions. This classification remains accurate when only a subset of species go dormant and drive stabilization. Our results clarify when dormancy can promote stability, indicating that dormancy may be an important but overlooked stabilizing factor in food webs.

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.

Coexistence of multiple predators in ecological communities and their combined effects on the abundance and diversity of shared prey are often difficult to predict. In some theoretical models, predator coexistence is limited by antagonistic interactions, especially in the form of intraguild predation (IGP) that typically leads to out-competition between predators and high prey densities. However, empirical studies show that predator coexistence is common even in the presence of IGP. This discrepancy between theoretical expectations and empirical observations can be highly relevant for practical applications like using multiple natural enemies for pest suppression in agriculture. It is proposed that greater functional differences between natural enemies (i.e. predators) could reduce competition and overcome the negative effects of IGP, thereby promoting their coexistence and enhancing herbivore (i.e. prey) suppression. In this study, we theoretically explore this proposition. We develop a theoretical model based on the types of natural enemies of aphids to identify how functional differences between predators in IGP modules affect predator coexistence and herbivore suppression. We show that pairwise combinations of four functional predator types (ladybird, predatory bug, hoverfly, and parasitoid) can increase the coexistence range for different intraguild predation and competition strengths between predators (IGP symmetry), along a productivity gradient. This outcome depends on the external food input rate for the predatory bug and hoverfly types, and on their position as IG predator or IG prey. Herbivore suppression was primarily driven by IGP symmetry (i.e. the relative intraguild predation and exploitative competition strength between predators) and was especially pronounced in competitive-like modules where the IG predator was excluded for most scenarios. However, for some competitive-like IGP modules with predatory bug and hoverfly types, both predators can persist and provide a high herbivore suppression across increasing productivity. Our results can help explain experimental findings in conservation biocontrol, where coexistence between natural enemies is joined with effective herbivore suppression, and offer additional support for the role of functional diversity in reconciling theoretical predictions with experimental observations in multiple-predator communities.

Predicting the outcome of species or pathogen strain competition is a fundamental aim in both community ecology and infectious disease dynamics. Recent work revealed major challenges in predicting strain co-circulation from ecological coexistence theory due to overcompensatory competition among pathogens for susceptible resources, which can prevent the re-invasion of other competing strains. This resource overcompensation is ubiquitous across host-pathogen systems, but not apparent in simple Lotka-Volterra competition system, highlighting fundamental differences between pathogen strain and species competition. To address this gap, we begin by deriving classical models of pathogen strain and species competition from a resource-consumer model. This generalization illustrates that the relative time scale between resource and consumer dynamics limits the degree of resource overcompensation and therefore dictates the outcome of stochastic competition. Moreover, by introducing a mathematical framework for quantifying pairwise and higher-order terms from general competition systems, we show that a simple, ecological competition model can accurately predict the equilibrium dynamics of strain competition. A case study of rotavirus strain competition reveals that the ability to predict the outcome of strain competition from ecological theory depends on the underlying cross immunity structure. This work synthesizes coexistence theory across two fields by providing a unifying framework for predicting the outcome of complex ecological competition.

Phytoplankton encounter a range of light and nutrient conditions in nature and must adjust their internal carbon and nitrogen allocations to grow across different resource environments. Current phytoplankton carbon budget models treat respiration simply as a carbon loss. In reality, respiration is a critical cellular process that produces energy for nutrient uptake and cellular maintenance. Drawing on empirical evidence, we developed an eco-physiological model that incorporates a more realistic role of respiration. In our model, photosynthetic carbon is partitioned into: (i) the Pentose Phosphate Pathway (PPP) for assimilation and (ii) respiration for energy production that is then used in nutrient uptake. Stored nitrogen is partitioned between three pools: cellular structure, photosynthesis and nutrient uptake. Using an optimality-based approach, we identify strategies that maximize either exponential growth rate or competitive ability. We find that optimal internal allocations follow a growth-maintenance tradeoff, favoring population growth through carbon acquisition in nitrogen-replete conditions and population maintenance through nitrogen acquisition in nitrogen-limited conditions. The optimal allocations match empirically observed shifts in carbon partitioning at different dilution rates. Our model also generates an interactive growth response surface with an asymmetry, where light is the dominant limiting factor at low light intensities and co-limitation by light and nitrogen only occurs at high light levels. Furthermore, the model recovers the widely accepted Droop function for growth vs nitrogen quota and predicts a hyperbolic decline in growth vs energy quotas. Through a simple growth-maintenance tradeoff, our model provides a mechanistic foundation for predicting phytoplankton productivity in biogeochemical models.

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.

