Theoretical Ecology

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.

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.

Three hypotheses help organize energetic thinking about living systems: Lotkas Maximum Power Principle, Odum-Pinkertons Intermediate Efficiency Principle, and Morowitzs Biological Cycling Principle. Here we show how these hypotheses fit together in consumer-resource systems, moving from qualitative principles to formal, testable statements. Using the Rosen-zweig-MacArthur model, we prove that the consumers maximum output power lies exactly on the Hopf boundary that separates stable points from cycles; at that point, the resulting power efficiency is intermediate. In the Rosenzweig-MacArthur model the Hopf is supercritical, so a stable limit cycle appears smoothly as the equilibrium loses stability. We treat the Hopf onset of time-periodic population oscillations as a population-level analogue of sustained cycling under energy flux. We then embed these energetic statements in adaptive dynamics: with convex trait costs, evolutionary singular strategies exist and are locally stable, but they coincide with the maximum-power state only under explicit marginal-cost conditions. Together, these results unify classic ideas in the concrete setting of consumer-resource systems and suggest measurements to evaluate when bifurcations, energetics, and evolution can converge.

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.

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.

Despite the rapid pace of global change altering temporal environmental patterning, we lack a general understanding of how periodic environments structure ecological communities. In fluctuating environments, nonlinear dynamics associated with temporal trade-offs between competing species can create the potential for both niche differentiation (coexistence) and seemingly unexpected outcomes (exclusion) that deviate from deterministic coexistence theory. Yet, the mechanisms behind these outcomes are not fully understood. Here, we show that periodic fluctuations between times of high and low growth (e.g., seasons), and adaptive temporal trade-offs within and between species, can drive counterintuitive over- and under-performance of competing species. Most notable is the counterintuitive outcome of seasonally-mediated competitive exclusion that would not occur in either season alone, but is rather the direct result of environmental variability itself. We find that seasonal trade-offs in species growth rates, seasonal differences in competition strength, and functional similarity between competing species have the potential to drive nonlinear responses in coexistence to changing seasonality under global change. These biological conditions collectively influence our models transient dynamics, further explaining the mechanisms behind counterintuitive outcomes and highlighting the importance of non-equilibrium theory for global change ecology. Importantly, the seasonal patterns and species trade-offs that magnify these results are biologically realistic, therefore providing important insight into the implications for the maintenance of biodiversity under global change.

Overexploitation, the depletion of a resource by its consumer on a short timescale, is widespread in nature but its general implications for biomass control and community stability are not clear. Most approaches investigating the interactions between trophic levels and variations in biomass patterns or in population dynamics generally ignore overexploitation. Here we use a resource-plant-herbivore food chain model allowing for overexploitation (i.e. the plant can overexploit the resource and/or the herbivore can overexploit the plant). We uncover the conditions under which either type of overexploitation occurs and show that they qualitatively change ecological patterns, mainly by suppressing top-down control when interaction strength is high. When plant productivity increases, top-down control patterns are suppressed above the level when the plant starts to overexploit resources. Similarly, when herbivory intensity increases, top-down control patterns disappear when plants become overex-ploited. Overexploitation also prevents enrichment-driven destabilization by capping the energy fluxes in the community. These findings connect top-down and bottom-up controls in a single framework, and highlight the role overexploitation can play in structuring and stabilizing food chains via the modulation of interaction strengths.

Mimicry is an anti-predator strategy in which prey species (the mimic) resemble an unprofitable species (the model) to deceive predators. Despite theoretical expectations for perfect mimicry, imperfect mimicry, where the mimic resembles its model imperfectly, is widespread in nature. To understand how imperfect mimicry can persist ecologically, we studied the effect of different predator recognition processes on the dynamics and stability of various mimicry systems. Specifically, we extended a dynamical model that integrates optimal foraging and signal detection theories by introducing a novel abundance-dependent recognition mechanism, where predators perception of the similarity between mimic and model is influenced by the relative abundance of prey types. We demonstrate that intermediate similarity promotes stable community dynamics and increases mimic abundance in single Batesian mimicry systems. Moreover, abundance-dependent recognition leads predators to reduce attack on mimics with low morphological similarity, further contributing to system stability. Extending the framework to a multi-mimicry system, we find that Batesian and Mullerian mimics have contrasting effects: intermediate Batesian similarity continues to stabilize the system, while high Mullerian similarity provides additional protection and can off-set destabilization caused by highly similar Batesian mimics. Our study offers a novel explanation for the prevalence of imperfect mimicry in nature and highlights how recognition processes shape the ecological stability of mimicry systems.

