On the structure and stability of mutualistic systems: Analysis of predator-prey and competition models as modified by the action of a slow-growing mutualist

Two basic models of mutualism are presented in which interactions among three species lead to mutualism between two of them. The models represent 2-species predator-prey or competition systems in which a third species acts as a mutualist with either the predator, the prey, or one of the competitors. The models include the assumptions that there is a cost of associating with the mutualist and that the mutualist population grows much more slowly than the other two populations. Special cases of these two models correspond to six qualitatively different types of mutualistic benefit, all of which are known to occur in nature: deterring predation, increasing prey availability, feeding on (or competing with) a predator, increasing competitive interactions, decreasing competitive interactions, and feeding on (or competing with) a competitor. These models and their special cases are subjected to a local stability analysis. The results show that mutualism based upon deterring predation, competing with a predator, or decreasing competitive interactions enhances local stability, while mutualism based upon increasing prey availability or increasing competitive interactions reduces local stability. These results clearly reject the idea that mutualism is an inherently unstable process, and reinforces the idea that each different kind of mutualism will have to be considered separately. Compared to 2-species models of mutualism, the 3-species models provide a more realistic representation of the structure of many mutualistic systems, the mechanisms by which one species benefits another, and the regulation of the interaction.     

Changes in community size affect the outcome of competition

We examine the role of stochasticity and competitive ability in affecting competition between two species using models derived for population genetics. Just as changing population size affects the fixation of a new mutation, we show that changing the total number of competitors (i.e., community size) can alter the course of competitive exclusion across a wide range of initial starting densities of the two competing species. Shifts in competitive exclusion occur because changes in community size affect the relative importance of competitive ability and stochasticity in affecting the outcome of competition, potentially allowing inferior invaders to usurp superior residents. By shifting the role of stochasticity and competitive ability, any process that changes the total number of competitors in a habitat (e.g., disturbance, eutrophication, fragmentation, predation) may lead to shifts in competitive exclusion and the composition of communities.     

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.     

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.     

Intraguild predation of lynxes on foxes: evidence of interference competition?

There is a growing focus among ecologists on the importance of predatory interactions between competing species, but because of its mixed character. it is difficult to pinpoint the possible, competitive component of the interaction. We tested degree of prey consumption in intraguild predation of Eurasian lynxes on red foxes against assumed 'pure' predation. i.e, roe deer and mountain hares. The proportion of uneaten fox carcasses was highly significantly larger than the proportion of both other prey species, indicating that interference competition may play a role in the intraguild predation of lynxes on red foxes.     

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.     

Competitive interactions change the pattern of species co‐occurrences under neutral dispersal

Non‐random patterns of species segregation and aggregation within ecological communities are often interpreted as evidence for interspecific interactions. However, it is unclear whether theoretical models can predict such patterns and how environmental factors may modify the effects of species interactions on species co‐occurrence. Here we extend a spatially explicit neutral model by including competitive effects on birth and death probabilities to assess whether competition alone is able to produce non‐random patterns of species co‐occurrence. We show that transitive and intransitive competitive hierarchies alone (in the absence of environmental heterogeneity) are indeed able to generate non‐random patterns with commonly used metrics and null models. Moreover, even weak levels of intransitive competition can increase local species richness. However, there is no simple rule or consistent directional change towards aggregation or segregation caused by competitive interactions. Instead, the spatial pattern depends on both the type of species interaction and the strength of dispersal. We conclude that co‐occurrence analysis alone may not able to identify the underlying processes that generate the patterns.     

Emerging niche clustering results from both competition and predation

Understanding species coexistence has been a central question in ecology for decades, and the notion that competing species need to differ in their ecological niche for stable coexistence has dominated. Recent theoretical and empirical work suggests differently. Species can also escape competitive exclusion by being similar, leading to clusters of species with similar traits. This theory has so far only been explored under competition. By combining mathematical and numerical analyses, we reveal that competition and predation are equally capable to promote clusters of similar species in prey–predator communities, their relative importance being modulated by resource availability. We further show that predation has a stabilizing effect on clustering patterns, making the clusters more diverse. Our results merge different ecological theories and bring new light to the emergent neutrality theory by adding the perspective of trophic interactions. These results open new perspectives to the study of trait distributions in ecological interaction networks.     

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.     

