Transient dynamics limit the effectiveness of keystone predation in bringing about coexistence

We analyze the transient dynamics of simple models of keystone predation, in which a predator preferentially consumes the dominant of two (or more) competing prey species. We show that coexistence is unlikely in many systems characterized both by successful invasion of either prey species into the food web that lacks it and by a stable equilibrium with high densities of all species. Invasion of the predator-resistant consumer species often causes the resident, more vulnerable prey to crash to such low densities that extinction would occur for many realistic population sizes. Subsequent transient cycles may entail very low densities of the predator or of the initially successful invader, which may also preclude coexistence of finite populations. Factors causing particularly low minimum densities during the transient cycles include biotic limiting resources for the prey, limited resource partitioning between the prey, a highly efficient predator with relatively slow dynamics, and a vulnerable prey whose population dynamics are rapid relative to the less vulnerable prey. Under these conditions, coexistence of competing prey via keystone predation often requires that the prey's competitive or antipredator characteristics fall within very narrow ranges. Similar transient crashes are likely to occur in other food webs and food web models.     

Impact of intraguild predation and stage structure on simple communities along a productivity gradient

We analyze the consequences of intraguild predation and stage structure for the possible composition of a three-species community consisting of resource, consumer, and predator. Intraguild predation, a special case of omnivory, induces two major differences with traditional linear food chain models: the potential for the occurrence of two alternative stable equilibria at intermediate levels of resource productivity and the extinction of the consumer at high productivities. At low productivities, the consumer dominates, while at intermediate productivities, the predator and the consumer can coexist. The qualitative behavior of the model is robust against addition of an invulnerable size class for the consumer population and against addition of an initial, nonpredatory stage for the predator population, which means that the addition of stage structure does not change the pattern. Unless the top predator is substantially less efficient on the bottom resource, it tends to drive the intermediate species extinct over a surprisingly large range of productivities, thus making coexistence generally impossible. These theoretical results indicate that the conditions for stable food chains involving intraguild predation cannot involve strong competition for the bottommost resource.     

Dynamics of a intraguild predation model with generalist or specialist predator

Intraguild predation (IGP) is a combination of competition and predation which is the most basic system in food webs that contains three species where two species that are involved in a predator/prey relationship are also competing for a shared resource or prey. We formulate two intraguild predation (IGP: resource, IG prey and IG predator) models: one has generalist predator while the other one has specialist predator. Both models have Holling-Type I functional response between resource-IG prey and resource-IG predator; Holling-Type III functional response between IG prey and IG predator. We provide sufficient conditions of the persistence and extinction of all possible scenarios for these two models, which give us a complete picture on their global dynamics. In addition, we show that both IGP models can have multiple interior equilibria under certain parameters range. These analytical results indicate that IGP model with generalist predator has “top down” regulation by comparing to IGP model with specialist predator. Our analysis and numerical simulations suggest that: (1) Both IGP models can have multiple attractors with complicated dynamical patterns; (2) Only IGP model with specialist predator can have both boundary attractor and interior attractor, i.e., whether the system has the extinction of one species or the coexistence of three species depending on initial conditions; (3) IGP model with generalist predator is prone to have coexistence of three species.     

Spatial dynamics of keystone predation

1. I investigated the effects of dispersal on communities of keystone predators and prey. I obtained two key results. 2. First, a strong trade-off between competitive ability and predator susceptibility allows consumer coexistence over a large resource productivity range, but it also lowers the predator-susceptible superior competitor's abundance and increases its risk of extinction. Thus, unexpectedly, dispersal plays a more important role in coexistence when predator-mediated coexistence is strong rather than weak. The interplay between the trade-off, small population sizes resulting from transient oscillations, and dispersal leads to qualitatively different species distributions depending on the relative mobilities of the consumers and predator. These differences yield comparative predictions that can be tested with data on trade-off strength, dispersal rates, and species distributions across productivity gradients. 3. Second, there is an asymmetry between species in their dispersal effects: the predator-resistant inferior competitor's dispersal has a large effect, but the predator-susceptible superior competitor's dispersal has no effect, on coexistence and species' distributions. The inferior competitor's dispersal also mediates the predator's dispersal effects: the predator's dispersal has no effect when the inferior competitor is immobile, and a large effect when it is mobile. The net outcome of the direct and indirect effects of the inferior competitor's dispersal is a qualitative change in the species' distributions from interspecific segregation to interspecific aggregation. 4. The important point is that differences between species in how they balance resource acquisition and predator avoidance can lead to unexpected differences in their dispersal effects. While consumer coexistence in the absence of dispersal is driven largely by the top predator, consumer coexistence in the presence of dispersal is driven largely by the predator-resistant inferior competitor.     

