The prerequisites for and likelihood of generalist-specialist coexistence

Mathematical models of three-consumer-two-resource systems are used to explore the possibility of coexistence when one consumer is a generalist utilizing both resources, and the other two are specialists utilizing only one. Such coexistence requires strongly saturating functional or numerical responses in at least one consumer and the presence of sustained asynchronous variation in resource abundances. Given these conditions, the effects of three dichotomous factors on the range of parameters allowing coexistence are examined: flexible versus inflexible resource choice by the generalist, endogenous or exogenous cause of resource cycles, and location of the two resources in a single habitat versus two habitats. Coexistence of all three species is found to be possible for all combinations of these factors except for inflexible choice in a two-habitat environment. Generalists experience frequency-dependent fitness because, when they are abundant, they synchronize resource cycles and/or reduce their amplitude. When the generalist can adaptively adjust its relative foraging on the two resources, coexistence conditions are broadened considerably, and coexistence commonly occurs readily with exogenous variation in resource growth and with resources located in distinct habitats. Adaptive behavior increases the generalist's ability to both synchronize and dampen resource cycles.     

Coexistence of cycling and dispersing consumer species: Armstrong and McGehee in space

Two competing consumer species may coexist using a single homogeneous resource when the more efficient consumer--the one having the lowest equilibrium resource density--has a more nonlinear functional response that generates consumer-resource cycles. We extend this model of nonequilibrium coexistence, as proposed by Armstrong and McGehee, by putting the interaction into a spatial context using two frameworks: a spatially explicit individual-based model and a spatially implicit metapopulation model. We find that Armstrong and McGehee's mechanism of coexistence can operate in a spatial context. However, individual-based simulations suggest that decreased dispersal restricts coexistence in most cases, whereas differential equation models of metapopulations suggest that a low rate of dispersal between subpopulations often increases the coexistence region. This difference arises in part because of two potentially opposing effects on coexistence due to the asynchrony in the temporal dynamics at different locations. Asynchrony implies that the less efficient species is more likely to be favored in some spatial locations at any given time, which broadens the conditions for coexistence. On the other hand, asynchrony and dispersal can also reduce the amplitude of local population cycles, which restricts coexistence. The relative influence of these two effects depends on details of the population dynamics and the representation of space. Our results also demonstrate that coexistence via the Armstrong-McGehee mechanism can occur even when there is little variation in the global densities of either the consumers or the resource, suggesting that empirical studies of the mechanisms should measure densities on several spatial scales.     

Grazers and Diggers: Exploitation Competition and Coexistence among Foragers with Different Feeding Strategies on a Single Resource

A mathematical model is presented that describes a system where two consumer species compete exploitatively for a single renewable resource. The resource is distributed in a patchy but homogeneous environment; that is, all patches are intrinsically identical. The two consumer species are referred to as diggers and grazers, where diggers deplete the resource within a patch to lower densities than grazers. We show that the two distinct feeding strategies can produce a heterogeneous resource distribution that enables their coexistence. Coexistence requires that grazers must either move faster than diggers between patches or convert the resources to population growth much more efficiently than diggers. The model shows that the functional form of resource renewal within a patch is also important for coexistence. These results contrast with theory that considers exploitation competition for a single resource when the resource is assumed to be well mixed throughout the system.     

The effect of the Holling type II functional response on apparent competition

This article analyzes the classical 2-resource-1-consumer apparent competition community module with the Holling type II functional response. Two types of resource regulation (top-down vs. combined top-down and bottom-up) and two types of consumer behaviors (inflexible consumers with fixed preferences for resources vs. adaptive consumers) are considered. When resources grow exponentially and consumers are inflexible foragers, one resource is always outcompeted due to strong apparent competition. Density dependent resource growth relaxes apparent competition so that resources can coexist. As multiple attractors (either equilibria or limit cycles) coexist, population dynamics and community composition depend on initial population densities. Population dynamics change dramatically when consumers forage adaptively. In this case, the results both for top-down, and combined top-down and bottom-up regulation are similar and they show that species persistence occurs for a much larger set of parameter values when compared with inflexible consumers. Moreover, population dynamics will be chaotic when resource carrying capacities are high enough. This shows that adaptive consumer switching can destabilize population dynamics.     