1A diverse array of social carnivores, such as orcas and wolves, also hunt cooperatively, but it is not well understood how prey availability feeds back with the size of social carnivore groups. Cooperative hunting may expand predators access to food by allowing them to hunt prey they could not catch alone, but many predator groups are much larger than the group size that would maximize individual food intake. One promising explanation is that if individuals can freely leave and join groups, then predators behaving adaptively should continue to join a group until the fitness that they achieve in the group is the same as that of being solitary. Here, we investigate the stable group sizes that form in a population of predator groups when predators hunt two types of prey: big prey that is best hunted in groups and small prey that is best hunted alone. In conjunction, we track the dynamics of the distribution of predator group sizes when individuals make decisions about whether to join or leave groups based on their own fitness. We find that if individual predators are able to freely leave groups and pair up with other individuals, starting new groups, then group sizes at equilibrium are much smaller than expected, generally staying at or below the size that maximizes individual fitness. Furthermore, accounting for flexible group sizes leads to ecological conditions that are not predicted if predator group sizes are held constant; in some regions of the parameter space, predators partition resources by forming a bimodal distribution of group sizes, and as a result, create situations where an increase in one prey type helps the other prey population grow. This result has applications to management of carnivore-livestock conflict, implying that increasing populations of wild prey may protect livestock.

As acknowledged by Optimal Foraging theories, predator diets depend on prey profitability. Parasites, ubiquitous in food webs, are known to affect simultaneously host vulnerability to predation and host energy contents, thereby affecting profitability. In this work, we study the eco-evolutionary consequences of prey infection by a non trophically-transmitted parasite, with a simple lifecycle, on predator diet. We also analyze the consequences for coexistence between prey, predators and parasites. We model a trophic module with one predator and two prey species, one of these prey being infected by a parasite, and distinguish between two effects of infection: a decrease in host fecundity (virulence effect) and an increase in vulnerability to predation (facilitation effect). Predator foraging may evolve toward specialist or generalist strategies, the latter being less efficient on a given resource. We show that the virulence effect leads to specialisation on the non-infected prey while the facilitation effect, by increasing prey profitability, favors specialisation on the infected prey. Combining the two effects at intermediate intensities promotes either generalist predators or the diversification of foraging strategies (coexistence of specialists), depending of trade-off shape. We then investigate how the evolution of predator diet affects the niche overlap between predator and parasite. We show that facilitation effects systematically lead to a high niche overlap, ultimately resulting in the loss of the parasite. Virulence effects conversely favor coexistence by allowing a separation of the predator and parasite niches.

The dynamics of biogeochemical, ecological, and astronomical systems are transient. Yet, predicting the occurrence of dynamical shifts remains a challenge due to inferential uncertainties from datasets and the limitations of asymptotic-dependent theories. To address this problem, we developed a theoretical framework that builds on the finite nature of observations. This framework assesses the relative importance of processes, defined as the mechanisms that contribute to the rate of change of the systems dynamic variables, and it predicts the critical values that would trigger a shift into a new regime. The number of observable dynamic regimes within the framework increases exponentially with the number of processes. Observers, however, only experience dynamic regimes associated with relevant processes-- those exceeding a tipping point--within their reference framework. A case study of the framework was tested for a classic predator-prey system with four processes parameterized for bacteria (prey) and lytic bacteriophages (predator). The analysis recovered the sixteen dynamic regimes predicted by the framework, including two non-trivial quasi-equilibrium dynamics. An adaptive Boolean model, which used only relevant observable processes, validated the accuracy of the framework, recovering the dynamics of the full model. The observational framework introduced here provides a strategy for identifying the processes and conditions that lead to tipping points, representing a conceptual paradigm shift in transient dynamics, placing the focus on the specific, finite context of the observer, rather than the intrinsic, asymptotic states of the system. SIGNIFICANCESudden shifts in ecological, climate, and biological systems--so-called tipping points or critical transitions--are notoriously difficult to predict. This study introduces a mathematical framework that redefines these transitions as outcomes shaped by the observers empirical limits. By accounting for finite observation time and resolution, the framework uncovers a rich spectrum of dynamic regimes that classical theories overlook. Its conceptual rigor and practical value are demonstrated in a predator-prey system. This new approach reframes how to forecast regime shifts in complex systems and offers a tool with broad relevance, from microbial ecosystems to planetary climate.

