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.     

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.     

Local community size mediates ecological drift and competition in metacommunities

The outcome of competitive interactions is likely to be influenced by both competitive dominance (i.e. niche-based dynamics) and ecological drift (i.e. neutral dynamics governed by demographic stochasticity). However, spatial models of competition rarely consider the joint operation of these two processes. We develop a model based on the original competition-colonization trade-off model that incorporates niche and neutral processes and several realistic facets of ecological dynamics: it allows local competition (i.e. competition within a patch) to occur within communities of a finite size, it allows competitors to vary in the degree of competitive asymmetry, and it includes the role of local migration (i.e. propagule pressure). The model highlights the role of community size, i.e. the number of competitors in the local community, in mediating the relative importance of stochastic and deterministic forces. In metacommunities where local communities are small, ecological drift is substantial enough that strong competitors become effectively neutral, creating abrupt changes in the outcome of competition not predicted by the standard competition-colonization trade-off. Importantly, the model illustrates that, even when other aspects of species interactions (e.g. migration ability, competitive ability) are unchanged, local community size can alter the dynamics of metacommunity persistence. Our work demonstrates that activities which reduce the size of local communities, such as habitat destruction and degradation, effectively compound the extinction debt.     

The form of direct interspecific competition modifies secondary extinction patterns in multi‐trophic food webs

Forcibly removing species from ecosystems has important consequences for the remaining assemblage, leading to changes in community structure, ecosystem functioning and secondary (cascading) extinctions. One key question that has arisen from single‐ and multi‐trophic ecosystem models is whether the secondary extinctions that occur within competitive communities (guilds) are also important in multi‐trophic ecosystems? The loss of consumer–resource links obviously causes secondary extinction of specialist consumers (topological extinctions), but the importance of secondary extinctions in multi‐trophic food webs driven by direct competitive exclusion remains unknown. Here I disentangle the effects of extinctions driven by basal competitive exclusion from those caused by trophic interactions in a multi‐trophic ecosystem (basal producers, intermediate and top consumers). I compared food webs where basal species either show diffuse (all species compete with each other identically: no within guild extinctions following primary extinction) or asymmetric competition (unequal interspecific competition: within guild extinctions are possible). Basal competitive exclusion drives extra extinction cascades across all trophic levels, with the effect amplified in larger ecosystems, though varying connectance has little impact on results. Secondary extinction patterns based on the relative abundance of the species lost in the primary extinction differ qualitatively between diffuse and asymmetric competition. Removing asymmetric basal species with low (high) abundance triggers fewer (more) secondary extinctions throughout the whole food web than removing diffuse basal species. Rare asymmetric competitors experience less pressure from consumers compared to rare diffuse competitors. Simulations revealed that diffuse basal species are never involved in extinction cascades, regardless of the trophic level of a primary extinction, while asymmetric competitors were. This work highlights important qualitative differences in extinction patterns that arise when different assumptions are made about the form of direct competition in multi‐trophic food webs.     

EVOLUTION IN FLUCTUATING ENVIRONMENTS: DECOMPOSING SELECTION INTO ADDITIVE COMPONENTS OF THE ROBERTSON–PRICE EQUATION

We analyze the stochastic components of the Robertson–Price equation for the evolution of quantitative characters that enables decomposition of the selection differential into components due to demographic and environmental stochasticity. We show how these two types of stochasticity affect the evolution of multivariate quantitative characters by defining demographic and environmental variances as components of individual fitness. The exact covariance formula for selection is decomposed into three components, the deterministic mean value, as well as stochastic demographic and environmental components. We show that demographic and environmental stochasticity generate random genetic drift and fluctuating selection, respectively. This provides a common theoretical framework for linking ecological and evolutionary processes. Demographic stochasticity can cause random variation in selection differentials independent of fluctuating selection caused by environmental variation. We use this model of selection to illustrate that the effect on the expected selection differential of random variation in individual fitness is dependent on population size, and that the strength of fluctuating selection is affected by how environmental variation affects the covariance in Malthusian fitness between individuals with different phenotypes. Thus, our approach enables us to partition out the effects of fluctuating selection from the effects of selection due to random variation in individual fitness caused by demographic stochasticity.     