The impact of consumer-resource cycles on the coexistence of competing consumers

This article seeks to determine the extent to which endogenous consumer-resource cycles can contribute to the coexistence of competing consumer species. It begins with a numerical analysis of a simple model proposed by Armstrong and McGehee. This model has a single resource and two consumers, one with a linear functional response and one with a saturating response. Coexistence of the two consumer species can occur when the species with a saturating response generates population cycles of the resource, and also has a lower resource requirement for zero population growth. Coexistence can be achieved over a wide range of relative efficiencies of the two consumers provided that the functional response of the saturating consumer reaches its half-saturation value when the resource population is a small fraction of its carrying capacity. In this case, the range of efficiencies allowing coexistence is comparable to that when two competitors have stable dynamics and a high degree of resource partitioning. A variety of modifications of this basic model are analyzed to investigate the consequences for coexistence of different resource growth equations, different functional and numerical response shapes, and other factors. Large differences in functional response shape appear to be the most important factor in producing robust coexistence via resource cycles. If the unstable species has a concave numerical response, this greatly expands the conditions allowing coexistence. If the stable consumer species has a convex (accelerating) functional and/or numerical response, the range of conditions allowing coexistence is also expanded. We argue that large between-species differences in functional response form can often be produced by between-consumer differences in the adaptive adjustments of foraging effort to food density. Consumer-resource cycles can also expand the conditions allowing coexistence when there is resource partitioning, but do so primarily when resource partitioning is relatively slight; this makes the ease of coexistence relatively independent of consumer similarity.     

The effects of enrichment on the dynamics of apparent competitive interactions in stage-structured systems

In the absence of other limiting factors, assemblages in which species share a common, effective natural enemy are not expected to persist. Although a variety of mechanisms have been postulated to explain the coexistence of species that share natural enemies, the role of productivity gradients has not been explored in detail. Here, we examine how enrichment can affect the outcome of apparent competition. We develop a structured resource/consumer/natural enemy model in which the prey are exposed to attacks during a vulnerable life phase, the length of which depends on resource availability. With a single prey species, the model exhibits the "paradox of enrichment," with unstable dynamics at high levels of resource productivity. We extend this model to consider two prey species linked by a shared predator, each with their own distinct resource base. We derive invasion and stability conditions and examine how enrichment influences prey species exclusion and coexistence. Contrary to expectations from simpler, prey-dependent models, apparent competition is not necessarily strong at high productivity, and prey species coexistence may thus be more likely in enriched environments. Further, the coexistence of apparent competitors may be facilitated by unstable dynamics. These results contrast with the standard theory that apparent competition in productive environments leads to nonpersistent interactions and that coexistence of multispecies interactions is more likely under equilibrial conditions.     

Size-dependent interactions inhibit coexistence in intraguild predation systems with life-history omnivory

Growth in body size during ontogeny often results in changes in diet, leading to life-history omnivory. In addition, growth is often dependent on food density. Using a physiologically structured population model, we investigated the effects of these two aspects of individual growth in a system consisting of two size-structured populations, an omnivorous top predator and an intermediate consumer. With a single shared resource for both populations, we found that life-history omnivory decreases the likelihood of coexistence between top predator and intermediate consumer in this intraguild predation (IGP) system. This result contrasts with previous unstructured models and stage-structured models without food-dependent development. Food-dependent development and size-dependent foraging abilities of the predator resulted in a positive feedback between foraging success on the shared resource at an early life stage and foraging success on the intermediate consumer later in life. By phenomenologically incorporating this feedback in an unstructured IGP model, we show that it also demotes coexistence in this simple setting, demonstrating the robustness of the negative effect of this feedback.     

