Consumer-resource Model Research Articles

Multistability and regime shifts in microbial communities explained by competition for essential nutrients.

Microbial communities routinely have several possible species compositions or community states observed for the same environmental parameters. Changes in these parameters can trigger abrupt and persistent transitions (regime shifts) between such community states. Yet little is known about the main determinants and mechanisms of multistability in microbial communities. Here, we introduce and study a consumer-resource model in which microbes compete for two types of essential nutrients each represented by multiple different metabolites. We adapt game-theoretical methods of the stable matching problem to identify all possible species compositions of such microbial communities. We then classify them by their resilience against three types of perturbations: fluctuations in nutrient supply, invasions by new species, and small changes of abundances of existing ones. We observe multistability and explore an intricate network of regime shifts between stable states in our model. Our results suggest that multistability requires microbial species to have different stoichiometries of essential nutrients. We also find that a balanced nutrient supply promotes multistability and species diversity, yet make individual community states less stable.

On the Consequences of the Interdependence of Stabilizing and Equalizing Mechanisms.

We present an overlooked but important property of modern coexistence theory (MCT), along with two key new results and their consequences. The overlooked property is that stabilizing mechanisms (increasing species' niche differences) and equalizing mechanisms (reducing species' fitness differences) have two distinct sets of meanings within MCT: one in a two-species context and another in a general multispecies context. We demonstrate that the two-species framework is not a special case of the multispecies one, and therefore these two parallel frameworks must be studied independently. Our first result is that, using the two-species framework and mechanistic consumer-resource models, stabilizing and equalizing mechanisms exhibit complex interdependence, such that changing one will simultaneously change the other. Furthermore, the nature and direction of this simultaneous change sensitively depend on model parameters. The second result states that while MCT is often seen as bridging niche and neutral modes of coexistence by building a niche-neutrality continuum, the interdependence between stabilizing and equalizing mechanisms acts to break this continuum under almost any biologically relevant circumstance. We conclude that the complex entanglement of stabilizing and equalizing terms makes their impact on coexistence difficult to understand, but by seeing them as aggregated effects (rather than underlying causes) of coexistence, we may increase our understanding of ecological dynamics.

Estimation of the Solution of the Kolmogorov-Fisher Type Biological Population Task by Taking Into Account the Reaction-Diffusion

The spatial-temporal dynamics of the population is one of the most interesting aspects and problems for environmental modeling. In this article, we will consider some mathematical models based on one-dimensional reaction-diffusion-advection equations for population growth in a heterogeneous habitat. Considering a number of models of increasing complexity, we investigate often the opposite roles of advection and diffusion for the conservation of the population. Whenever possible, we demonstrate basic mathematical methods and provide critical conditions that ensure the survival of the population, in simple systems and in more complex resourceconsumer models.

Temperature triggers a non‐linear response in resource–consumer interaction strength

AbstractAlthough temperature is recognized as a major determinant of many ecological processes, it is still not clear whether temperature increase caused by climate change will strengthen or weaken species interactions. One hypothesis is that interactions will respond non‐monotonically to temperature because thermal performance curves, which determine the strength of these interactions, are also non‐monotonic. To evaluate this hypothesis, we developed a temperature‐dependent consumer–resource model and tested predictions from this model in large freshwater mesocosms populated with green algae (Chlorella vulgaris) and herbivorous zooplankton (Daphnia magna). We found both in the model simulations and empirical investigations that the suppressive effect of the consumer depended non‐monotonically on the temperature. As predicted by the model, Daphnia suppressed the algal maximum per capita growth rate at the temperature that maximized algal growth rate but had little effect on resource growth at either lower or higher temperatures. This finding could help explain why effects of temperature variation on species interaction are variable in the literature and suggests that predicting the effects of temperature on the strength of food web interactions requires knowledge of the thermal performance curves for multiple traits, for multiple species and over a range of temperatures.

