Theoretical Ecology

The interplay of host-parasite and predator-prey interactions is critical in ecological dynamics because both predators and parasites play an important role in regulating populations and communities. But what is the prevalence of infected prey and predators when a parasite is transmitted through trophic interactions, particularly when stochastic fluctuations of demographical changes are allowed arising from individual-level dynamics? Here, we analysed the system stability and the frequency of infected and uninfected host subpopulations in a complex predator-prey-parasite system, where infection happens through trophic interactions transmitting parasites from prey to predators. We varied the parasite virulence implemented as reproductive costs imposed on infected hosts and the probabilities of parasites infecting the hosts per encounter, to investigate how those important evolutionary factors will determine the species coexistence and population composition. We further explored the role of stochasticity in our system by comparing our deterministic analysis with stochastic simulations. Our results show that parasites go extinct when the infection probabilities of either host are small. The success in infecting the final host (the predator) is more critical for the survival of the parasite species, as the threshold for infection probability of the predator is higher than that of the prey for three-species coexistence. While our stochastic simulations agree with deterministic predictions well in most parameter regions. However, in the border parameter regions between coexistence and extinction typically with high infection probabilities, while only one possible outcome in deterministic dynamics, both coexistence and extinction can happen in stochastic repeats under the same parameter values. This illustrates the importance of stochasticity and demographic fluctuations in species coexistence. In addition, the proportion of infected individuals increases with the infection probabilities in our deterministic analysis and stochastic simulations as expected. Interestingly, we found that in some parameter space, the relative frequencies of infected and uninfected individuals are different between the intermediate host (prey) and the final host (predator) populations. This counterintuitive observation shows that the interplay of host-parasite and predator-prey interactions lead to more complex dynamics than a simple resource-consumer relationship.

Although the eco-evolutionary effects of individual variation for species coexistence are still widely debated, theoretical evidence appears to support a negative impact on coexistence. Mechanistic models of eco-evolutionary effects of individual variation focus largely on pairwise interactions, while the dynamics of communities where both pairwise and higher-order interactions (HOIs) are pervasive are not known. In addition, most studies have focused on effects of high dimensional HOIs on species coexistence when in reality such HOIs could be highly structured and low-dimensional, as species interactions could primarily be mediated through phenotypic traits. Here, combining quantitative genetics and Lotka-Volterra equations, we explored the eco-evolutionary effects of individual variation on the patterns of species coexistence in a competitive community dictated by pairwise interactions and HOIs. Specifically, we compare six different models in which HOIs were modelled to be trait-mediated (low-dimensional) or random (high-dimensional) and evaluated its impact on robustness of species coexistence in the presence of different levels of individual variation. Across the six different models, we found that individual variation did not promote species coexistence, irrespective of whether interactions were pairwise or were of higher-order. However, individual trait variation could stabilize communities to external perturbation more so when interactions were of higher order. When compared across models, species coexistence is promoted when HOIs strengthen pairwise intraspecific competition more so than interspecific competition, and when HOIs act in a hierarchical manner. Additionally, across the models, we found that species traits tend to cluster together when individual variation in the community was low. We argue that, while individual variation can influence community patterns in many different ways, they more often lead to fewer species coexisting together.

Ecological and evolutionary effects of individual variation on species coexistence remains unclear. Competition models for coexistence have emphasized species-level differences in pairwise interactions, and invoked no role for intraspecific variation. These models show that stronger competitive interactions result in smaller numbers of coexisting species. However, the presence of higher-order interactions (HOIs) among species appears to have a stabilizing influence on communities. How species coexistence is affected in a community where both pairwise and higher-order interactions are pervasive is not known. Furthermore, the effect of individual variation on species coexistence in complex communities with pairwise and HOIs remains untested. Using a Lotka-Volterra model, we explore the effects of intraspecific variation on the patterns of species coexistence in a competitive community dictated by pairwise and HOIs. We found that HOIs greatly stabilize species coexistence across different levels of strength in competition. Notably, high intraspecific variation promoted species coexistence, particularly when competitive interactions were strong. However, species coexistence promoted by higher levels of variation was less robust to environmental perturbation. Additionally, species traits tend to cluster together when individual variation in the community increased. We argue that individual variation can promote species coexistence by reducing trait divergence and attenuating the inhibitory effects of dominant species through HOIs