Environmental variation, stochastic extinction, and competitive coexistence

Understanding how environmental fluctuations affect population persistence is essential for predicting the ecological impacts of expected future increases in climate variability. However, two bodies of theory make opposite predictions about the effect of environmental variation on persistence. Single-species theory, common in conservation biology and population viability analyses, suggests that environmental variation increases the risk of stochastic extinction. By contrast, coexistence theory has shown that environmental variation can buffer inferior competitors against competitive exclusion through a storage effect. We reconcile these two perspectives by showing that in the presence of demographic stochasticity, environmental variation can increase the chance of extinction while simultaneously stabilizing coexistence. Our stochastic simulations of a two-species storage effect model reveal a unimodal relationship between environmental variation and coexistence time, implying maximum coexistence at intermediate levels of environmental variation. The unimodal pattern reflects the fact that the stabilizing influence of the storage effect accumulates rapidly at low levels of environmental variation, whereas the risk of extinction due to the combined effects of environmental variation and demographic stochasticity increases most rapidly at higher levels of variation. Future increases in environmental variation could either increase or decrease an inferior competitor's expected persistence time, depending on the distance between the present level of environmental variation and the optimal level anticipated by this theory.     

Differentiating between niche and neutral assembly in metacommunities using null models of β‐diversity

The β‐null deviation measure, developed as a null model for β‐diversity, is increasingly used in empirical studies to detect the underlying structuring mechanisms in communities (e.g. niche versus neutral and stochastic versus deterministic). Despite growing use, the ecological interpretation of the presence/absence and abundance‐based versions of the β‐null diversity measure have not been tested against communities with known assembly mechanisms, and thus have not been validated as an appropriate tool for inferring assembly mechanisms. Using a mechanistic model with known assembly mechanisms, we simulated replicate metacommunities and examined β‐null deviation values 1) across a gradient of niche (species‐sorting) to neutrally structured metacommunities, 2) through time, and 3) we compared the effect of changes in assembly mechanism on the performance of the β‐null deviation measures. The impact of stochasticity on assembly outcomes was also considered. β‐null deviation measures proved to be interpretable as a measure of niche or neutral assembly. However, the presence/absence version of the β‐null deviation measure could not differentiate between niche and neutral metacommunities if demographic stochasticity were present. The abundance‐based β‐null deviation measure was successful in distinguishing between niche and neutral metacommunities and was robust to the presence of stochasticity, changes through time, and changing assembly mechanisms. However, we suggest that it is not robust to changing abundance evenness distributions or sampling of communities, and so its interpretation still requires some care. We encourage the testing of the assumptions behind null models for ecology and care in their application.     

A minimum stochastic model evaluating the interplay between population density and drift for species coexistence

Despite the general acknowledgment of the role of niche and stochastic process in community dynamics, the role of species relative abundances according to both perspectives may have different effects regarding coexistence patterns. In this study, we explore a minimum probabilistic stochastic model to determine the relationship of populations relative and total abundances with species chances to outcompete each other and their persistence in time (i.e., unstable coexistence). Our model is focused on the effects drift (i.e., random sampling of recruitment) under different scenarios of selection (i.e., fitness differences between species). Our results show that taking into account the stochasticity in demographic properties and conservation of individuals in closed communities (zero-sum assumption), initial population abundance can strongly influence species chances to outcompete each other, despite fitness inequalities between populations, and also, influence the period of coexistence of these species in a particular time interval. Systems carrying capacity can have an important role in species coexistence by exacerbating fitness inequalities and affecting the size of the period of coexistence. Overall, the simple stochastic formulation used in this study demonstrated that populations initial abundances could act as an equalizing mechanism, reducing fitness inequalities, which can favor species coexistence and even make less fitted species to be more likely to outcompete better-fitted species, and thus to dominate ecological communities in the absence of niche mechanisms. Although our model is restricted to a pair of interacting species, and overall conclusions are already predicted by the Neutral Theory of Biodiversity, our main objective was to derive a model that can explicitly show the functional relationship between population densities and community mono-dominance odds. Overall, our study provides a straightforward understanding of how a stochastic process (i.e., drift) may affect the expected outcome based on species selection (i.e., fitness inequalities among species) and the resulting outcome regarding unstable coexistence among species.     