Stage-structured ontogeny in resource populations generates non-additive stabilizing and de-stabilizing forces in populations and communities

Demographic heterogeneity influences how populations respond to density dependent intraspecific competition and trophic interactions. Distinct stages across an organism's development, or ontogeny, are an important example of demographic heterogeneity. In consumer populations, ontogenetic stage structure has been shown to produce categorical differences in population dynamics, community dynamics and even species coexistence compared to models lacking explicit ontogeny. The study of consumer–resource interactions must also consider the ontogenetic stage structure of the resource itself, particularly plants, given their fundamental role at the basis of terrestrial food webs. We incorporate distinct ontogenetic stages of plants into an adaptable multi-stage consumer–resource modeling framework that facilitates studying how stage specific consumers shape trophic dynamics at low trophic levels. We describe the role of density dependent demographic rates in mediating the dynamics of stage-structured plant populations. We then investigate how these demographic rates interact with consumer pressure to influence stability and coexistence in multiple stage-specific consumer–resource interactions. Results detail how density dependent effects across distinct ontogenetic stages in plant development produce non-additivity in the drivers of dynamic stability both in single populations and in consumer–resource settings, challenging the ubiquity of certain traditional ecological dynamic paradigms. We also find categorical differences in the population variability induced by herbivores consuming separate plant stages. Consumer–resource models, such as plant–herbivore interactions, often average out demographic heterogeneity in populations. Here, we show that explicitly including plant demographic heterogeneity through ontogeny yields distinct dynamic expectations for both plants and herbivores compared to traditional consumer–resource formulations. Our results indicate that efforts to understand the demographic effect of herbivores on plant populations may need to also consider the effects of plant demographics on herbivores and the reciprocal relationship between them.     

Omnivory and stability of food webs

The role and prevalence of omnivory, defined as feeding on more than one trophic level, are critical to understand food web structure and dynamics. Whether omnivory stabilizes or destabilizes food webs depends on the assumptions of theoretical models. Recently, Tanabe and Namba [Tanabe, K., Namba, T., 2005. Omivory creates chaos in simple food web models. Ecology 86, 3411–3414] found that omnivory can create chaos in a simple food web model with linear functional responses and 12 model parameters. In this paper, first we numerically examined bifurcation diagrams with all the parameters as bifurcation parameters, including self-limitation of the intermediate consumer and predator. Chaos spontaneously appears when the intraguild predator’s consumption rates are low for nutrient-rich intraguild prey and high for nutrient-poor basal resource and the intraguild prey reproduces efficiently feeding on the basal resource. Second, we investigated effects of the addition of a species into the basic model food web which exhibits chaos. The additional species is assumed to consume only one of the basal resource, intermediate consumer, or omnivorous predator. Consequences of the addition greatly depend on the trophic level on which the additional species feeds. While the increased diversity of predators feeding on the intermediate consumer stabilizes the web, the increased diversity of prey feeding on the basal resource induces collapse of the food web through exploitative competition for the basal resource. The food chain with the top predator feeding on the omnivorous predator is highly unstable unless the mortality of the top predator is extremely low. We discuss the possibility of real-world chaos and the reason why stability of food webs strongly depends on the topological structure of the webs. Finally, we consider the implications of our results for food web theory and resource management.     

Not attackable or not crackable—How pre‐ and post‐attack defenses with different competition costs affect prey coexistence and population dynamics

It is well‐known that prey species often face trade‐offs between defense against predation and competitiveness, enabling predator‐mediated coexistence. However, we lack an understanding of how the large variety of different defense traits with different competition costs affects coexistence and population dynamics. Our study focusses on two general defense mechanisms, that is, pre‐attack (e.g., camouflage) and post‐attack defenses (e.g., weaponry) that act at different phases of the predator—prey interaction. We consider a food web model with one predator, two prey types and one resource. One prey type is undefended, while the other one is pre‐ or post‐attack defended paying costs either by a higher half‐saturation constant for resource uptake or a lower maximum growth rate. We show that post‐attack defenses promote prey coexistence and stabilize the population dynamics more strongly than pre‐attack defenses by interfering with the predator's functional response: Because the predator spends time handling “noncrackable” prey, the undefended prey is indirectly facilitated. A high half‐saturation constant as defense costs promotes coexistence more and stabilizes the dynamics less than a low maximum growth rate. The former imposes high costs at low resource concentrations but allows for temporally high growth rates at predator‐induced resource peaks preventing the extinction of the defended prey. We evaluate the effects of the different defense mechanisms and costs on coexistence under different enrichment levels in order to vary the importance of bottom‐up and top‐down control of the prey community.     

幼年竞争瓶颈对动力学行为的影响（英文）

通过建立具有非线性成熟率的食物网模型研究了幼年竞争瓶颈对种群动力学行为的影响,结论显示当竞争瓶颈比较弱的时,捕食者生活史中的幼年瓶颈对系统的影响要大于成年.模型存在两种可能的共存态或双稳定性,即消费者-捕食者和消费者平衡态共存,但是瓶颈不能诱导系统的双稳定性.进一步研究说明了选择不同的瓶颈或初始条件,瓶颈能够改变次级消费者对捕食者的净影响.     