Climate change and other anthropogenic impacts are rapidly altering natural environmental periodicities on a variety of time scales. Despite this, a general theoretical foundation describing the role of periodic environmental variation in structuring species interactions and ecological communities is still underdeveloped. Alarmingly, this leaves us unprepared to understand and predict implications for the maintenance of biodiversity under global change. Here, we extend a two-species Lotka-Volterra competition model that incorporates periodic forcing between seasons of high and low production to investigate the effects of changing environmental patterns on species coexistence. Towards this, we define coexistence criteria for periodic environments by approximating isocline solutions akin to classical coexistence outcomes. This analytical approach illustrates that periodic environments (i.e., seasonality) in and of themselves can mediate different competitive outcomes, and these patterns are general across varying time scales. Importantly, species coexistence may be incredibly sensitive to changes in these abiotic periods, suggesting that climate change has the potential to drastically impact the maintenance of biodiversity in the future.

Environmental stochasticity and the temporal variations of demographic rates associated with it are ubiquitous in nature. The ability of these fluctuations to stabilize a coexistence state of competing populations (sometimes known as the storage effect) is a counterintuitive feature that has aroused much interest. Here we consider the performance of environmental stochasticity as a stabilizer in diverse communities. We review the results of previous studies which suggest that the stabilizing effects of stochasticity weaken as the number of species increases, provide a systematic numerical exploration of the phenomenon and identify the relevant parameter regimes. Of particular importance is the ratio between the dwell time of the environment and the generation time: we show that stochasticity promotes diversity only when this ratio is smaller than the inverse of the fundamental biodiversity parameter. In an opposite regime, when stochasticity impedes coexistence and lowers the species richness, its effect is determined by the ratio between the strength of environmental variations and the rate at which new types are added to the community via speciation, mutation or immigration.

O_LIConsumers can potentially adjust their diet in response to changing resource abundances, thereby achieving better foraging payoffs. Although previous work has explored how such adaptive foraging scales up to determine the structure and dynamics of food webs, consumers may not be able to perform perfect diet adjustment due to sensory or cognitive limitations. Whether the effectiveness of consumers diet adjustment alters food-web consequences remains unclear. C_LIO_LIHere, we study how adaptive foraging, specifically the effectiveness (i.e. rate) with which consumers adjust their diet, influences the structure, dynamics, and overall species persistence in synthetic food webs. C_LIO_LIWe model metabolically-constrained optimal foraging as the mechanistic basis of adaptive diet adjustment and ensuing population dynamics within food webs. We compare food-web dynamical outcomes among simulations sharing initial states but differing in the effectiveness of diet adjustment. C_LIO_LIWe show that adaptive diet adjustment generally makes food-web structure resilient to species loss. Effective diet adjustment that maintains optimal foraging in the face of changing resource abundances facilitates species persistence in the community, particularly reducing the extinction of top consumers. However, a greater proportion of intermediate consumers goes extinct as optimal foraging becomes less-effective and, unexpectedly, slow diet adjustment leads to higher extinction rates than no diet adjustment at all. Therefore, food-web responses cannot be predicted from species responses in isolation, as even less-effective adaptive foraging benefits individual species (better than non-adaptive) but can harm species persistence in the food web as a whole (worse than non-adaptive). C_LIO_LIWhether adaptive foraging helps or harms species coexistence has been contradictory in literature Our finding that it can stabilise or destabilise the food web depending on how effectively it is performed help reconcile this conflict. Inspired by our simulations, we deduce that there may exist a positive association between consumers body size and adaptive-foraging effectiveness in the real world. We also infer that such effectiveness may be higher when consumers cognise complete information about their resources, or when trophic interactions are driven more by general traits than by specific trait-matching. We thereby suggest testable hypotheses on species persistence and food-web structure for future research, in both theoretical and empirical systems. C_LI

