Clumped versus scattered: how does the spatial correlation of disturbance events affect biodiversity?

In this study, we systematically explore the effects of rate and spatial correlation (level of clumping) of disturbance events on a community of sessile species differing in their life history traits. A spatially explicit individual-based model shows that long-term coexistence is very sensitive to spatial correlation when the trade-off in life history traits includes differences in dispersal distances. Highest biodiversity emerges at highly correlated disturbances of intermediate rates. Diversity peaks shift to larger rates when clumping decreases. Scattered disturbances lead to competitive exclusion. Interestingly, we observed additional peaks in the diversity–disturbance curves at certain levels of clumping. Thus, subject to the differences in life history traits, particular combinations of disturbance rate and spatial correlation may enable subsets of species to coexist, which opens new possibilities for explaining diversity. Our results suggest that observation of high biodiversity under spatially correlated disturbances points to a competition–colonisation trade-off, which includes dispersal distances.     

The effect of colonization and competition processes on the relation between disturbance and diversity in plant communities

Many theoretical and field studies have emphasized the impact of disturbance in the dynamics and diversity of sessile organism communities. This view is best reflected by the Intermediate Disturbance Hypothesis (IDH), which states that a maximum of diversity is found in ecosystems or communities experiencing intermediate disturbance regimes or at an intermediate stage of development since the last major disturbance event. Although theoretical models based on competitive interactions tend to validate this hypothesis, a recent meta-analysis of field experiments revealed that the mono-modal relationship between disturbance and diversity might not be a general pattern. In this article, we investigate the relationship between disturbance and diversity through the study of patch models, combining two types of competitive interactions: with or without competitive hierarchy, with two mechanisms influencing colonization: negative frequency dependence in colonization rates and immigration. These combinations led to various disturbance-diversity patterns. In the model without competitive hierarchy (founder effect model), a decreasing relationship appeared to be the rule as mentioned in previous studies. In the model with competitive hierarchy, the IDH pattern was obtained for low frequency dependence and low immigration. Nevertheless, high negative frequency dependence in colonization rates led to a decreasing relationship between disturbance and diversity. In contrast, high immigration led to an increasing relationship. The coexistence window (the range of disturbance intensity allowing coexistence) was the widest for intermediate immigration rates. For random species assemblages, patterns with multiple peaks were also possible. These results highlight the fact that the mono-modal IDH pattern should not be considered a rule. Competition and colonization mechanisms have a profound impact on the relationship between disturbance and diversity.     

Quantifying and testing coexistence mechanisms arising from recruitment fluctuations

Temporal fluctuations in recruitment are involved in two distinct coexistence mechanisms, the storage effect and relative nonlinearity of competition, which may act simultaneously to stabilize species coexistence. It is shown that comparisons of recruitment variation between species at high versus low densities can test whether these mechanisms are responsible for stable coexistence. Moreover, under certain circumstances, these comparisons can measure the total coexistence stabilizing effect of the mechanism. These comparisons are clearest for the situation of an invader (a species perturbed to low density) in the presence of its competitors, termed residents. Then average invader-resident differences in the variances of log recruitment, potentially weighted by adult survival rates and species' sensitivities to competition, are proportional to the overall stabilizing effect of the storage effect and relative nonlinearity of competition. Less effective comparisons are available for species naturally at high and low densities or with substantial mean differences in average fitness. These developments lead also to a technique of partitioning the long-term low-density growth rate of a species into community average measures of stabilizing mechanisms, deviations from these measures, and other factors. The community average measure is argued as most appropriate for understanding the ability of a coexistence mechanism to stabilize coexistence. Individual species' deviations from the community average indicate the ways in a which a coexistence mechanism may affect average fitness differences between species either enhancing or diminishing the ability of a given set of species to coexist, depending on other factors. This approach provides a general new tool for analyzing species coexistence.     

Preemption of space can lead to intransitive coexistence of competitors

Intransitive competition has the potential to be a powerful contributor to species coexistence, but there are few proposed biological mechanisms that could create intransitivities in natural communities. Using a three‐species model of competition for space, we demonstrate a mechanism for coexistence that combines a colonization–competition tradeoff between two species with the ability of a third species to preempt space from the other competitors. The combination of differential abilities to colonize, preempt, and overtake space creates a community where no single species can exclude both of its competitors. The dynamics of this kind of community are analogous to rock‐paper‐scissors competition, and the three‐species community can persist even though not all pairs of species can coexist in isolation. In distinction to prior results, this is a mechanism of intransitivity that does not require nonhierarchical local interference competition. We present parameter estimates from a subtidal marine community illustrating how documented competitive traits can lead to preemption‐based intransitivities in natural communities, and we describe methods for an empirical test of the occurrence of this mechanism.     