Biodiversity,habitat area,resource growth rate and interference competition

For the majority of species, per capita growth rate correlates negatively with population density. Although the popular logistic equation for the growth of a single species incorporates this intraspecific competition, multi-trophic models often ignore self-limitation of the consumers. Instead, these models often assume that the predator-prey interactions are purely exploitative, employing simple Lotka-Volterra forms in which consumer species lack intraspecific competition terms. Here we show that intraspecific interference competition can account for the stable coexistence of many consumer species on a single resource in a homogeneous environment. In addition, our work suggests a potential mechanism for field observations demonstrating that habitat area and resource productivity strongly positively correlate to biodiversity. In the special case of a modified Lotka-Volterra model describing multiple predators competing for a single resource, we present an ordering procedure that determines the deterministic fate of each specific consumer. Moreover, we find that the growth rate of a resource species is proportional to the maximum number of consumer species that resource can support. In the limiting case, when the resource growth rate is infinite, a model with intraspecific interference reduces to the conventional Lotka-Volterra competition model where there can be an unlimited number of coexisting consumers. This highlights the crucial role that resource growth rates may play in promoting coexistence of consumer species.     

Productivity, dispersal and the coexistence of intraguild predators and prey

A great deal is known about the influence of dispersal on species that interact via competition or predation, but very little is known about the influence of dispersal on species that interact via both competition and predation. Here, I investigate the influence of dispersal on the coexistence and abundance-productivity relationships of species that engage in intraguild predation (IGP: competing species that prey on each other). I report two key findings. First, dispersal enhances coexistence when a trade-off between resource competition and IGP is strong and/or when the Intraguild Prey has an overall advantage, and impedes coexistence when the trade-off is weak and/or when the Intraguild Predator has an overall advantage. Second, the Intraguild Prey's abundance-productivity relationship depends crucially on the dispersal rate of the Intraguild Predator, but the Intraguild Predator's abundance-productivity relationship is unaffected by its own dispersal rate or that of the Intraguild Prey. This difference arises because the two species engage in both a competitive interaction as well as an antagonistic (predator-prey) interaction. The Intraguild Prey, being the intermediate consumer, has to balance the conflicting demands of resource acquisition and predator avoidance, while the Intraguild Predator has to contend only with resource acquisition. Thus, the Intraguild Predator's abundance increases monotonically with resource productivity regardless of either species' dispersal rate, while the Intraguild Prey's abundance-productivity relationship can increase, decrease, or become hump-shaped with increasing productivity depending on the Intraguild Predator's dispersal rate. The important implication is that a species' trophic position determines the effectiveness of dispersal in sampling spatial environmental heterogeneity. The dispersal behavior of a top predator is likely to have a stronger effect on coexistence and spatial patterns of abundance than the dispersal behavior of an intermediate consumer.     

A schistosomiasis model with mating structure and time delay

A system of homogeneous equations with a time delay is used to model the population dynamics of schistosomes. The model includes the parasite’s mating structure, multiple resistant schistosome strains, and biological complexity associated with the parasite’s life cycle. Invasion criteria of resistant strains and coexistence threshold conditions are derived. These results are used to explore the impact of drug treatment on resistant strain survival. Numerical simulations indicate that the dynamical behaviors of the current model are not qualitatively different from those derived from an earlier model that ignores the impact of time delays associated with the multiple stages in parasite’s life cycle. However, quantitatively the time delays make it more likely for drug-resistant strains to invade in a parasite population.     

A ratio-dependent food chain model and its applications to biological control

While biological controls have been successfully and frequently implemented by nature and human, plausible mathematical models are yet to be found to explain the often observed deterministic extinctions of both pest and control agent in such processes. In this paper we study a three trophic level food chain model with ratio-dependent Michaelis-Menten type functional responses. We shall show that this model is rich in boundary dynamics and is capable of generating such extinction dynamics. Two trophic level Michaelis-Menten type ratio-dependent predator-prey system was globally and systematically analyzed in details recently. A distinct and realistic feature of ratio-dependence is its capability of producing the extinction of prey species, and hence the collapse of the system. Another distinctive feature of this model is that its dynamical outcomes may depend on initial populations levels. Theses features, if preserved in a three trophic food chain model, make it appealing for modelling certain biological control processes (where prey is a plant species, middle predator as a pest, and top predator as a biological control agent) where the simultaneous extinctions of pest and control agent is the hallmark of their successes and are usually dependent on the amount of control agent. Our results indicate that this extinction dynamics and sensitivity to initial population levels are not only preserved, but also enriched in the three trophic level food chain model. Specifically, we provide partial answers to questions such as: under what scenarios a potential biological control may be successful, and when it may fail. We also study the questions such as what conditions ensure the coexistence of all the three species in the forms of a stable steady state and limit cycle, respectively. A multiple attractor scenario is found.     

