Dispersal-mediated coexistence of competing predators

Models of metapopulations have often ignored local community dynamics and spatial heterogeneity among patches. However, persistence of a community as a whole depends both on the local interactions and the rates of dispersal between patches. We study a mathematical model of a metacommunity with two consumers exploiting a resource in a habitat of two different patches. They are the exploitative competitors or the competing predators indirectly competing through depletion of the shared resource. We show that they can potentially coexist, even if one species is sufficiently inferior to be driven extinct in both patches in isolation, when these patches are connected through diffusive dispersal. Thus, dispersal can mediate coexistence of competitors, even if both patches are local sinks for one species because of the interactions with the other species. The spatial asynchrony and the competition-colonization trade-off are usual mechanisms to facilitate regional coexistence. However, in our case, two consumers can coexist either in synchronous oscillation between patches or in equilibrium. The higher dispersal rate of the superior prompts rather than suppresses the inferior. Since differences in the carrying capacity between two patches generate flows from the more productive patch to the less productive, loss of the superior by emigration relaxes competition in the former, and depletion of the resource by subsidized consumers decouples the local community in the latter.     

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.     

Coexistence in metacommunities: a tree-species model

Simple patch-occupancy models of competitive metacommunities have shown that coexistence is possible as long as there is a competition-colonization tradeoff such as that of superior competitors and dispersers. In this paper, we present a model of competition between three species in a dynamic landscape, where patches are being created and destroyed at a different rate. In our model, species interact according to a linear non-transitive hierarchy, such that species Y(3) outcompetes and can invade patches occupied by species Y(2) and this species in turn can outcompete and invade patches occupied by the inferior competitor Y(1). In this hierarchy, inferior competitors cannot invade patches of species with higher competitive ability. Analytical results show that there are regions in the parameter space where coexistence can occur, as well as regions where each of the species exists in isolation depending on species' life-history traits associated with their colonization abilities and extinction proneness as well as with the dynamics of habitat patches. In our model, the condition for coexistence depends explicitly on patch dynamics, which in turn modulate the limiting similarity for species coexistence. Coexistence in metacommunities inhabiting dynamic landscapes although possible is harder to attain than in static ones.     

High reproductive rates result in high predation risks: a mechanism promoting the coexistence of competing prey in spatially structured populations

I tested the hypothesis that spatial structure provides a trade-off between reproduction and predation risk and thereby facilitates predator-mediated coexistence of competing prey species. I compared a cellular automata model to a mean-field model of two prey species and their common predator. In the mean-field model, the prey species with the higher reproductive rate (the superior competitor) always outcompeted the other species (the inferior competitor), both in the presence of and the absence of the predator. In the cellular automata model, both prey species, which differed only in their reproductive rates, coexisted for a long time in the presence of their common predator at intermediate levels of predation. At low predation rates, the superior competitor dominated, while high predation rates favored the inferior competitor. This discrepancy in the results of the different models was due to a trade-off that spontaneously emerged in spatially structured populations; that is, the more clustered distribution of the superior competitor made it more susceptible to predation. In addition, coexistence of competing prey species declined with increasing dispersal ranges of either prey or predator, which suggests that the trade-off that results from spatial structure becomes less important as either prey or predator disperse over a broader range.     

Movement behaviour determines competitive outcome and spread rates in strongly heterogeneous landscapes

Classical models for biological invasions were single-species models in homogeneous landscapes, but most invasions happen in the presence of interacting species and in heterogeneous environments. The combination of spatial variation and species interaction could alter the spreading process significantly. For example, the ‘environmental heterogeneity hypothesis of invasions’ posits that heterogeneity offers more opportunities for invaders and reduces the negative impact on native species. Environmental heterogeneity offers an obvious coexistence mechanism on the regional scale if two or more competing species have different spatial niches, i.e. if the local competitive advantage changes in space. We consider a more subtle mechanism of space use through individual movement behaviour when the local competitive advantage remains with the same species. Specifically, we model the densities of two species, diffusing and competing in an infinite landscape consisting of two types of patches. We include individual behaviour in terms of movement rate and patch preference. We consider the scenario that one of the species is the stronger local competitor in both patch types. We then uncover a number of mechanisms—based solely on movement behaviour—through which these two species can coexist regionally, how the inferior competitor can replace the superior competitor globally, or how a bistable situation can arise between the two. We calculate mutual invasion conditions as well as mutual spatial spread rates, and we show that spread rates may depend on movement parameters in unexpected ways.     