Using exclusion rate to unify niche and neutral perspectives on coexistence

The competitive exclusion principle is one of the most influential concepts in ecology. The classical formulation suggests a correlation between competitor species similarity and competition severity, leading to rapid competitive exclusion where species are very similar; yet neutral models show that identical species can persist in competition for long periods. Here, we resolve the conflict by examining two components of similarity – niche overlap and competitive similarity – and modeling the effects of each on exclusion rate (defined as the inverse of time to exclusion). Studying exclusion rate, rather than the traditional focus on binary outcomes (coexistence versus exclusion), allows us to examine classical niche and neutral perspectives using the same currency. High niche overlap speeds exclusion, but high similarity in competitive ability slows it. These predictions are confirmed by a well‐known model of two species competing for two resources. Under ecologically plausible scenarios of correlation between these two factors, the strongest exclusion rates may be among moderately similar species, while very similar and highly dissimilar competitors have very low exclusion rates. Adding even small amounts of demographic stochasticity to the model blurs the line between deterministic and probabilistic coexistence still further. Thus, focusing on exclusion rate, instead of on the binary outcome of coexistence versus exclusion, allows a variety of outcomes to result from competitive interactions. This approach may help explain species coexistence in diverse competitive communities and raises novel issues for future work.     

Predicting coexistence of plants subject to a tolerance-competition trade-off

Ecological trade-offs between species are often invoked to explain species coexistence in ecological communities. However, few mathematical models have been proposed for which coexistence conditions can be characterized explicitly in terms of a trade-off. Here we present a model of a plant community which allows such a characterization. In the model plant species compete for sites where each site has a fixed stress condition. Species differ both in stress tolerance and competitive ability. Stress tolerance is quantified as the fraction of sites with stress conditions low enough to allow establishment. Competitive ability is quantified as the propensity to win the competition for empty sites. We derive the deterministic, discrete-time dynamical system for the species abundances. We prove the conditions under which plant species can coexist in a stable equilibrium. We show that the coexistence conditions can be characterized graphically, clearly illustrating the trade-off between stress tolerance and competitive ability. We compare our model with a recently proposed, continuous-time dynamical system for a tolerance-fecundity trade-off in plant communities, and we show that this model is a special case of the continuous-time version of our model.     

Influence of predation on species coexistence in Volterra models

The possibility of predator-mediated coexistence of all species in model ecosystems of the Volterra type is discussed, that is, asymptotic behaviors of systems of two competing species are analyzed when one or two predators are added. All species in the communities can coexist in two distinct ways mathematically, that is, the species may coexist at equilibrium or may coexist in persistent oscillations. The stability of all species at equilibrium increases when one or two predators are added. The conditions for oscillatory coexistence in limit cycles or in chaotic behaviors of two-predator systems are more complicated than in those of one-predator systems. It is concluded that predator-mediated coexistence can be promoted by an intimate relationship between the competitive ability of the prey and the diet preference of the predators.     

Coexistence of species competing for shared resources

In this paper we develop a mathematical model in which any number of competing species can coexist on four resources which regenerate according to an algebraic relationship. We show that previous attempts to prove that n species cannot coexist on fewer that n resources (the “competitive exclusion principle”) all make use of the very restrictive assumption that the specific growth rates of all competing species are linear functions of resource densities. When this restriction is relaxed, it becomes possible to find situations in which n species can coexist on fewer than n resources. On the basis of this and other observations we conclude that the competitive exclusion principle should be considered to apply only to coexistence at fixed densities.     

Trade-offs between dispersal and competitive ability: a comparative study of wind-dispersed Asteraceae forbs

An underlying assumption in many models of coexistence and species response to fragmentation is the trade-off between dispersal and competitive abilities among species. Despite a well-founded theoretical ground for this assumption, the mechanism itself has not been as thoroughly explored. Empirical studies of the dispersal/competition trade-off have so far mainly concerned the dispersal distance of single offspring, whereas most models where the trade-off is assumed concern dispersal rate, i.e. the number of offspring that is dispersed outside a local patch per time unit. When species differ in fecundity this should also affect the dispersal rate. We therefore investigated different aspects of dispersal ability and competitive ability in the recruitment phase for 15 wind-dispersed Asteraceae species. A trade-off was found between dispersal ability at the offspring level, i.e. distance travelled by single seeds, and competitive ability in the recruitment phase, but no trade-off was found between dispersal ability at the brood level, i.e. the dispersal ability of single seeds in combination with fecundity, and competitive ability in the recruitment phase. The results were supported both by cross-species analysis and analyses by phylogenetically independent contrast. If this is a general pattern then it is troublesome for models making the assumption that there is a trade-off between dispersal rate and competitive ability.     