CHAOTIC COEXISTENCE IN A RESOURCE–CONSUMER MODEL

We study the interspecies competition in a simple resource–consumer model which includes the resource supply as a dynamic variable. In the model, an organism of each species needs to consume a certain minimum rate of resource (food) to survive; a higher rate of consumption is required for reproduction. We analyze the orbit diagrams and Lyapunov exponents in order to characterize the system dynamical behavior. We observe that under a periodic food supply, the system can exhibit coexistence in the form of limit cycle oscillations. For a certain parameter range, we observe chaotic behavior emerging from successive period doublings and quasi-periodicity.

Constrained optimization as ecological dynamics with applications to random quadratic programming in high dimensions.

Quadratic programming (QP) is a common and important constrained optimization problem. Here, we derive a surprising duality between constrained optimization with inequality constraints, of which QP is a special case, and consumer resource models describing ecological dynamics. Combining this duality with a recent "cavity solution," we analyze high-dimensional, random QP where the optimization function and constraints are drawn randomly. Our theory shows remarkable agreement with numerics and points to a deep connection between optimization, dynamical systems, and ecology.

How Does the Evolution of Universal Ecological Traits Affect Population Size? Lessons from Simple Models.

This article argues that adaptive evolutionary change in a consumer species should frequently decrease (and maladaptive change should increase) population size, producing adaptive decline. This conclusion is based on analysis of multiple consumer-resource models that examine evolutionary change in consumer traits affecting the universal ecological parameters of attack rate, conversion efficiency, and mortality. Two scenarios are investigated. In one, evolutionary equilibrium is initially maintained by opposing effects on the attack rate and other growth rate parameters; the environment or trait is perturbed, and the trait then evolves to a new (or back to a previous) equilibrium. Here evolution exhibits adaptive decline in up to one-half of all cases. The other scenario assumes a genetic perturbation having purely fitness-increasing effects. Here adaptive decline in the consumer requires that the resource be self-reproducing and overexploited and requires a sufficient increase in the attack rate. However, if the resource exhibits adaptive defense via behavior or evolution, adaptive decline may characterize consumer traits affecting all parameters. Favorable environmental change producing parameter shifts similar to those produced by adaptive evolution has similar counterintuitive effects on consumer population size. Many different food web models have already been shown to exhibit such counterintuitive changes in some species.

A note on the complexity of evolutionary dynamics in a classic consumer-resource model

We study how the complexity of evolutionary dynamics in the classic MacArthur consumer-resource model depends on resource uptake and utilization rates. The traditional assumption in such models is that the utilization rate of the consumer is proportional to the uptake rate. More generally, we show that if these two rates are related through a power law (which includes the traditional assumption as a special case), then the resulting evolutionary dynamics in the consumer is necessarily a simple hill-climbing process leading to an evolutionary equilibrium, regardless of the dimension of phenotype space. When utilization and uptake rates are not related by a power law, more complex evolutionary trajectories can occur, including the chaotic dynamics observed in previous studies for high-dimensional phenotype spaces. These results draw attention to the importance of distinguishing between utilization and uptake rates in consumer-resource models.

Impacts of consumer–resource interaction transitions on persistence and long‐term interaction outcomes of random ecological networks

Despite the prevalence of context‐dependent interaction transitions in ecological systems, their impacts on persistence and interaction diversity have scarcely been explored in complex ecological networks. By using multispecies bi‐directional and unidirectional consumer–resource models, representing a continuum of interaction transitions (sign change of interaction outcomes), we investigated the effects of structural interaction transitions on persistence (the fraction of remaining species) and long‐term interaction outcomes in random ecological networks. We found that high interaction strength of exploiting resources generally decreased persistence, and high strength of providing resources increased persistence when the strength of exploiting resources was low in more complex networks; also, the networks with high persistence had a high proportion of mutualistic interactions relative to antagonistic interactions present initially and over the long term. The shifting of interaction strengths shaped the long‐term interaction compositions. Meanwhile, population dynamics, especially species extinction, affected the difference between initial and long‐term interactions. Based on classical consumer–resource theory, these results establish a transitional continuum of interaction outcomes in ecological networks and imply a theoretical association among interaction transition, community persistence and interaction diversity.