The trade-off between dispersability and longevity - an important aspect of plant species diversity

Abstract. Local presence of plant species is determined by population colonizations and extinctions. All traits that influence the capacity of individuals to colonize patches and survive within patches, are therefore important for community diversity. Spatial models can explain the coexistence of species provided that the inferior competitor has a greater spatial mobility and thereby can avoid competition. We searched the literature for empirical evidence for such trade-offs and included all available information on correlations between traits associated with the capacity to colonize and traits promoting the ability to survive. A lower reproductive effort of a species is associated with a longer life span and a higher competitive ability. Morphological adaptations for dispersal are less common in species which better tolerate stress, that are better competitors or possess seed dormancy. Such patterns suggest that species that are good survivors may have a limited ability to colonize new patches and vice versa. A negative correlation between dispersability and longevity has important effects on the regional dynamics of single species as well as on the coexistence of species. From a conservation perspective differences in the colonization capacity among species imply that restoration of plant biodiversity must not only focus on conditions within patches, but also consider the spatial arrangement of patches in order to enable plants to bridge gaps in time and space.     

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.     

Spatial dynamics in a host–multiparasitoid community

1. The harlequin bug, a herbivore on bladderpod, is attacked by two specialist egg parasitoids Trissolcus murgantiae and Ooencyrtus johnsonii . Ooencyrtus can out-compete Trissolcus in the laboratory, but coexistence is the norm in field populations. Despite the heavy mortality inflicted by the two parasitoids, the host–parasitoid interaction is persistent in all sites that have been studied in southern California.
2. I manipulated inter-patch distances in a field experiment to determine whether spatial processes drive parasitoid coexistence and/or host–parasitoid dynamics. I first tested the hypothesis that the parasitoids coexist via a dispersal–competition trade-off. Both parasitoid species took significantly longer to colonize isolated patches than well-connected patches, suggesting that they have comparable dispersal abilities. Ooencyrtus did not exclude Trissolcus even when inter-patch distances were reduced to 25–30% of those observed in natural populations. These data suggest that parasitoid coexistence can occur in the absence of a dispersal advantage to the inferior competitor.
3. Since the treatments with isolated vs. well-connected patches did not differ in parasitoid composition, I next asked whether isolation would destabilize, or drive extinct, the host–multiparasitoid interaction. No local extinctions of bugs or parasitoids were observed during the 18-month study period. Bug populations in the isolated patches were no more variable than those in the well-connected patches. In fact, temporal variability in the experimentally isolated patches was comparable to that observed in highly isolated natural populations.
4. These data argue against a strong effect of spatial processes on host–parasitoid dynamics. Local processes may mediate both parasitoid coexistence as well as the host–parasitoid interaction.     

Population size dependence, competitive coexistence and habitat destruction

1. Spatial dynamics can lead to coexistence of competing species even with strong asymmetric competition under the assumption that the inferior competitor is a better colonizer given equal rates of extinction. Patterns of habitat fragmentation may alter competitive coexistence under this assumption.
2. Numerical models were developed to test for the previously ignored effect of population size on competitive exclusion and on extinction rates for coexistence of competing species. These models neglect spatial arrangement.
3. Cellular automata were developed to test the effect of population size on competitive coexistence of two species, given that the inferior competitor is a better colonizer. The cellular automata in the present study were stochastic in that they were based upon colonization and extinction probabilities rather than deterministic rules.
4. The effect of population size on competitive exclusion at the local scale was found to have little consequence for the coexistence of competitors at the metapopulation (or landscape) scale. In contrast, population size effects on extinction at the local scale led to much reduced landscape scale coexistence compared to simulations not including localized population size effects on extinction, especially in the cellular automata models. Spatially explicit dynamics of the cellular automata vs. deterministic rates of the numerical model resulted in decreased survival of both species. One important finding is that superior competitors that are widespread can become extinct before less common inferior competitors because of limited colonization.
5. These results suggest that population size–extinction relationships may play a large role in competitive coexistence. These results and differences are used in a model structure to help reconcile previous spatially explicit studies which provided apparently different results concerning coexistence of competing species.     

Competition-colonization trade-offs in a ciliate model community

There is considerable theoretical evidence that a trade-off between competitive and colonization ability enables species coexistence. However, empirical studies testing for the presence of a competition–colonization (CC) trade-off and its importance for species coexistence have found mixed results. In a microcosm experiment, we looked for a CC trade-off in a community of six benthic ciliate species. For each species, we measured the time needed to actively disperse to and colonize an empty microcosm. By measuring dispersal rates and growth rates of the species, we were able to differentiate between these two important components of colonization ability. Competitive ability was investigated by comparing species’ growth with or without a competitor in all pairwise species combinations. Species significantly differed in their colonization abilities, with good colonizers having either high growth rates or high dispersal rates or both. Although species showed a clear competitive hierarchy, competitive and colonization ability were uncorrelated. The weakest competitors were also the weakest colonizers, and the strongest competitor was an intermediate colonizer. However, some of the inferior competitors had higher colonization abilities than the strongest competitor, indicating that a CC trade-off may enable coexistence for a subset of the species. Absence of a community-wide CC trade-off may be based on the lack of strong relationships between the traits underlying competitive and colonization ability. We show that temporal effects and differential resource use are alternative mechanisms of coexistence for the species that were both slow colonizers and poor competitors.     