Body size and species coexistence in consumer–resource interactions: A comparison of two alternative theoretical frameworks

Species coexistence involving trophic interactions has been investigated under two theoretical frameworks—partitioning shared resources and accessing exclusive resources. The influence of body size on coexistence is well studied under the exclusive resources framework, but has received less attention under the shared-resources framework. We investigate body-size-dependent allometric extensions of a classical MacArthur-type model where two consumers compete for two shared resources. The equilibrium coexistence criteria are compared against the general predictions of the alternative framework over exclusive resources. From the asymmetry in body size allometry of resource encounter versus demand our model shows, counterintuitively, and contrary to the exclusive resource framework, that a smaller consumer should be competitively superior across a wide range of supplies of the two resource types. Experimental studies are reviewed to resolve this difference among the two frameworks that arise from their respective assumptions over resource distribution. Another prediction is that the smaller consumer may have relatively stronger control over equilibrium resource abundance, and the loss of smaller consumers from a community may induce relatively stronger trophic cascades. Finally, from satiating consumers’ functional response, our model predicts that greater difference among resource sizes can allow a broader range of consumer body sizes to coexist, and this is consistent with the predictions of the alternative framework over exclusive resources. Overall, this analysis provides an objective comparison of the two alternative approaches to understand species coexistence that have heretofore developed in relative isolation. It advances classical consumer–resource theory to show how body size can be an important factor in resource competition and coexistence.     

Coexistence of competitors in metacommunities due to spatial variation in resource growth rates; does R * predict the outcome of competition?

Simple mathematical models are used to investigate the coexistence of two consumers using a single limiting resource that is distributed over distinct patches, and that has unequal growth rates in the different patches. Relatively low movement rates or high demographic rates of an inefficient resource exploiter allow it to coexist at a stable equilibrium with a more efficient species whose ratio of movement to demographic rates is lower. The range of conditions allowing coexistence depends on the between‐patch heterogeneity in resource growth rates, but this range can be quite broad. The between‐patch movement of the more efficient consumer turns patches with high resource growth rates into sources, while low‐growth‐rate patches effectively become sinks. A less efficient species can coexist with or even exclude the more efficient species from the global environment if it is better able to bias its spatial distribution towards the source patches. This can be accomplished with density independent dispersal if the less efficient species has a lower ratio of per capita between‐patch movement rate to demographic rates. Conditions that maximize the range of efficiencies allowing coexistence of two species are: a relatively high level of heterogeneity in resource growth conditions; high dispersal (or low demographic rates) of the superior competitor; and low dispersal (or high demographic rates) of the inferior competitor. Global exclusion of the more efficient competitor requires that the inferior competitor have sufficient movement to also produce a source‐sink environment.     

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.     

When does greater mortality increase population size? The long history and diverse mechanisms underlying the hydra effect

The phenomenon of a population increasing in response to an increase in its per-capita mortality rate has recently been termed the 'hydra effect'. This article reviews and unifies previous work on this phenomenon. Some discrete models of density-dependent growth were shown to exhibit hydra effects in 1954, but the topic was then ignored for decades. Here the history of research on the hydra effect is reviewed, and the key factors producing it are explored. Mortality that precedes overcompensatory density dependence always has the potential to produce hydra effects. Even when mortality follows density dependence, hydra effects may occur in unstable systems due to changes in the amplitude and/or form of population cycles. An increase in resource productivity due to lower consumption rates following increased consumer mortality can also produce a hydra effect. Lower consumption can come about as the result of increased satiation of the consumers or changes in behaviour of either consumer or resource species that reduce the mean attack rate. Changes in species composition of a resource community may also decrease the average attack rate. Population structure can promote hydra effects by allowing separation of the timing of density dependence and mortality, although stage-specific density dependence usually decreases hydra effects.     

Remarks on antipredator behavior and food chain dynamics

When consumers feeding on a resource spend time in avoiding high risks of predation, the predator functional response declines with predator density. While this is well established, less attention has been paid to the dependence of the consumer functional response on predator density. Here we show how the separation of behavioral and ecological timescales allows one to determine both responses starting from an explicit behavioral model. Within the general set-up considered in this paper, the two functional responses can tend toward Holling type II responses when consumers react only weakly to predation. Thus, the main characteristics of the standard Rosenzweig-MacArthur tritrophic food chain (logistic resource and Holling type II consumer and predator) remain valid also when consumers have weak antipredator behavior. Moreover, through numerical analysis, we show that in a particular but interesting case pronounced antipredator behaviors stabilize the system.     