Population dynamics of different species across food web models of diverse spatial scales have been extensively investigated over the past three decades. Chaotic fluctuations in species populations are generally associated with increased extinction risk due to frequent periods of low species density leading to cascading effects. The existence of a food web where the cohabiting species population oscillates chaotically has been largely attributed to chaos control or death of chaos, mediated either by internal mechanisms, such as the food web favoring parameter values that keep the species population out of the chaotic region, or external mechanisms like environmental forcing. Yet, this picture is not complete, as food webs do not exist in isolation, but are generally connected to each other through dispersal of species, forming a metacommunity. A metacommunity of food webs whose dynamics is that of chaotic attractors can only persist through control and particularly the the quenching of chaos. We claim that habitat heterogeneity in such a metacommunity fulfills this purpose. We address this question by analyzing the dynamics of a drive-response metacommunity composed of five chaotic food webs, each located in a distinct patch. Each patch contains an inherently chaotic tritrophic food web, with habitat heterogeneity present among patches. The first patch functions as the drive, exerting external influence on the dynamics of the remaining four response patches. Our results establish that in a drive-response metacommunity, strong influence from the drive quenches dynamical chaos in both drive and response patches, often leading to steady states. This phenomenon is observed in two distinct metacommunity network structures. The heterogeneity of the response systems (food web models) and the dissimilarity between drive and response systems are found to play significant roles in suppressing chaotic population dynamics. These findings strongly imply that the persistence of such inherently chaotic metacommunities may result from the quenching of chaos through the interplay of chaos, habitat heterogeneity, and to some degree network structure shaped by dispersal. Furthermore, we illustrate that these metacommunities are also susceptible to extinction due to dispersal-induced synchronization. Accordingly, this study also investigates dispersal-induced complete synchronization among the constituent patches.

Temporal environmental variations may promote diversity in communities of competing populations. Here we compare the effect of environmental stochasticity with the effect of periodic (e.g., seasonal) cycles, using analytic solutions and individual-based Monte-Carlo simulations. Even when stochasticity facilitates coexistence it still allows for rare sequences of bad years that may drive a population to extinction, therefore the stabilizing effect of periodic variations is stronger. Correspondingly, the mean time to extinction grows exponentially with community size in periodic environment and switch to power-law dependence under stochastic fluctuations. On the other hand, the number of temporal niches in periodic environment is typically lower, so as diversity increases stochastic temporal variations may support higher species richness.

The sustainability of renewable resource harvesting may be threatened by environmental and socioeconomic changes that induce tipping points. Here, we propose a synthetic harvesting model with a comprehensive set of socioecological factors that have not been explored together, including market price and stock value, effort and processing costs, labour and natural capital elasticities, societal risk aversion, maximum sustainable yield (MSY), and population growth shape. We solve for harvest rate and stock biomass solutions by applying a timescale-separation between fast ecological dynamics and slow institutional adaptation that responds myopically to short-term net profit. The result is a cusp bifurcation with two composite bifurcation parameters: 1. consumptive scarcity{lambda} c or the ratio of market price-to-processing cost divided by MSY (leading to a pitchfork), and 2. non-consumptive scarcity{lambda} n or the stock value minus a scaled effort cost (leading to saddle-nodes or folds). Together, consumptive and non-consumptive scarcities create a cusp catastrophe. We further identify four tipping phenomena: 1. process (harvest rate) noise-induced tipping; 2. exogenous ({lambda}c) rate+process noise-induced tipping; 3. exogenous noise-induced reduction in tipping; and 4. exogenous cycle-induced reduction in tipping. Case 2 represents the first mechanistically motivated example of rate-associated tipping in socioecological systems, while cases 3 and 4 resemble noise-induced stability. We discuss the empirical relevance of catastrophe and tipping in natural resource management. Our work shows that human institutional behaviour coupled with changing socioecological conditions can cause counterintuitive sustainability and resilience outcomes.