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.     

Allee effect,spatial structure and species coexistence

Both positive and negative interactions among species are common in communities. Until recently, attention has focused on negative interactions such as competition. However, the importance of positive interactions such as the Allee effect has recently been recognized. We construct a single-patch model that incorporates both an Allee effect and competition between two species. A species that experiences an Allee effect cannot establish in a patch which is already occupied by a competitor unless its density is over a critical value. This effect, when translated into a metapopulation, makes migrants of a species unable to colonize patches where another species has established. This interaction between the Allee effect and inter-specific competition creates and stabilizes spatial segregation of species. Therefore, under circumstances in which competition would preclude local coexistence, the presence of an Allee effect can allow coexistence at a metapopulation scale. Furthermore, we found that a species can resist displacement if stronger competitors experience an Allee effect.     

Competition and species coexistence in a metapopulation model: Can fast asymmetric migration reverse the outcome of competition in a homogeneous environment?

We investigate whether asymmetric fast migration can modify the predictions of classical competition theory and, in particular revert species dominance. We consider a model of two species competing for an implicit resource on a habitat divided into two patches. Both patches are connected through constant migration rates and in each patch local dynamics are driven by a Lotka-Volterra competition system.Local competition is asymmetric with the same superior competitor in both patches. Migration is asymmetric, species dependent and fast in comparison to local competitive interactions. The species and patches are taken to be otherwise similar: in both patches we assume the same carrying capacities for both species, and the same growth rates and pair-wise competition coefficients for each species.We show that global dynamics can be described by a classical Lotka-Volterra competition model. We found that by modifying the ratio of intraspecific migration rates for both species all possible combinations of global species relative dominance can be achieved. We find specific conditions for which the local superior competitor is globally excluded. This is to our knowledge the first study showing that fast asymmetric migration can lead to inferior competitor dominance in a homogeneous environment. We conclude that disparity of temporal scales between migration and local dynamics may have important consequences for the maintenance of biodiversity in spatially structured populations.     

Competition and coexistence in regional habitats

Habitat heterogeneity plays a key role in the dynamics and structures of communities. In this article, a two-species metapopulation model that includes local competitive dynamics is analyzed to study the population dynamics of two competing species in spatially structured habitats. When local stochastic extinction can be ignored, there are, as in Lotka-Volterra equations, four outcomes of interspecific competition in this model. The outcomes of competition depend on the competitive intensity between the competing pairs. An inferior competitor and a superior competitor, or two strongly competing species, can never stably coexist, whereas two weak competitors (even if they are very similar species) may coexist over the long term in such environments. Local stochastic extinction may greatly affect the outcomes of interspecific competition. Two competing species can or cannot stably coexist depending not only on the competitive intensity between the competing pairs but also on their precompetitive distributions. Two weak competitors that have similar precompetitive distributions can always regionally coexist. Two strongly competing species that competitively exclude each other in more stable habitats may be able to stably coexist in highly heterogenous environments if they have similar precompetitive distributions. There is also a chance for an inferior competitor to coexist regionally or even to exclude a superior competitor when the superior competitor has a narrow precompetitive distribution and the inferior competitor has a wide precompetitive distribution.     

Cellular automaton models for competition in patchy environments: Facilitation, inhibition, and tolerance

We have developed cellular automaton models for two species competing in a patchy environment. We have modeled three common types of competition: facilitation (in which the winning species can colonize only after the losing species has arrived) inhibition (in which either species is able to prevent the other from colonizing) and tolerance (in which the species most tolerant of reduced resource levels wins). The state of a patch is defined by the presence or absence of each species. State transition probabilities are determined by rates of disturbance, competitive exclusion, and colonization. Colonization is restricted to neighboring patches. In all three models, disturbance permits regional persistence of species that are excluded by competition locally. Persistence, and hence diversity, is maximized at intermediate disturbance frequencies. If disturbance and dispersal rates are sufficiently high, the inferior competitor need not have a dispersal advantage to persist. Using a new method for measuring the spatial patterns of nominal data, we show that none of these competition models generates patchiness at equilibrium. In the inhibition model, however, transient patchiness decays very slowly. We compare the cellular automaton models to the corresponding mean-field patch-occupancy models, in which colonization is not restricted to neighboring patches and depends on spatially averaged species frequencies. The patch-occupancy model does an excellent job of predicting the equilibrium frequencies of the species and the conditions required for coexistence, but not of predicting transient behavior.     