Consequences of varying regional heterogeneity in source–sink metacommunities

Although the influence of dispersal on coexistence mechanisms in metacommunities has received great emphasis, few studies have addressed how such influence is affected varying regional heterogeneity. We present a mechanistic model of resource competition in a metacommunity based on classical models of plant competition for limiting resources. We defined regional heterogeneity as the differences in resource supply rates (or resource availabilities) across local communities. As suggested by previous work, the highest diversify occurred at intermediate levels of dispersal among local communities. However our model shows how the effects of dispersal depend on the amount of heterogeneity among local communities and vice versa. Both regional and local species richness were the highest when heterogeneity was intermediate. We suggest that empirical studies that found no evidence for source–sink or mass effects at the community level may have examined communities with limited ranges of dispersal and regional heterogeneity. This model of species coexistence contributes to a broader understanding of patterns in real communities.     

Matrix models for quantifying competitive intransitivity from species abundance data

In a network of competing species, a competitive intransitivity occurs when the ranking of competitive abilities does not follow a linear hierarchy (A > B > C but C > A). A variety of mathematical models suggests that intransitive networks can prevent or slow down competitive exclusion and maintain biodiversity by enhancing species coexistence. However, it has been difficult to assess empirically the relative importance of intransitive competition because a large number of pairwise species competition experiments are needed to construct a competition matrix that is used to parameterize existing models. Here we introduce a statistical framework for evaluating the contribution of intransitivity to community structure using species abundance matrices that are commonly generated from replicated sampling of species assemblages. We provide metrics and analytical methods for using abundance matrices to estimate species competition and patch transition matrices by using reverse‐engineering and a colonization–competition model. These matrices provide complementary metrics to estimate the degree of intransitivity in the competition network of the sampled communities. Benchmark tests reveal that the proposed methods could successfully detect intransitive competition networks, even in the absence of direct measures of pairwise competitive strength. To illustrate the approach, we analyzed patterns of abundance and biomass of five species of necrophagous Diptera and eight species of their hymenopteran parasitoids that co‐occur in beech forests in Germany. We found evidence for a strong competitive hierarchy within communities of flies and parasitoids. However, for parasitoids, there was a tendency towards increasing intransitivity in higher weight classes, which represented larger resource patches. These tests provide novel methods for empirically estimating the degree of intransitivity in competitive networks from observational datasets. They can be applied to experimental measures of pairwise species interactions, as well as to spatio‐temporal samples of assemblages in homogenous environments or environmental gradients.     

How does spatio-temporal disturbance influence species diversity in a hierarchical competitive system? Prospective order of species coexistence and extinction

To address how habitat destruction and hierarchical competition among species affect the spatio-temporal dynamics of a multi-species community, we present a compartment model in which multiple species undergo dispersal and competitive interactions in a patchy habitat arranged in a two-dimensional lattice. We assume that disturbances are periodically imposed on some parts of the lattice in a block, followed by a period free of disturbance. For convenience, species are ranked in order of competitive ability. We further assume that the intrinsic growth rate of species i, _i , and the dispersal ability, D _i , increase in decreasing order of rank. Our model can analytically determine the exact number of surviving species when disturbance is absent. In the presence of disturbance, we numerically examine how spatio-temporal changes in environmental heterogeneity affect species coexistence and extinction, for the case in which the value of _i /D _i monotonically increases or decreases with rank. The results demonstrate that (1) when the interspecific competition is smaller than the intraspecific competition, we can provide predictions on the prospective order of species to be driven extinct and the order of potential species to revive with increasing extents of disturbance; (2) when the interspecific competition is stronger than intraspecific competition, a small difference in the disturbance level can lead to drastic changes in the species composition, their densities and the order of species extinction. In addition, comparison with other similar models reveals that differences in species interaction in local population dynamics critically affect the disturbance-mediated species diversity.     

Relative roles of dispersal dynamics and competition in determining the isotopic niche breadth of a wetland fish