Combined effect of environmental temperature and density-dependent processes on the evolution of seasonal metabolic rate patterns

Species exhibit large diversity in their seasonal metabolic patterns which are traditionally explained by habitat specific seasonal temperature changes and various thermoregulatory adaptations. However, due to seasonal changes in resource abundances, density-dependent, ecological processes can also be important selective forces shaping the evolution of metabolic patterns. In the present theoretical study, the combined effect of environmental temperature and resource availability on the evolutionarily stable metabolic strategies is investigated in a consumer–resource model. Our results suggest that, under a broad range of circumstances, density-dependent mechanisms favor the selection of active metabolic regulation, where the metabolic rate differs from the thermally optimal value. This effect may be temporary, limited only to a brief period at seasonal changes, or permanent depending on the implied energetic cost and the relative timescale of environmental changes as compared to the generation time.

Considering the effects of temperature×nutrient interactions on the thermal response curve of carrying capacity.

Climate warming will likely destabilize populations or drive consumers locally extinct. These predictions arise from consumer-resource models incorporating temperature-dependent parameters, and the accuracy of these predictions hinges on the validity of temperature scalings for each parameter. Among all parameters, carrying capacity (K) is the most ill-defined and the temperature scaling of this parameter has no empirically verified foundation. Most studies assume that K declines exponentially with warming, but others have assumed a positive or no relationship between K and temperature. Here, I developed a theoretical foundation for a temperature scaling of K based on physiological principles of temperature and nutrient limitation of phytoplankton growth. The trade-off between thermodynamics and nutrient uptake yields a unimodal thermal response curve for K, and this prediction is supported by empirical data on both phytoplankton and insects. Analyses of consumer-resource models demonstrate the primacy of K in determining predictions of coexistence and stability. Since K exerts a dominant influence on model predictions, ecologists should carefully consider the temperature scaling of K for the species and region in question to ensure accurate estimates of population stability and extinction risk.

Effects of Predator Avoidance Behavior on the Coexistence of Competing Prey

Predator avoidance behavior, in which prey limit foraging activities in the presence of predation threats, affects the dynamics of many ecological communities. Despite the growing theoretical appreciation of the role predation plays in coexistence, predator avoidance behavior has yet to be incorporated into the theory in a general way. We introduce adaptive avoidance behavior to a consumer-resource model with three trophic levels to ask whether the ability of prey-the middle trophic level-to avoid predators alters their ability to coexist. We determine the characteristics of cases in which predator avoidance behavior changes prey coexistence or the order of competitive dominance. The mechanism underlying such changes is the weakening of apparent competition relative to resource competition in determining niche overlap, even with resource intake costs. Avoidance behavior thus generally promotes coexistence if prey partition resources but not predators, whereas it undermines coexistence if prey partition predators but not resources. For any given case, the changes in the average fitness difference between two species resulting from avoidance behavior interact with changes in niche overlap to determine coexistence. These results connect the substantial body of theoretical work on avoidance behavior and population dynamics with the body of theory on competitive coexistence.

Temperature Modifies Consumer-Resource Interaction Strength Through Its Effects on Biological Rates and Body Mass

Temperature is the most significant environmental gradient at the global scale, impacting the distributions of species and their ecological interactions. It is now established that temperature affects several biological rates and body mass, and can, in turn, alter interaction strength. Latitudinal variation in the strength of interactions has been observed for trophic and competitive interactions and many studies support that biotic interactions are more intense at low latitudes. Nevertheless, the mechanisms underlying the temperature dependence of trophic regulation, the effect of consumers on their preys, remain unclear. The aim of our study is to get better insights on the effects of temperature on trophic regulation. We used a consumer-resource model and considered that organisms' biological rates present a unimodal thermal response and that body mass decreases with temperature. We compared three measures of interaction strength: per capita, per population and net interaction strength. Our results demonstrate that the effect of temperature on interaction strength is contingent upon which species’ biological rates are temperature dependent. When all biological rates are temperature dependent, the thermal response of interaction strength is hump-shaped following the scaling of search rate, whilst it is monotonically decreasing when only mortality rates vary with temperature. Finally, we show that temperature can indirectly impact trophic interaction strength through the temperature-size rule. A decrease in organisms' body size due to temperature induces a decrease in per capita and per population interaction strength and tend to decrease net interaction strength, depending on which trophic level follows the temperature-size rule. Our analysis gives an overview of how temperature, through various effects, may impact different measures of interaction strength.