We describe a statistical agent-based model (SABM) for binary spatio-temporal data in which the occupancy of each cell evolves as a Bernoulli mixture of three mechanistically distinct processes: local persistence, anisotropic neighborhood dispersal, and long-distance dispersal. The model is embedded in a hierarchical Bayesian framework with conjugate Beta full-conditionals for the persistence and long-distance parameters and a Dirichlet prior on the directional dispersal kernel. A nonstationary extension links the dispersal kernel to a latent habitat-suitability surface through directional gradients of a Gaussian process. We show that, in the small-step regime, the Lagrangian recurrence for the dispersal kernel scales to a classical two-dimensional advection-diffusion partial differential equation whose drift and dispersion coefficients are the first and second moments of the dispersal probabilities. We provide an MCMC algorithm exploiting the exact full-conditionals and demonstrate parameter recovery and PDE-scaling agreement in a simulated example.

Non-compliance with regulations threatens the sustainability of fisheries worldwide. Understanding the interconnected feedbacks of this complex social-ecological problem is key for sustainability but rarely integrated into fisheries management. We provide an adaptive stochastic modelling framework that integrates economic, social behavior, and ecological aspects of the Chilean kelp fishery, which plays a critical economic and ecological role in coastal social-ecological ecosystem. High levels of non-compliance is threatening sustainability, fishers well-being, and ecosystem health. Our model considers inherent environmental uncertainties and enables the assessment of different harvesting and compliance scenarios and the role of market-based economic incentives in reducing non-compliance. Results show that, unlike the sustainability obtained under an idealized full-compliance scenario, under dynamic compliance the social, economic, and ecological feedbacks leads to system collapse. Importantly, price premiums can promote compliance and sustainability, but the probability of collapse, albeit small, still exist. Our generalizable stochastic modeling framework evidenced that accounting for inherent uncertainty in natural resource management is key to designing interventions for sustainability.

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.

A recurring lesson from random ecological models is that coexistence is hard to come by: in the Generalized Lotka-Volterra (GLV) model with pairwise interactions, the probability that randomly sampled parameters admit a positive (feasible) equilibrium - a necessary condition for coexistence - is exactly 1/2n in n species, vanishing rapidly with diversity. This rarity is often read as evidence that coexistence demands specific ecological mechanisms. Real interactions, however, are rarely strictly pairwise: any nonlinear dependence of one species growth rate on anothers abundance, Taylor-expanded, generates higher-order interactions (HOIs) of increasing degree. Treating the interaction order d as a knob that indexes this nonlinearity, we map the random GLV with HOIs onto the Kostlan-Shub-Smale class of random polynomial systems and approximate the probability of feasibility (Pf ) analytically. We find a phase transition at d = 4: below this threshold, Pf decays with diversity as in the pairwise case; above it, the exponential proliferation of equilibria outpaces the probability that any given equilibrium is feasible, and the probability of feasibility increases with n, approaching one. The transition appears to be universal across symmetric coefficient distributions, but vanishes when sign symmetry of the parameter distribution is broken. This work uncovers a route by which feasibility emerges from nonlinearity alone, with no fine-tuning of parameters and no appeal to specific ecological mechanisms.

Infectious disease time series often show signs of epidemic transitions, such as the peaks and troughs of the time series. In these time series, key system parameters can lead to catastrophic changes in the dynamical system behaviour (often called critical transitions). Modellers have increasingly shown that early warning signals can anticipate these transitions, both critical and non-critical, in infectious disease time series. Existing methods, however, generally focus on univariate time series data, or ignore spatiotemporal patterns that may be present as a disease spreads through a population. Recent ecological literature developments expand existing temporal and spatial methods to consider the covariance matrix of multiple, related time series. However, many of these proposed signals still make an assumption of stationary time series/system equilibrium. Whilst often true in ecological modelling, disease systems are seldom at equilibrium. In this paper, we propose the usage of the eigendecomposition of the non-stationary covariance matrix as a more suitable early warning signal for epidemiological data. We first analyse the expected trends in the eigenvalues and eigenbasis of the covariance matrix on approach to a transition. Next we apply these methods to a spatially-structured susceptible-infectious-recovered model to explore how the eigenbasis may provide extra information to modellers. Finally, we test these methods on SARS-CoV-2 case data during the 2020-2021 pandemic period in England.

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.