1. The niche variation hypothesis predicts that among‐individual variation in niche use will increase in the presence of intraspecific competition and decrease in the presence of interspecific competition. We sought to determine whether the local isotopic niche breadth of fish inhabiting a wetland was best explained by competition for resources and the niche variation hypothesis, by dispersal of individuals from locations with different prey resources or by a combination of the two. We analysed stable isotopes of carbon and nitrogen as indices of feeding niche and compared metrics of within‐site spread to characterise site‐level isotopic niche breadth. We then evaluated the explanatory power of competing models of the direct and indirect effects of several environmental variables spanning gradients of disturbance, competition strength and food availability on among‐individual variation of the eastern mosquitofish (Gambusia holbrooki). 2. The Dispersal model posits that only the direct effect of disturbance (i.e. changes in water level known to induce fish movement) influences among‐individual variation in isotopic niche. The Partitioning model allows for only direct effects of local food availability on among‐individual variation. The Combined model allows for both hypotheses by including the direct effects of disturbance and food availability. 3. A linear regression of the Combined model described more variance than models limited to the variables of either the Dispersal or Partitioning models. Of the independent variables considered, the food availability variable (per cent edible periphyton) explained the most variation in isotopic niche breadth, followed closely by the disturbance variable (days since last drying event). 4. Structural equation modelling provided further evidence that the Combined model was best supported by the data, with the Partitioning and the Dispersal models only modestly less informative. Again, the per cent edible periphyton was the variable with the largest direct effect on niche variability, with other food availability variables and the disturbance variable only slightly less important. Indirect effects of heterospecific and conspecific competitor densities were also important, through their effects on prey density. 5. Our results support the Combined hypotheses, although partitioning mechanisms appear to explain the most diet variation among individuals in the eastern mosquitofish. The results also support some predictions of the niche variation hypothesis, although both conspecific and interspecific competition appeared to increase isotopic niche breadth in contrast to predictions that interspecific competition would decrease it. We think this resulted from high diet overlap of co‐occurring species, most of which consume similar macroinvertebrates.     

Translucent windows: how uncertainty in competitive interactions impacts detection of community pattern

Traits can provide a window into the mechanisms that maintain coexistence among competing species. Recent theory suggests that competitive interactions will lead to groups, or clusters, of species with similar traits. However, theoretical predictions typically assume complete knowledge of the map between competition and measured traits. These assumptions limit the plausible application of these patterns for inferring competitive interactions in nature. Here, we relax these restrictions and find that the clustering pattern is robust to contributions of unknown or unobserved niche axes. However, it may not be visible unless measured traits are close proxies for niche strategies. We conclude that patterns along single niche axes may reveal properties of interspecific competition in nature, but detecting these patterns requires natural history expertise firmly tying traits to niches.     

Historical factors mediate the effects of interspecific competition

Biotic interactions, such as interspecific competition, are potentially important in determining whether introduced species succeed or fail to establish wild populations. Such effects may be difficult to detect, however, because the outcome of interspecific competition may depend on historical and largely unpredictable circumstances such as the timing of introductions and the number of individuals of each species introduced. I used a stochastic birth-death model to explore the effects of interspecific competition, the timing of introductions and the numbers of individuals of each species introduced, on invasion success in a two-species competitive system. I then compared the model predictions with actual data on establishment outcomes for passerine birds introduced to New Zealand, for which we have data on the timing of introductions, the size of release populations, and a measure of the strength of per capita competition (the degree of morphological similarity among species). The model and data agree well, suggesting that interspecific competition was an important determinant of invasion success in this assemblage, but that the outcome of competition depended critically on circumstances such as the timing of introductions and number of individuals released. Hence, while there is a deterministic component to invasion success in this assemblage (morphologically similar species are less likely to establish), historical circumstances played a critical role in mediating the outcomes.     

The interaction between predation and competition: a review and synthesis

This review discusses the interface between two of the most important types of interactions between species, interspecific competition and predation. Predation has been claimed to increase, decrease, or have little effect on, the strength, impact or importance of interspecific competition. There is confusion about both the meaning of these terms and the likelihood of, and conditions required for, each of these outcomes. In this article we distinguish among three measures of the influence of predation on competitive outcomes: short‐term per capita consumption or growth rates, long‐term changes in density, and the probability of competitive coexistence. We then outline various theoretical mechanisms that can lead to qualitatively distinct effects of predators. The qualitative effect of predators can depend both on the mechanism of competition and on the definition of competitive strength/impact. In assessing the empirical literature, we ask: (1) What definitions of competitive strength/impact have been assumed? (2) Does strong evidence exist to support one or more of the possible mechanisms that can produce a given outcome? (3) Do biases in the choice of organism or manipulation exist, and are they likely to have influenced the conclusions reached? We conclude by discussing several unanswered questions, and espouse a stronger interchange between empirical and theoretical approaches to this important question.     