Grazing by zooplankton can maintain diversity in phytoplankton communities by allowing coexistence between competitors in situations that would otherwise lead to competitive exclusion. In mathematical models, grazing is represented by a functional response that describes the consumption rate by an individual zooplankter as a function of phytoplankton concentration. Since its initial description, the Kill-the-Winner functional response has been increasingly adopted for large-scale biogeochemical modeling. Here, we analyze how two properties of the Kill-the-Winner functional response--preference and switching--interact to promote coexistence and increase diversity in two simple models: a diamond-shaped nutrient-phytoplankton-zooplankton model and a size-structured phytoplankton community model. We found that, compared to preference, switching leads to coexistence and increased diversity over a much wider range of environmental conditions (nutrient supply and mixing rate). In the absence of switching, preference only allows for coexistence within the narrow range of environmental conditions where the preference is precisely balanced against the competitive difference between phytoplankton types. We also explored a counterintuitive aspect of the Kill-the-Winner functional response that we have termed "synergistic grazing". Synergistic grazing occurs when the grazing rate on one phytoplankton type increases as the biomass of an alternative phytoplankton type increases. This unrealistic effect is most evident when switching is strong and when zooplankton have a preference for the weaker competitor.

Explaining how competing species coexist remains a challenge in ecology. A major hypothesis is that disturbance opens up the opportunity for types with different "life history" strategies to coexist, allowing types better at getting to and using recently disturbed patches to coexist with better competitor types. A simple model introduced several decades ago demonstrated this, but its focus on patch dynamics (i.e. the dynamics of the number of patches a species occupies) gives limited insight into how coexistence-enabling variation arises from within-patch demographic strategies. Here we present, and demonstrate how to analyze, a partial differential equation model that captures the emergence of larger-scale competitive dynamics from within-patch population dynamics of species competing for patches subject to disturbance. We analyze key cases of the model framework, with competition acting in turn on each aspect of within-patch demography included in the model: reproduction, offspring-survival, and adult-survival. Insights arising from these analyses include: 1) variation between species on a simple reproduction-adult-survival trade-off can enable disturbance-generated coexistence, 2) variation along trade-offs with species robustness-to-competition can also generate coexistence 3) disturbance-generated coexistence may or may not involve classical "successional dynamics" within patches, and 4) coexistence is easier to generate at intermediate disturbance rates. Our work here provides new tools for more complete development of the theory of disturbance-generated coexistence.

1Coexistence theory and food web theory are two cornerstones of the longstanding effort to understand how species coexist. Although competition and predation are known to act simultaneously in communities, theory and empirical study of the two processes continue to be developed independently. Here, we integrate modern coexistence theory and food web theory to simultaneously quantify the relative importance of predation, competition, and environmental fluctuations for species coexistence. We first examine coexistence in a classic multi-trophic model, adding complexity to the food web using a novel machine learning approach. We then apply our framework to a parameterized rocky intertidal food web model, partitioning empirical coexistence dynamics. We find that both environmental fluctuation and variation in predation contribute substantially to species coexistence. Unexpectedly, covariation in these two forces tends to destabilize coexistence, leading to new insights about the role of bottom-up versus top-down forces in both theory and the rocky intertidal ecosystem.