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.     

Predator selectivity alters the effect of dispersal on coexistence among apparent competitors

While the majority of studies on dispersal effects on patterns of coexistence among species in a metacommunity have focused on resource competitors, dispersal in systems with predator–prey interactions may provide very different results. Here, we use an analytical model to study the effect of dispersal rates on coexistence of two prey species sharing a predator (apparent competition), when the traits of that predator vary. Specifically, we explore the range in immigration rates where apparent competitors are able to coexist, and how that range changes with predator selectivity and efficiency. We find that if the inferior apparent competitor has a higher probability of being consumed, it will require less immigration to invade and to exclude the superior prey as the predator becomes more opportunistic. However, if the inferior apparent competitor has a lower probability of being consumed (and lower growth rates), higher immigration is required for the inferior prey to invade and exclude the superior prey as the predator becomes more opportunistic. We further find that the largest range of immigration rates where prey coexist occurs when predator selectivity is intermediate (i.e. they do not show much bias towards consuming one species or the other). Increasing predator efficiency generally reduces the immigration rates necessary for the inferior apparent competitor to invade and exclude the superior apparent competitor, but also reduces the range of immigration rates where the two apparent competitors can coexist. However, when the superior apparent competitor has a higher probability of being consumed, increased predator efficiency can increase the range of parameters where the species can coexist. Our results are consistent with some of the variation observed in the effect of dispersal on prey species richness in empirical systems with top predators.     

Intraspecific variation and species coexistence

We use a two-species model of plant competition to explore the effect of intraspecific variation on community dynamics. The competitive ability ("performance") of each individual is assigned by an independent random draw from a species-specific probability distribution. If the density of individuals competing for open space is high (e.g., because fecundity is high), species with high maximum (or large variance in) performance are favored, while if density is low, species with high typical (e.g., mean) performance are favored. If there is an interspecific mean-variance performance trade-off, stable coexistence can occur across a limited range of intermediate densities, but the stabilizing effect of this trade-off appears to be weak. In the absence of this trade-off, one species is superior. In this case, intraspecific variation can blur interspecific differences (i.e., shift the dynamics toward what would be expected in the neutral case), but the strength of this effect diminishes as competitor density increases. If density is sufficiently high, the inferior species is driven to extinction just as rapidly as in the case where there is no overlap in performance between species. Intraspecific variation can facilitate coexistence, but this may be relatively unimportant in maintaining diversity in most real communities.     

Evolutionary stability of coexistence due to the storage effect in a two-season model

The question of species coexistence has been central to ecology since its founding. Ever-present environmental variation may be one answer to that question. Previous models have demonstrated that species can exploit this variation to coexist with competitors by having different environmental responses (the storage effect). When traits governing species’ environmental response can evolve, however, coexistence is not assured. In this study, we use a continuous time, two-season model to determine the evolutionary outcome of competing species evolving in their seasonal performance trait. We extend the competitive exclusion principle to show that the storage effect can allow no more than N species to coexist on N discrete seasons with no relative nonlinearity. We find a broad region of parameter space where coexistence is evolutionarily stable. The size of this region depends on the period of fluctuations relative to the individual lifespan. Relatively long period fluctuations yield a large coexistence region, but as the period decreases, the region narrows and disappears asymptotically. Finally, we cast our adaptive dynamics technique in terms of Chesson’s concept of equalizing and stabilizing mechanisms to demonstrate that the breakdown in coexistence at short periods is due to loss of the stabilizing covariance between the environment and competition.     