Available energy fluxes drive a transition in the diversity, stability, and functional structure of microbial communities.

A fundamental goal of microbial ecology is to understand what determines the diversity, stability, and structure of microbial ecosystems. The microbial context poses special conceptual challenges because of the strong mutual influences between the microbes and their chemical environment through the consumption and production of metabolites. By analyzing a generalized consumer resource model that explicitly includes cross-feeding, stochastic colonization, and thermodynamics, we show that complex microbial communities generically exhibit a transition as a function of available energy fluxes from a “resource-limited” regime where community structure and stability is shaped by energetic and metabolic considerations to a diverse regime where the dominant force shaping microbial communities is the overlap between species’ consumption preferences. These two regimes have distinct species abundance patterns, different functional profiles, and respond differently to environmental perturbations. Our model reproduces large-scale ecological patterns observed across multiple experimental settings such as nestedness and differential beta diversity patterns along energy gradients. We discuss the experimental implications of our results and possible connections with disorder-induced phase transitions in statistical physics.

The mechanistic basis for higher-order interactions and non-additivity in competitive communities.

Motivated by both analytical tractability and empirical practicality, community ecologists have long treated the species pair as the fundamental unit of study. This notwithstanding, the challenge of understanding more complex systems has repeatedly generated interest in the role of so-called higher-order interactions (HOIs) imposed by species beyond the focal pair. Here we argue that HOIs - defined as non-additive effects of density on per capita growth - are best interpreted as emergent properties of phenomenological models (e.g. Lotka-Volterra competition) rather than as distinct 'ecological processes' in their own right. Using simulations of consumer-resource models, we explore the mechanisms and system properties that give rise to HOIs in observational data. We demonstrate that HOIs emerge under all but the most restrictive of assumptions, and that incorporating non-additivity into phenomenological models improves the quantitative and qualitative accuracy of model predictions. Notably, we also observe that HOIs derive primarily from mechanisms and system properties that apply equally to single-species or pairwise systems as they do to more diverse communities. Consequently, there exists a strong mandate for further recognition of non-additive effects in both theoretical and empirical research.

Dynamics of a consumer-resource reaction-diffusion model : Homogeneous versus heterogeneous environments.

We study the dynamics of a consumer-resource reaction-diffusion model, proposed recently by Zhang et al. (Ecol Lett 20(9):1118-1128, 2017), in both homogeneous and heterogeneous environments. For homogeneous environments we establish the global stability of constant steady states. For heterogeneous environments we study the existence and stability of positive steady states and the persistence of time-dependent solutions. Our results illustrate that for heterogeneous environments there are some parameter regions in which the resources are only partially limited in space, a unique feature which does not occur in homogeneous environments. Such difference between homogeneous and heterogeneous environments seems to be closely connected with a recent finding by Zhang et al. (2017), which says that in consumer-resource models, homogeneously distributed resources could support higher population abundance than heterogeneously distributed resources. This is opposite to the prediction by Lou (J Differ Equ 223(2):400-426, 2006. https://doi.org/10.1016/j.jde.2005.05.010 ) for logistic-type models. For both small and high yield rates, we also show that when a consumer exists in a region with a heterogeneously distributed input of exploitable renewed limiting resources, the total population abundance at equilibrium can reach a greater abundance when it diffuses than when it does not. In contrast, such phenomenon may fail for intermediate yield rates.

Evolution of size-dependent intraspecific competition predicts body size scaling of metabolic rate.