We use global sensitivity analysis (specifically, Partial Rank Correlation Coefficients) to explore the roles of ecological and epidemiological processes in shaping the temporal dynamics of a parameterized SIR-type model of two host species and an environmentally transmitted pathogen. We compute the sensitivities of disease prevalence in each host species to model parameters. Sensitivity rankings and subsequent biological interpretations are calculated and contrasted for cases were the pathogen is introduced into a disease-free community and where a second host species is introduced into an endemic single-host community. In some cases the magnitudes and dynamics of the sensitivities can be predicted only by knowing the host species characteristics (i.e., their competitive abilities and disease competence) whereas in other cases they can be predicted by factors independent of the species characteristics (specifically, intraspecific versus interspecific processes or the species roles of invader versus resident). For example, when a pathogen is initially introduced into a disease-free community, disease prevalence in both hosts is more sensitive to the burst size of the first host than the second host. In comparison, disease prevalence in each host is more sensitive to its own infection rate than the infection rate of the other host species. In total, this study illustrates that global sensitivity analysis can provide useful insight into how ecological and epidemiological processes shape disease dynamics and how those effects vary across time and system conditions. Our results show that sensitivity analysis can provide quantification and direction when exploring biological hypotheses.

Janzen Connell Effects (JCEs), specialized predation of seeds and seedlings near conspecific trees, are hypothesized to promote high species richness. While past modeling studies show JCEs can maintain higher diversity than a neutral community, recent theoretical work indicates JCEs may weakly inhibit competitive exclusion when species exhibit interspecific fitness variation. However, recent models make somewhat restrictive assumptions about the functional form of specialized predation - that JCEs occur at a fixed rate when seeds/seedlings are within a fixed distance of a conspecific tree. Using a theoretical model, I show that the functional form of JCEs largely impacts their ability to promote coexistence. If specialized predation pressure increases additively with adult tree density and decays exponentially with distance, JCEs maintain considerably higher diversity than predicted by recent models. Parameterizing the model with values from a Panamanian tree community indicates JCEs can maintain high diversity in communities exhibiting high interspecific fitness variation.

Natural enemies are thought to promote coexistence of competing victim species. Although existing theory suggests victim coexistence increases with enemy specialization, the dynamics and potential extinction of enemies is generally discounted. Where enemy dynamics have been considered, empirically atypical linear functional responses have been studied. These limitations could over-simplify inferences about enemy-mediated coexistence. We studied the dynamics of two competing victim species and two enemy species with a deterministic model. We derived equilibrium points, and used linear stability analysis, numerical simulations and Floquet theory to determine the influence of enemy specificity and non-linear functional responses on coexistence in this victim-enemy community. We found greater specificity could drive enemy equilibrium points to infeasible values. We found only accelerating enemy functional responses result in stable equilibrium point coexistence of otherwise equivalent competitor victims, in which case greater specificity results in greater stability. Linear and saturating responses produce complex dynamics (neutral or limit cycles, chaos) or extinction, with limit cycle stability highest at intermediate specificity. Our results indicate strict specificity may not maximize coexistence, and enemy functional response critically influences whether enemies promote victim coexistence. They highlight the need to incorporate enemy dynamics into the growing body of theory regarding enemy-mediated diversity maintenance.

Understanding the factors that influence the persistence and stability of complex ecological networks is a central focus of ecological research. Recent research into these factors has predominantly attempted to unveil the ecological processes and structural constraints that influence network stability. Comparatively little attention has been given to the consequences of evolutionary events, despite the fact that the interplay between ecology and evolution has been recognised as fundamental to understand the formation of ecological communities and predict their reaction to change. In light of current environmental challenges, there is a compelling need for a quantitative framework to predict biodiversity loss under environmental perturbations while accounting for evolutionary processes. We extend existing mutualistic population dynamical models by incorporating evolutionary adaptation events to address this critical gap. We relate ecological aspects of mutualistic community stability to the stability of persistent evolutionary pathways. Our findings highlight the significance of the structural stability of ecological systems in predicting biodiversity loss under both evolutionary and environmental changes, particularly in relation to species-level selection. Notably, our simulations reveal that the evolution of mutualistic networks tends to increase a network-dependent parameter termed critical competition, which places systems in a regime in which mutualistic interactions enhance structural stability and, consequently, biodiversity. This research emphasizes the pivotal role of natural selection in shaping ecological networks, steering them towards reduced effective competition below a critical threshold where mutualistic interactions foster stability. The outcomes of our study contribute to the development of a predictive framework for eco-evolutionary dynamics, offering insights into the interplay between ecological and evolutionary processes in the face of environmental change.