Successful ecosystem restoration is intimately linked to the persistence of species in local communities and across landscapes. As such quantitative approaches to ecological restoration require the integration of community and metapopulation ecology. Together these disciplines demonstrate that local colonisation, via habitat connectivity and size, and species interactions, both modulate the process of community assembly. However, thus far restoration ecology still remains disconnected from network ecology this preventing a holistic, community-wide perspective to restoration. We aim to inform ecological restoration using a multi-layer modelling framework integrating ecological interactions and species dispersal dynamics. We explore the drivers that modulate recolonisation dynamics of species across restored landscapes. We further investigate how restoration improves the structural properties of food webs, the number of successful recolonisations and the role of configuration of restored patches in restoration outcomes. We find that recolonisation is the result of a trade-off between dispersal ability and energy requirements. 97% of plant recolonisation and 88% of herbivore recolonisations happened within close proximity to the source patches. Better dispersers - intermediate and top species in the food webs - were able to recolonise habitat by benefitting from the increased biomass influx from restoration. When only a small proportion of the landscape could be restored, the location and connectivity of restored areas strongly influenced the outcome of restoration: more connected patches enabled on average the recolonisation of about 1 additional intermediate species compared to that of isolated patches. However, this difference faded as soon as more patches were restored, and improving larger portions of the landscape always resulted in better outcomes. Restoring 1/3 of the landscape enabled on average the recolonisation of ~4 additional species. Our findings suggest that quantitative models can inform restoration efforts necessary to bring native species back to restored areas. They also suggest that attention should be given to the requirements of the recolonisers, the distance of their introduction from restored areas and their trophic and ecological niche. These aspects are crucial to assess their energy and habitat requirements for successful establishment.

Under complex perturbation regimes, biodiversity dynamics show temporal variability in species and community abundance around long-term population trends. Many species indeed show long-term declines while other species increase, putting natural communities far from stationary regimes, while variability is often studied near equilibrium. We contribute to bridging this gap by investigating population and community variability during long-term trends caused by press perturbations in stochastic models of population dynamics. By estimating the deterministic changes in mean and variance during the transient regime, we show that population variability deviates from stationary expectations. Moreover, the deviation strongly depends on the sign of the population trends: increases generate excesses of variability while declines generate deficits. Scaling up to community variability, we propose a decomposition of community variability deviation, allowing to highlight that community variability in the transient regime depends on how the press perturbation is distributed within species relative abundances and growth rates. These results challenge the equilibrium assumption and open new perspectives for the study of the variability of ecological systems under multiple perturbation types.

Existing theory examining the coevolutionary dynamics of species range borders assumes random dispersal, which causes maladaptive gene flow from the range core to the range margins and contributes to the formation of range limits. However, dispersal is unlikely to be random for many organisms in nature, calling into question existing theoretical predictions. For example, if individuals exhibit phenotype-dependent adaptive dispersal strategies such as matching habitat choice, then the resulting adaptive gene flow toward species range margins could facilitate range expansions and potentially prevent the formation of range limits by interspecific competition. To test this idea, we use a comprehensive mathematical model to develop a quantitative theory of range border coevolution that incorporates phenotype-optimal dispersal--a particular form of matching habitat choice in which individuals follow the gradient in an environmental optimum phenotype to settle in the habit best suited for their phenotype. We find that instead of preventing competitively formed range limits, adaptive dispersal leads to sharper range limits and reduced character displacement in sympatry. These differences are particularly remarkable when natural selection is weak, when individuals are specialized in their resource use, or when individuals are highly sensitive to environmental conditions. We show that matching habitat choice causes backward edge-to-core movements which dynamically interact with the effects of interspecific competition to establish the range limits. Thus, the formation of range limits by interspecific competition is robust to assumptions about individual dispersal. Further, our results identify the competitive advantage of evolving matching habitat choice in steep environmental gradients, especially for slowly-growing species in rapidly fluctuating climates.

Microbes exhibit complex dynamic behavior as the result of a large number of biochemical processes, spatial and temporal interactions, environmental variations, and evolutionary pressure. Although significant progress has been achieved in understanding microbial ecological dynamics, multiple open questions remain, including the microscopic mechanisms of growth and the roles of nutrients and stochasticity. In this work, we present a minimal theoretical approach to clarify the link between consumption of resources by microbes and their growth. A stochastic model that accounts for a single microbial species consuming a single type of resource while growing via cell division is studied analytically and via Monte Carlo computer simulations. We identify three distinct dynamical regimes of microbial growth determined by the relative magnitudes of resource uptake and division rates and initial conditions. We also show that stochasticity influences the dynamic behavior when the amounts of microbes or resources are low. The model recovers Monod growth kinetics and provides a mechanistic interpretation of the Monod constant and maximal growth rate. The theoretical framework presented captures a wide spectrum of dynamic behaviors in microbial systems, providing a clearer microscopic picture to explain their underlying complex mechanisms.