Dynamic phenotypic clustering in noisy ecosystems

In natural ecosystems, hundreds of species typically share the same environment and are connected by a dense network of interactions such as predation or competition for resources. Much is known about how fixed ecological niches can determine species abundances in such systems, but far less attention has been paid to patterns of abundances in randomly varying environments. Here, we study this question in a simple model of competition between many species in a patchy ecosystem with randomly fluctuating environmental conditions. Paradoxically, we find that introducing noise can actually induce ordered patterns of abundance-fluctuations, leading to a distinct periodic variation in the correlations between species as a function of the phenotypic distance between them; here, difference in growth rate. This is further accompanied by the formation of discrete, dynamic clusters of abundant species along this otherwise continuous phenotypic axis. These ordered patterns depend on the collective behavior of many species; they disappear when only individual or pairs of species are considered in isolation. We show that they arise from a balance between the tendency of shared environmental noise to synchronize species abundances and the tendency for competition among species to make them fluctuate out of step. Our results demonstrate that in highly interconnected ecosystems, noise can act as an ordering force, dynamically generating ecological patterns even in environments lacking explicit niches.     

Starve a competitor: evolution of luxury consumption as a competitive strategy

Organisms are often observed to acquire an excess of non-limiting resources, a process known as luxury consumption. Luxury consumption has been largely treated as a bet hedging strategy for temporal variation in resource supply, but may also function as a competitive strategy. We incorporate luxury resource consumption into a derivation of the classic resource ratio model for competition between terrestrial plant, and explore its consequences for population dynamics and competition. We show that luxury consumption reduces the potential for coexistence between two species competing for two resources. Furthermore, we demonstrate that luxury consumption can be selected for because of the competitive advantage that luxury consumers gain. Luxury consumption evolves when competition for resources is local rather than global, there is potential for coexistence between the two species and the competitive environment remains stable over a sufficient period of time to allow selection to act. The evolutionary outcome can be either extinction of one of the competing species or coexistence of the two species with maximum luxury consumption. The potential for selection to favor luxury consumption is well predicted by the competitive outcome between individuals of the two species with and without luxury consumption.     

Predation, competition, and nutrient recycling: a stoichiometric approach with multiple nutrients

A model for two competing prey species and one predator is formulated in which three essential nutrients can limit growth of all populations. Prey take up dissolved nutrients and predators ingest prey, assimilating a portion of ingested nutrients and recycling or respiring the balance. For all species, the nutrient contents of individuals vary and growth is coupled to increasing content of the limiting nutrient. This model was parameterized to describe a flagellate preying on two bacterial species, with carbon (C), nitrogen (N), and phosphorus (P) as nutrients. Parameters were chosen so that the two prey species would stably coexist without predators under some nutrient supply conditions. Using numerical simulations, the long-term outcomes of competition and predation were explored for a gradient of N:P supply ratios, varying C supply, and varying preference of the predator for the two prey. Coexistence and competitive exclusion both occurred under some conditions of nutrient supply and predator preference. As in simpler models of competition and predation these outcomes were largely governed by apparent competition mediated by the predator, and resource competition for nutrients whose effective supply was partly governed by nutrient recycling also mediated by the predator. For relatively small regions of parameter space, more complex outcomes with multiple attractors or three-species limit cycles occurred. The multiple constraints posed by multiple nutrients held the amplitudes of these cycles in check, limiting the influence of complex dynamics on competitive outcomes for the parameter ranges explored.     

Reduction of species coexistence through mixing in a spatial competition model

Many ecological systems exhibit self-organized spatial patterns due to local interactions. Such patterns can promote species diversity and therefore serve as an important mechanism for biodiversity maintenance. Previous work has shown that when species interactions occurred at local spatial scales, species diversity was greatest when robust mosaic spatial patterns formed. Also, intransitive interactions led to the emergence of spiral patterns, frequently resulting in multispecies coexistence. In some instances, intransitive interactions reduced species diversity as the consequence of competitive hierarchies. Here, we extend and broaden this line of investigation and examine the role of global competition along a continuum ranging from spatial mosaics to spiral patterns. While previous models have predicted that species diversity is reduced when interactions occur over larger spatial scales, our model considers the effects of various levels of mixing on species diversity, in the context of various network structures as measured by the covariance of row and column sums of the competition matrix. First, we compare local competition (unmixed system) versus global competition (mixed systems) and show that greater species diversity is maintained under a positive covariance. Second, we show that under various levels of mixing, species diversity declines more rapidly under a negative covariance. Lastly, we demonstrate that time to extinction in our model occurs much more rapidly under a negative covariance.