物种对资源竞争的动力机制及数值模拟

建立了集合种群物种在两个斑块中对资源竞争的数学模型,并进行了数值模拟实验,结果表明：（1）通过R^＊来预测竞争物种的结局,存在几种可能性：一是具有低R^＊值的物种竞争取代高R^＊值的物种;二是具有不同R^＊值的物种,甚至是具有相同R^＊值的物种也存在共存的可能性;三是具有高R^＊值的物种也可以竞争排斥低R^＊值的物种,结论存在不确定性。（2）竞争物种的随机迁移形成了源一汇结构,对物种竞争共存具有促进作用,但弱的资源利用者（较高的R^＊）的迁移率不宜过高。（3）在种群统计率相同的条件下,资源增长率差异越大,越不利于消费者物种的共存;若种群统计率不相同,在资源增长率相同的情况下,物种共存又是不可能的,在自然界中,物种共存需要资源增长率的差异。（4）不同类型的资源增长对竞争物种的稳定性的影响是不同的。     

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 effect of density-independent mortality on the coexistence of exploitative competitors for renewing resources

Many ecologists believe that higher mortality imposed on competing species increases the probability that they will coexist. This belief has persisted in spite of many theoretical counterarguments. However, few of those counterarguments have been based on models having explicit representation of the resources for which competition is occurring. This article analyzes a series of consumer-resource models of competition for nutritionally substitutable renewable resources and determines the range of relative resource requirements that allow coexistence. In most cases, if consumers are initially efficient at reducing resource densities, increasing density-independent mortality widens the range of resource requirements of the consumers that allow coexistence, provided the increase in mortality is not too great. The coexistence-promoting effects of mortality occur because a very efficient consumer species usually reduces the diversity of the set of resources it consumes. This lessens the extent to which resource utilization differences between consumer species can be expressed. Mortality, in this case, increases the diversity of resource types, widening the conditions for coexistence. However, sufficiently high mortality will usually reduce the range of parameters allowing coexistence, in agreement with much previous theory. The results presented here also predict maximal diversity at intermediate levels of productivity. Previous empirical studies and theory are reviewed in light of the theory developed here.     

Body size mediated coexistence of consumers competing for resources in space

Body size is a major phenotypic trait of individuals that commonly differentiates co-occurring species. We analyzed inter-specific competitive interactions between a large consumer and smaller competitors, whose energetics, selection and giving-up behaviour on identical resource patches scaled with individual body size. The aim was to investigate whether pure metabolic constraints on patch behaviour of vagile species can determine coexistence conditions consistent with existing theoretical and experimental evidence. We used an individual-based spatially explicit simulation model at a spatial scale defined by the home range of the large consumer, which was assumed to be parthenogenic and semelparous. Under exploitative conditions, competitive coexistence occurred in a range of body size ratios between 2 and 10. Asymmetrical competition and the mechanism underlying asymmetry, determined by the scaling of energetics and patch behaviour with consumer body size, were the proximate determinant of inter-specific coexistence. The small consumer exploited patches more efficiently, but searched for profitable patches less effectively than the larger competitor. Therefore, body-size related constraints induced niche partitioning, allowing competitive coexistence within a set of conditions where the large consumer maintained control over the small consumer and resource dynamics. The model summarises and extends the existing evidence of species coexistence on a limiting resource, and provides a mechanistic explanation for decoding the size-abundance distribution patterns commonly observed at guild and community levels.     

Coexistence via resource partitioning fails to generate an increase in community function

Classic ecological theory suggests that resource partitioning facilitates the coexistence of species by reducing inter-specific competition. A byproduct of this process is an increase in overall community function, because a greater spectrum of resources can be used. In contrast, coexistence facilitated by neutral mechanisms is not expected to increase function. We studied coexistence in laboratory microcosms of the bactivorous ciliates Paramecium aurelia and Colpidium striatum to understand the relationship between function and coexistence mechanism. We quantified population and community-level function (biomass and oxygen consumption), competitive interactions, and resource partitioning. The two ciliates partitioned their bacterial resource along a size axis, with the larger ciliate consuming larger bacteria than the smaller ciliate. Despite this, there was no gain in function at the community level for either biomass or oxygen consumption, and competitive effects were symmetrical within and between species. Because other potential coexistence mechanisms can be ruled out, it is likely that inter-specific interference competition diminished the expected gain in function generated by resource partitioning, leading to a system that appeared competitively neutral even when structured by niche partitioning. We also analyzed several previous studies where two species of protists coexisted and found that the two-species communities showed a broad range of biomass levels relative to the single-species states.     

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.     

Coexistence and community structure in a consumer resource model with implicit stoichiometry

We combine stoichiometry theory and optimal foraging theory into the MacArthur consumer-resource model. This generates predictions for diet choice, coexistence, and community structure of heterotroph communities. Tradeoffs in consumer resource-garnering traits influence community outcomes. With scarce resources, consumers forage opportunistically for complementary resources and may coexist via tradeoffs in resource encounter rates. In contrast to single currency models, stoichiometry permits multiple equilibria. These alternative stable states occur when tradeoffs in resource encounter rates are stronger than tradeoffs in elemental conversion efficiencies. With abundant resources consumers exhibit partially selective diets for essential resources and may coexist via tradeoffs in elemental conversion efficiencies. These results differ from single currency models, where adaptive diet selection is either opportunistic or selective. Interestingly, communities composed of efficient consumers share many of the same properties as communities based on substitutable resources. However, communities composed of relatively inefficient consumers behave similarly to plant communities as characterized by Tilman’s consumer resource theory. The results of our model indicate that the effects of stoichiometry theory on community ecology are dependent upon both consumer foraging behavior and the nature of resource garnering tradeoffs.     