Trophic supplements to intraguild predation

Intraguild predation (IGP) is a dominant community module in terrestrial food webs that occurs when multiple consumers feed both on each other and on a shared prey. This specific form of omnivory is common in terrestrial communities and is of particular interest for conservation biology and biological control given its potential to disrupt management of threatened or pest species. Extensive theory exists to describe the dynamics of three-species IGP, but these models have largely overlooked the potential for other, exterior interactions, to alter the dynamics within the IGP module. We investigated how three forms of feeding outside of the IGP module by intraguild predators (i.e. trophic supplementation) affect the dynamics of the predators (both IG predator and IG prey) and their shared resource. Specifically, we examined how the provision of a constant donor-controlled resource, the availability of an alternative prey species, and predator plant-feeding affect the dynamics of IGP models. All three forms of trophic supplements modified the basic expectations of IGP theory in two important ways, and their effects were similar. First, coexistence was possible without the IG prey being a superior competitor for the original shared resource if the IG prey could effectively exploit one of the types of trophic supplements. However, supplements to the IG predator restricted the potential for coexistence. Second, supplements to the IG prey ameliorated the disruptive effects of the IG predator on the suppression of the shared resource, promoting effective control of the resource in the presence of both predators. Consideration of these three forms of trophic supplementation, all well documented in natural communities, adds substantial realism and predictive power to intraguild predation theory.     

Grassland-herbivore interactions: how do grazers coexist?

We develop a new approach to modeling grazing systems that links foraging characteristics (intake and digestive constraints) with resource dynamics via the probability of encounter with different grass heights. Three complementary models are presented: the generation of a grass height structure through selective grazing; investigating the conditions for consumer coexistence; and, using a simplified resource structure, the consequences for consumer abundance. The main finding is that coexistence between grazers differing in body size is possible if a single-resource type becomes differentiated in its height structure. Large grazers can facilitate food availability for smaller species but with the latter being competitively dominant. The relative preference given to different resource partitions is important in determining the nature of population interactions. Large-body and small-body grazer populations can interact through competitive, parasitic, commensalist, or amensalist relationships, depending on the way they partition the resource as well as their relative populations and the dynamics of resource renewal. The models provide new concepts of multispecies carrying capacity (stock equilibrium) in grazed systems with implications for conservation and management. We conclude that consumer species are not substitutable; therefore, the use of rangeland management concepts such as "livestock units" may be inappropriate.     

Influence of consumer mutual interference on the stabilization of a three-level trophic system

In this paper, we present a three-level (food–prey–predator) trophic food chain which includes consumer mutual interference (MIF). In contrast with other analyses, we consider the effect of both prey and predator MIF on the dynamics of a three-level trophic system. MIF is generally considered to exert a stabilizing effect on population dynamics based on the predator–prey model. However, results from analytical and numerical simulations utilizing a simple three-species food chain model suggest that while the addition of prey MIF to the model provides a stabilizing influence, as the chaotic dynamics collapse to a stable steady state, adding only predator MIF to the model can only stabilize the system at intermediate MIF values. The three-species trophic food chain is also stabilized when combination of both prey and predator MIF is added to the model. Our work serves to provide insight into the effects of MIF in the real world.     

Compartmentalization and niche differentiation: causal patterns of competition and coexistence

The current major models of coexistence of species on the same resources are briefly summarized. It is then shown that analysis of supposedly competitive systems in terms of the physical four dimensions of phase-space is sufficient to understand the causes for coexistence and for competitive exclusion. Thus, the multiple dimensions of niche theory are reduced to factors which define the magnitudes of the phase-spatial system, in particular the boundaries of population spaces and of periods of activity. Excluding possible cooperative interaction between consumers, it appears that coexistence of species on thesame kind of limiting resource is possible only in cases of compartmentalization either in space, or in time, of resource consumption, i.e. if each consumer species disposes of a separate resource supply. Three criteria were found to be decisive for successful compartmentalization (i.e. for coexistence): 1. the vector of the resource flow; 2. relative mobility between consumers and resource units; 3. dependence or independence of resource flow on previous consumption. The traditional terminology of niche theory and of competition theory in general proved to be inadequate for analytical treatment of problems of coexistence.