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.

Agriculture is found in numerous taxa such as humans, ants, beetles, fishes and even bacteria. This type of niche construction has evolved independently from hunting, though many species remain primarily predators. When a consumer has a positive effect on its resource, we can expect an allocative cost of agriculture, as the agricultural care diverts time and energy from other activities. Defending the resource against predators may divert time from its consumption (exploitation cost). The cost may also occur on the foraging of alternative resources, for instance if the consumer spends more time nearby the farmed resource and underexploiting resources elsewhere (opportunity cost). We here investigate transitions from predation to agriculture in a simple three-species model of a farmer that consumes two resources and has a positive effect on one. We study the conditions for the (co)evolution of the investment into agriculture and specialization on the two resources, and its consequences on the ecological dynamics of the community. Eco-evolutionary dynamics generate a feedback between the evolution of agriculture and specialization on the helped resource, that can lead to varying selected intensity of agriculture, from generalist strategies with no agriculture, to specialist farmers, with possible coexistence between these two extreme strategies.

Whether interspecific competition is a major contributing factor to setting species range limits has been debated for a long time. Theoretical studies using evolutionary models have proposed that the interaction between interspecific competition and disruptive gene flow along an environmental gradient can halt range expansion of ecologically related species where they meet. However, the stability of such range limits has not been well addressed. We use a deterministic PDE model of adaptive range evolution over a continuous habitat to show that the range limits set by interspecific competition between two closely related species are unlikely to be evolutionarily stable if the environmental optima for fitness-related traits vary linearly in space. That is, in a (almost) linear environment without a dispersal barrier or a third (or more) related species, the range limits formed at the interface of two competing species constantly move towards the weaker species. Through extensive numerical computations, we then demonstrate that environmental nonlinearities such as "knees" and "wiggles"--wherein an isolated sharp change or a step-like change occurs in the steepness of a trait optimum--can strongly stabilize competitively formed range limits. The stabilization mechanism relies on the contrast that such nonlinearities create in the level of disruptive gene flow to the peripheral population of each species. We show that the stability of the range limits established at these nonlinearities, which are likely prevalent in nature, is robust against moderate environmental disturbances. Whether or not strong disturbances such as rapid high-amplitude changes in climate can destabilize such range limits depends on how the competitive dominance of the competing species changes across the environmental nonlinearity. Therefore, our results identify habitat regions where species ranges are fairly insensitive to climate change, and highlight the importance of measuring the competitive ability of species when predicting their response to climate change.

The functional response, or rate of resource acquisition for a consumer should decline proportionately in the presence of other consumers vying for the same resources. Aggressive behavior should be adaptive when it serves as a leverage mechanism for enhancing resource gain above what would be obtained under a premise of equal access. Model development expands on the implications of this assertion to make several predictions pertaining to the expression and magnitude of gainful aggressive interference with respect to leverage strength,consumer density, and resource density.

We introduce the group-based approach, use it to develop a multi-group biodiversity theory, and apply it find solutions to the multi-species maximum sustainable yield problem for a mixed species fishery. The group-based approach to community ecology is intermediate between classical species-centric and more recent trait-based (species-less) approaches. It describes ecological communities as composed of conspecific groups rather than species (as in classical models) or species-less individuals (as in trait-based models), and reconsiders community structure as results of inter-group resource competition. The approach respects species affiliation and recognises the importance of trait trade-offs at the conspecific group level. It offers an alternative to both classical and trait-based approaches and, remarkably, provides a complete analytical description of the community structure in the bench-mark case of zero-sum resource redistribution. HighlightsO_LIWe introduce a group-based approach to modelling of ecological communities and develop a multi-group biodiversity theory. C_LIO_LIA classification of intergroup interactions is established, based on the type of contest (which is determined by the relative role of qualitative vs. quantitative factors) and the accounting of resource redistribution. C_LIO_LIFor pure resource competition, we obtain the full analytic description of multi-group and multi-species community structure and its dynamics, including the processes of fission-fusion and invasion-extinction among groups. C_LIO_LIA principle of competitive coexistence is formulated, which explains the existence of conspecific groups as a mechanism for avoiding competitive exclusion. C_LIO_LIWe apply the theory to harvesting multi-species communities (e.g., for fisheries) and derive analytic expression for total catch and approximate solutions for multi-species maximum sustainable yield (MSY). C_LI