Coexistence of Habitat Specialists and Generalists in Metapopulation Models of Multiple-Habitat Landscapes

In coarse-grained environments specialists are generally predicted to dominate. Empirically, however, coexistence with generalists is often observed. We present a simple, but previously unrecognized, mechanism for coexistence of a habitat generalist and a number of habitat specialist species. In our model all species have a metapopulation structure in a landscape consisting of patches of different habitat types, governed by local extinction and colonization. Each specialist is limited to its specific type of habitat. The generalist can use more types of habitat, has a lower local competitive ability but can exploit patches left open by the specialists. Our modeling shows that coexistence is easily possible. The mechanism amounts to a colonization/competition trade-off at the landscape level, where the colonization advantage of the inferior competitor does not arise from a higher colonization rate but from its ability to use more types of habitat. Habitat availability has to be intermediate: when there are few patches of each habitat, only the generalist is able to maintain itself and when there are many patches, high propagule pressure of the specialists excludes the generalist. Habitat selection or temporal variations in relative habitat quality are not necessary for coexistence. Increased niche-width, colonization rate or local competitive ability of the generalist enhances its performance compared to the specialists. Various types of habitat degradation favour generalism. When able to use a broad range of habitats, generalists can generate so much propagule pressure that only a low level of local competitive ability is needed to globally exclude the specialists. Hence, in a reversal of the original problem, the question is why there are so many specialist metapopulations?     

Potential mechanisms of coexistence in closely related forbs

The stable coexistence of very similar species has perplexed ecologists for decades and has been central to the development of coexistence theory. According to modern coexistence theory, species can coexist stably (i.e. persist indefinitely with no long‐term density trends) as long as species' niche differences exceed competitive ability differences, even if these differences are very small. Recent studies have directly quantified niche and competitive ability differences in experimental communities at small spatial scales, but provide limited information about stable coexistence across spatial scales in heterogeneous natural communities. In this study, we use experimental and observational approaches to explore evidence for niche and competitive ability differences between two closely related, ecologically similar and widely coexisting annual forbs: Trachymene cyanopetala and T. ornata. We experimentally tested for stabilizing niche differences and competitive ability differences between these species by manipulating species' frequencies, under both well‐watered and water‐stressed conditions. We considered these experimental results in light of extensive field observations to explore evidence of niche segregation at a range of spatial scales. We found little evidence of intra‐specific stabilization or competitive ability differences in laboratory experiments while observational studies suggested niche segregation across pollinator assemblages and small‐scale microclimate heterogeneity. Though we did not quantify long‐term stabilization of coexisting populations of these species, results are consistent with expectations for stable coexistence of similar species via a spatial storage effect allowing niche differences to overcome even small (to absent) competitive ability differences.     

Rock-scissors-paper game in a chaotic flow: the effect of dispersion on the cyclic competition of microorganisms

Laboratory experiments and numerical simulations have shown that the outcome of cyclic competition is significantly affected by the spatial distribution of the competitors. Short-range interaction and limited dispersion allows for coexistence of competing species that cannot coexist in a well-mixed environment. In order to elucidate the mechanisms that destroy species diversity we study the intermediate situation of imperfect mixing, typical in aquatic media, in a model of cyclic competition between toxin producing, sensitive and resistant phenotypes. It is found, that chaotic mixing, by changing the character of the spatial distribution, induces coherent oscillations in the populations. The magnitude of the oscillations increases with the strength of mixing, leading to the extinction of some species beyond a critical mixing rate. When mixing is non-uniform in space, coexistence can be sustained at much stronger mixing by the formation of partially isolated regions, that prevent global extinction. The heterogeneity of mixing may enable toxin producing and sensitive strains to coexist for very long time at strong mixing.     

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.     

Do plants need niches? Some recent developments in plant community ecology

Species-rich plant communities appear to defy the competitive exclusion principle, showing relatively few obvious niche differences between coexisting species. Here we explore alternatives to the potentially endless search for new niche axes. Spatial aggregation in populations, non-transitive competition, episodes of density-independent mortality and various non-equilibrium theories allow trophically similar species to coexist for extended periods. In perennial plants or annuals with a seed pool, asynchrony between species in recruitment permits coexistence by the 'storage effect'. There is increasing evidence that species-specific herbivores and pathogens regulate populations of tropical trees to low levels at which competitive exclusion does not occur. The wide variety of alternatives to niche differentiation lead us to question whether plants need occupy different niches to coexist.     

Effects of productivity and disturbance on species richness: a neutral model

Productivity and disturbance are major determinants of species diversity, and results from theoretical models predict that species richness should peak at intermediate levels of both factors. Such "unimodal" responses have been documented in many field and laboratory studies and have usually been attributed to differences among species in competitive ability and/or trade-offs between competitive ability and tolerance to disturbance. Here we show that most documented patterns of disturbance-richness and productivity-richness relationships, as well as the observed interactions between the two factors, can be explained by a simple neutral model where all species are ecologically identical and lack trade-offs in species characteristics. This finding suggests that current neutral theories can be extended to explain patterns of species responses to productivity and disturbance.     

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.