Growth in body size is accompanied by changes in foraging capacity and metabolic costs, which lead to changes in competitive ability during ontogeny. The resulting size‐dependent competitive asymmetry influences population dynamics and community structure, but it is not clear whether natural selection leads to asymmetry in intraspecific competition.We address this question by using a size‐structured consumer–resource model, in which the strength and direction of competitive asymmetry between different consumer individuals depends on the scaling of maximum ingestion and maintenance metabolism with consumer body size. We use adaptive dynamics to study selection on the scaling exponents of these processes.Selection leads to an identical scaling of maximum ingestion and maintenance metabolism with consumer body size. Equal scaling exponents neutralize strong competitive differences within the consumer population, because all consumer individuals require the same amount of resources to cover maintenance requirements. Furthermore, the scaling exponents respond adaptively to changes in mortality such that biomass production through growth or reproduction increases in the life stage that is subject to increased mortality. Also, decreasing size at birth leads to increased investment in juvenile growth, while increasing maximum size leads to increased investment in post‐maturation growth and reproduction.These results provide an explanation for observed variation in the ontogenetic scaling of metabolic rate with body size. Data of teleost fish are presented that support these predictions. However, selection towards equal scaling exponents is contradicted by empirical findings, which suggests that additional ecological complexity beyond this basic consumer–resource interaction is required to understand the evolution of size‐dependent asymmetry in intraspecific competition. A plain language summary is available for this article.

Optimal control of irrupting pest populations in a climate-driven ecosystem.

Irruptions of small consumer populations, driven by pulsed resources, can lead to adverse effects including the decline of indigenous species or increased disease spread. Broad-scale pest management to combat such effects benefits from forecasting of irruptions and an assessment of the optimal control conditions for minimising consumer abundance. We use a climate-based consumer-resource model to predict irruptions of a pest species (Mus musculus) population in response to masting (episodic synchronous seed production) and extend this model to account for broad-scale pest control of mice using toxic bait. The extended model is used to forecast the magnitude and frequency of pest irruptions under low, moderate and high control levels, and for different timings of control operations. In particular, we assess the optimal control timing required to minimise the frequency with which pests reach ‘plague’ levels, whilst avoiding excessive toxin use. Model predictions suggest the optimal timing for mouse control in beech forest, with respect to minimising plague time, is mid-September. Of the control regimes considered, a seedfall driven biannual-biennial regime gave the greatest reduction in plague time and plague years for low and moderate control levels. Although inspired by a model validated using house mouse populations in New Zealand forests, our modelling approach is easily adapted for application to other climate-driven systems where broad-scale control is conducted on irrupting pest populations.

Некоторые особенности групповой динамики в агентной модели «ресурс-потребитель»

Некоторые особенности групповой динамики в агентной модели «ресурс-потребитель»

Size-dependent movement explains why bigger is better in fragmented landscapes.

Body size is a fundamental trait known to allometrically scale with metabolic rate and therefore a key determinant of individual development, life history, and consequently fitness. In spatially structured environments, movement is an equally important driver of fitness. Because movement is tightly coupled with body size, we expect habitat fragmentation to induce a strong selection pressure on size variation across and within species. Changes in body size distributions are then, in turn, expected to alter food web dynamics. However, no consensus has been reached on how spatial isolation and resource growth affect consumer body size distributions. Our aim was to investigate how these two factors shape the body size distribution of consumers under scenarios of size‐dependent and size‐independent consumer movement by applying a mechanistic, individual‐based resource–consumer model. We also assessed the consequences of altered body size distributions for important ecosystem traits such as resource abundance and consumer stability. Finally, we determined those factors that explain most variation in size distributions. We demonstrate that decreasing connectivity and resource growth select for communities (or populations) consisting of larger species (or individuals) due to strong selection for the ability to move over longer distances if the movement is size‐dependent. When including size‐dependent movement, intermediate levels of connectivity result in increases in local size diversity. Due to this elevated functional diversity, resource uptake is maximized at the metapopulation or metacommunity level. At these intermediate levels of connectivity, size‐dependent movement explains most of the observed variation in size distributions. Interestingly, local and spatial stability of consumer biomass is lowest when isolation and resource growth are high. Finally, we highlight that size‐dependent movement is of vital importance for the survival of populations or communities within highly fragmented landscapes. Our results demonstrate that considering size‐dependent movement is essential to understand how habitat fragmentation and resource growth shape body size distributions—and the resulting metapopulation or metacommunity dynamics—of consumers.