Recent empirical studies have uncovered the coexistence of cryptic species that are morphologically indistinguishable yet genetically different. As they lack known ecological differentiation between them, it has been suggested that species-specific sexual interactions may be able to stabilize their coexistence. We investigated two types of such interactions: (1) traumatic mating suffered by females and (2) interference competition among males. We have learned that the consequences of the two types of sexual interactions are markedly different. Traumatic mating may affect the fertility and/or survival of females. In both cases it introduces negative density dependence and, alone, can regulate the growth of a single population. Also, traumatic mating is able to stabilize the coexistence of ecologically equivalent populations, provided that it is stronger within species than between them. In contrast, male competition cannot constrain population growth without density dependence of a different origin. Accordingly, it destabilizes, rather than stabilizes, neutral coexistence of ecologically equivalent species. A targeted, species-specific study of traumatic mating suffered by females would provide empirical support for the diversity-maintaining role of sexual interactions.

O_LISpecies interactions are fundamental to the stability and productivity of ecosystems. To improve our capacity to predict and understand how climate change shapes the distribution of species and the dynamics of biotic interactions, we need to develop spatially explicit multi-species models that are built upon species-specific responses to changing conditions. C_LIO_LIWe developed a two-dimensional diffusion-advection-reaction predator-prey model that integrates species-specific responses to heterogeneous landscapes, affecting species dispersal, reproduction and survival rates. We derived conditions for the stability and feasibility of the coexistence steady-state and observed how temperature variation stabilises or destabilises the system. C_LIO_LIWe conducted numerical simulations to explore the effect of predicted extreme temperatures on the spatial dynamics of a parasitoid-butterfly system and their interactions. Applied to four different climatic environments, the numerical approximations demonstrate the asymmetric impact of a warming climate on interacting species. The output density distribution maps highlight the capability of our model to produce interpretable multiscale predictions which can be used to identify and evaluate species vulnerability locally and across their range. C_LIO_LIBy building upon a solid mechanistic understanding of species-specific responses to environmental change, our model can be extended to other species and variables, including environments where the availability of empirical data is limited, and explore the dynamics and distribution of interacting species under different scenarios of environmental change. C_LI

Plant-soil feedbacks (PSFs) are considered a key mechanism generating frequency-dependent dynamics in plant communities. Negative feedbacks, in particular, are often invoked to explain coexistence and the maintenance of diversity in species-rich communities. However, the primary modeling framework used to study PSFs considers only two plant species, and we lack clear theoretical expectations for how these complex interactions play out in communities with natural levels of diversity. Here, we demonstrate that this canonical model for PSFs is equivalent to a well-studied model from evolutionary game theory, and use this equivalence to characterize the dynamics with an arbitrary number of plant species. Surprisingly, we find that coexistence of more than two species is virtually impossible, suggesting that alternative theoretical frameworks are needed to describe feedbacks observed in diverse natural communities. Drawing on our analysis, we discuss future directions for PSF models and implications for experimental study of PSF-mediated coexistence in the field.

On a global scale, fisheries harvest an estimated 96 million tonnes of fish biomass annually, making them one of the most important drivers of marine ecosystem biodiversity. Yet little is known about the interactions between fisheries and the dynamics of complex food webs in which the harvested species are embedded. We have developed a synthetic model that combines resource economics with complex food webs to examine the direct effects of fishing on exploited species and the indirect impact on other species in the same community. Our model analyses show that the sensitivity of the targeted species increases with its trophic level and decreases with its local interaction complexity (i.e. its number of interactions with prey, predators, and competitors). In addition, we also document a strikingly positive effect of community species richness on the resilience of the harvested species to this disturbance. The indirect effects on other species show specific patterns of spreading across trophic modules that differ systematically from how other disturbances spread across ecological networks. While these results call for further research on how human resource exploitation in general and fishery in particular affect ecological dynamics and biodiversity in naturally complex systems, they also allow for some cautious conclusions. Taken together, our results suggest that the sustainability concerning fishery yield and ecosystem integrity can be maximised by focusing the harvest on low trophic level species with a high local interaction complexity in high biodiversity ecosystems. In this sense, our complex network approach offers a promising avenue for integrating the necessities of generating economic revenue with the protection of natural biodiversity.