Temporally explicit habitat ecology and the coexistence of species

Habitats may have dynamics that exist independently of the population densities of species occupying the habitat. For example, ephemeral habitat patches may disappear regardless of whether a particular species is present or not. Such habitat dynamics are frequently modelled by ignoring age-related variation in patch turnover rates. This can be thought of as a temporally implicit approach. An alternative, temporally explicit approach involves using age-structured models in order to describe variations in habitat dynamics. Simple models of coexistence between competing species show that temporally implicit models may be misleading where there is age-related variation in patch dynamics. Changing the shape of the patch survivorship function but not the average patch survivorship can result in mutual extinction, monocultures or coexistence of an inferior and a superior competitor. An explicit treatment of habitat demography may therefore offer improved predictive models and alternative landscape management strategies.     

The effects of metapopulation structure on indirect interactions in host-parasitoid assemblages.

The interaction between two species that do not compete for resources but share a common natural enemy is known as apparent competition. In the absence of other limiting factors, such three-species interactions are impermanent, with one species being excluded from the assemblage by the natural enemy. Here, the effects of metapopulation structure are explored in a system of two hosts that experience apparent competition through a shared parasitoid. A coupled-map lattice model is developed and used to explore species coexistence and patterns of patch occupancy at the metapopulation scale. Linking local and regional dynamics favours coexistence by uncoupling the dynamics of the three species in space. Coexistence is promoted by the inferior species being either a fugitive or a sedentary species. The occurrence of these two mutually exclusive mechanisms of coexistence is influenced by the relative dispersal of the inferior apparent competitor.     

Variation in the degree of specialization can maintain local diversity in model communities

We hypothesize that the continuum between generalist and specialist adaptations is an important general trade-off axis in the maintenance of local diversity, and we explore this idea with a simple model in which there are patch types to which species arrive as propagules and compete. Each patch type is defined by a competitive ranking of all species. A highly specialist species is the top competitor in one patch type but has a relatively low average ranking across different patch types, while a generalist species has a high average rank across patch types but is not the top competitor in any patch type. We use random dispersal and vary the fecundity of all species together to vary total propagule density and therefore recruitment limitation and density-dependent mortality. When fecundity is very high, each patch becomes occupied by its specialist species and generalists go extinct, so the number of species at equilibrium is equal to the number of patch types. If fecundity is very low, generalists dominate and specialists go extinct. There is a range of fecundity levels in which specialists, generalists, and intermediates coexist, and the number of species is substantially greater than the number of patch types. While coexistence of specialists and generalists has been considered a problem in evolutionary ecology, our results suggest to the contrary that this trade-off contributes to the maintenance of local diversity.     

Community dynamic models of two dioecious tree species

The effects of dioecy on community dynamics were examined by using transition matrix models for two dioecious tree species, one a superior competitor with a narrow dispersal range and the other an inferior competitor with a wide dispersal range. The models are based on tree-by-tree replacements in each identical microsite occupied by either male or female canopy trees of the superior competitor and canopy trees of the inferior competitor. Coexistence of the two species is possible not only because of a trade-off between competitive and dispersal abilities but also because of the existence of a competitor gap, which the superior competitor cannot occupy. The competitor gap is created under the male trees of the superior competitor. The inferior competitor occupies the competitor gap because of its wide dispersal range. The relative abundance of the two species depends on the dispersal ability and sex ratios of the superior competitor. The decreasing dispersal ability and the female abundance of the superior competitor increase the competitor gap, which allows the regeneration of the inferior competitor.An erratum to this article can be found at     

Evolution of the maturation rate collapses competitive coexistence

Most theoretical studies on character displacement and the coexistence of competing species have focused attention on the evolution of competitive traits driven by inter-specific competition. We investigated the evolution of the maturation rate which is not directly related to competition and trades off with the birth rate and how it influences competitive outcomes. Evolution may result in the superior competitor becoming extinct if, initially, the inferior competitor has a lower, and the superior one a higher, maturation rate at the coexistence equilibrium. This counterintuitive result is explained by an explosive increase in the adult population of the inferior competitor as a result of the more rapid evolution of its maturation rate, which is caused by differences in the intensity and direction of selection on the maturation rates of the two species and in their adult densities, which are related to differences in their life histories. Thus, a life history trait trade-off with a competitive trait may cause a competitive ecological coexistence to collapse.