Difference Inadaptive Dispersal Ability Can Promote Species Coexistence in Fluctuating Environments

Theories and empirical evidence suggest that random dispersal of organisms promotes species coexistence in spatially structured environments. However, directed dispersal, where movement is adjusted with fitness-related cues, is less explored in studies of dispersal-mediated coexistence. Here, we present a metacommunity model of two consumers exhibiting directed dispersal and competing for a single resource. Our results indicated that directed dispersal promotes coexistence through two distinct mechanisms, depending on the adaptiveness of dispersal. Maladaptive directed dispersal may promote coexistence similar to random dispersal. More importantly, directed dispersal is adaptive when dispersers track patches of increased resources in fluctuating environments. Coexistence is promoted under increased adaptive dispersal ability of the inferior competitor relative to the superior competitor. This newly described dispersal-mediated coexistence mechanism is likely favored by natural selection under the trade-off between competitive and adaptive dispersal abilities.     

Adaptive feeding across environmental gradients and its effect on population dynamics

This paper analyzes a consumer's adaptive feeding response to environmental gradients. We consider a consumer-resource system where resources are distributed among many discrete resource patches. Each consumer exhibits a feeding morphology allowing it to remove resources from a patch down to some threshold density (or level) before having to seek resources elsewhere. Assuming consumers trade off resource extraction with patch access and predation, we show that for a given environment there often exists a single evolutionarily stable feeding threshold and it is an evolutionary attractor. We then investigate how the population dynamics of the resource and the consumer change as the environment changes. Two cases are considered: (i) all consumers exhibit a fixed feeding threshold that is adaptive for an intermediate environment; and (ii) the consumer population adapts and adopts the evolutionarily stable feeding threshold associated with the current environment. In less harsh environments (i.e., environments where consumers experience a lower risk of predation, or environments where resource patches are more abundant) the adaptive consumer population is predicted to evolve so that resources within a patch are depleted to lower densities. We show that the change in consumer density due to environmental change can be rather different depending on whether or not the population can adapt. In some situations we observe that when the consumer's environment becomes harsher, the consumer population may increase in density before a rapid crash to extinction. This result has implications for monitoring and managing a population.     

Does competition between resources change the competition between their consumers to mutualism? Variations on two themes by Vandermeer

How does competition between resources affect the interaction between consumer species that share those resources? Existing theory suggests that high resource competition can lead to mutualism. However, this is based on an analysis that need only apply near equilibrium, and experimental demonstrations of such mutualism are rare. Two alternative approaches to measuring food web mutualism are examined here. These are based on the population-level effects of adding or removing a consumer species or on the amount of additional mortality that can be applied to one consumer without excluding it. Both measures suggest that mutualism is likely to be confined to two situations: when overlap in resource use by the consumers is very low and when the consumers are inefficient users of their resources. Competition between resources is also likely to increase the occurrence and magnitude of "hypercompetition" between consumers, where the reduction in population size caused by the introduced consumer is greater than that caused by a consumer that is identical to the resident species. Competition between resources can also increase the negative interaction between consumers by destabilizing the dynamics of the system. Such destabilization can cause negative indirect interactions between specialist consumers having no overlap in resource use.     

Habitat choice in predator-prey systems: spatial instability due to interacting adaptive movements

The role of habitat choice behavior in the dynamics of predator-prey systems is explored using simple mathematical models. The models assume a three-species food chain in which each population is distributed across two or more habitats. The predator and prey adjust their locations dynamically to maximize individual per capita growth, while the prey's resource has a low rate of random movement. The two consumer species have Type II functional responses. For many parameter sets, the populations cycle, with predator and prey "chasing" each other back and forth between habitats. The cycles are driven by the aggregation of prey, which is advantageous because the predator's saturating functional response induces a short-term positive density dependence in prey fitness. The advantage of aggregation in a patch is only temporary because resources are depleted and predators move to or reproduce faster in the habitat with the largest number of prey, perpetuating the cycle. Such spatial cycling can stabilize population densities and qualitatively change the responses of population densities to environmental perturbations. These models show that the coupled processes of moving to habitats with higher fitness in predator and prey may often fail to produce ideal free distributions across habitats.