The Lotka-Volterra equations, a cornerstone of predator-prey modeling, offer a versatile framework for understanding population dynamics in the context of sustainability. This chapter explores how these equations, through the analysis of dynamic equilibrium and stability, illuminate principles of both sustainable ecological interactions and the mechanisms leading to detrimental long-term out-comes in various systems (negative sustainability). We first analyze predator-prey interactions to gain insights into population management, resource conservation, and the delicate balance of ecosystems. Furthermore, we extend the Lotka-Volterra model to discuss its broader implications for complex systems dynamics in diverse fields, such as in modeling economic competition and arms races, where the framework helps identify pathways that lead to unsustainable resource consumption, increased risk, or collapse.

Vertical transmission of an infectious disease from parent to offspring is a common transmission route in many systems. Here we investigate the dynamics of a pathogen with both horizontal and vertical transmission within a spatially structured population. We introduce a lattice model with a pair approximation that includes both local and global transmission and reproduction. We find that vertical transmission can determine pathogen invasion and reduce the horizontal transmission rate required for invasion. When the majority of transmission and reproduction is local, vertical transmission can destabilise a host population to cause limit cycles. Given the advantages of a pathogen having both horizontal and vertical transmission routes, we extend the model to investigate the likelihood a mutant strain with both transmission modes will outcompete a resident strain with only horizontal transmission. When there is no trade-off the mutant always invades and when there is a trade-off with horizontal transmission, the mutant emerges when the cost to the horizontal transmission rate is not too large. Depending on how the mutant appears within the host population, it may have an initial advantage over the resident strain even if it cannot outcompete in the long-term. Our work demonstrates the potential importance of vertical transmission within host-pathogen dynamics.

In many metapopulation and metacommunity models, individuals disperse between discrete habitat patches. When those models treat time as a discrete variable, the formulation of the dispersal term must be handled with care. A commonly made mistake is to model dispersal with terms identical to those found in continuous-time models. Such terms can inadvertently resurrect dead individuals, effectively creating "zombie dispersers." Zombie dispersal, in turn, can have dramatic, but spurious, effects on model dynamics. In this manuscript, we illustrate the misleading effects generated by zombie dispersal in a published model used to investigate how dispersal mediates synchrony in population dynamics.

The competition-colonization trade-off has been a classic paradigm to understand the maintenance of biodiversity in natural ecosystems. However, species-specific dispersal heterogeneities are not well integrated into our general understanding of how spatial coexistence emerges between competitors. Combining both network and metapopulation approaches, we construct a spatially explicit, patch-occupancy dynamic model for communities with hierarchically preemptive competition, to explore species coexistence in shared vs. non-shared dispersal networks with contrasting heterogeneities (including regular, random, exponential and scale-free networks). Our model shows that species with the same demography (i.e. identical colonization and extinction rates) cannot coexist stably in shared networks (i.e. the same dispersal pathways), regardless of dispersal heterogeneity. In contrast, increasing dispersal heterogeneity (even at very low levels of heterogeneity) in non-shared networks can greatly promote spatial coexistence, owing to the segregation-aggregation mechanism by which each species is restricted to self-organized clusters with a core of the most connected patches. However, these competitive patterns are largely mediated by species life-history attributes, for example, a unimodal biodiversity response to an increase of species dispersal rate emerges in non-shared heterogeneous networks, with species richness peaking at intermediate dispersal levels. Interestingly, increasing network size can foster species coexistence, leading to a monotonic increase in species-area curves. This strongly suggests that, unexpectedly, many more species can co-occur than the number of limiting resources. Overall, this modelling study, filling the gap between network structure and spatial competition, provides new insights into the coexistence mechanisms of spatial heterogeneity.