Fluctuating Environments and Phytoplankton Community Structure: A Stochastic Model

Spatial heterogeneity in organism and resource distributions can generate temporal heterogeneity in resource access for simple organisms like phytoplankton. The role of temporal heterogeneity as a structuring force for simple communities is investigated via models of phytoplankton with contrasting life histories competing for a single fluctuating resource. A stochastic model in which environmental and demographic stochasticity are treated separately is compared with a model with deterministic resource variation to assess the importance of stochasticity. When compared with the deterministic model, the stochastic model allows for coexistence over a wider range of parameter values (or life-history types). The model suggests that demographic stochasticity alone is far more important in increasing the possibility of coexistence than environmental stochasticity alone. However, the combined effects of both types of stochasticity produce the largest likelihood of coexistence. Finally, the influence of relative nutrient levels and nutrient pulse frequency on these results is addressed. We relate our findings to variable environment theory with evidence for both relative nonlinearity and the storage effect acting in this model. We show for the first time that temporal dynamics generated by demographic stochasticity may operate like the storage effect at particular spatial scales.     

Environmental changes affect the assembly of soil bacterial community primarily by mediating stochastic processes

Both ‘species fitness difference’‐based deterministic processes, such as competitive exclusion and environmental filtering, and ‘species fitness difference’‐independent stochastic processes, such as birth/death and dispersal/colonization, can influence the assembly of soil microbial communities. However, how both types of processes are mediated by anthropogenic environmental changes has rarely been explored. Here we report a novel and general pattern that almost all anthropogenic environmental changes that took place in a grassland ecosystem affected soil bacterial community assembly primarily through promoting or restraining stochastic processes. We performed four experiments mimicking 16 types of environmental changes and separated the compositional variation of soil bacterial communities caused by each environmental change into deterministic and stochastic components, with a recently developed method. Briefly, because the difference between control and treatment communities is primarily caused by deterministic processes, the deterministic change was quantified as (mean compositional variation between treatment and control) – (mean compositional variation within control). The difference among replicate treatment communities is primarily caused by stochastic processes, so the stochastic change was estimated as (mean compositional variation within treatment) – (mean compositional variation within control). The absolute of the stochastic change was greater than that of the deterministic change across almost all environmental changes, which was robust for both taxonomic and functional‐based criterion. Although the deterministic change may become more important as environmental changes last longer, our findings showed that changes usually occurred through mediating stochastic processes over 5 years, challenging the traditional determinism‐dominated view.     

Departures from neutrality induced by niche and relative fitness differences

Breaking the core assumption of ecological equivalence in Hubbell’s “neutral theory of biodiversity” requires a theory of species differences. In one framework for characterizing differences between competing species, non-neutral interactions are said to involve both niche differences, which promote stable coexistence, and relative fitness differences, which promote competitive exclusion. We include both in a stochastic community model in order to determine if relative fitness differences compensate for changes in community structure and dynamics induced by niche differences, possibly explaining neutral theory’s apparent success. We show that species abundance distributions are sensitive to both niche and relative fitness differences, but that certain combinations of differences result in abundance distributions that are indistinguishable from the neutral case. In contrast, the distribution of species’ lifetimes, or the time between speciation and extinction, differs under all combinations of niche and relative fitness differences. The results from our model experiment are inconsistent with the hypothesis of “emergent neutrality” and support instead a hypothesis that relative fitness differences counteract effects of niche differences on distributions of abundance. However, an even more developed theory of interspecific variation appears necessary to explain the diversity and structure of non-neutral communities.     

Assessing the relative importance of neutral stochasticity in ecological communities

A central current debate in community ecology concerns the relative importance of deterministic versus stochastic processes underlying community structure. However, the concept of stochasticity presents several profound philosophical, theoretical and empirical challenges, which we address here. The philosophical argument that nothing in nature is truly stochastic can be met with the following operational concept of neutral stochasticity in community ecology: change in the composition of a community (i.e. community dynamics) is neutrally stochastic to the degree that individual demographic events – birth, death, immigration, emigration – which cause such changes occur at random with respect to species identities. Empirical methods for identifying the stochastic component of community dynamics or structure include null models and multivariate statistics on observational species‐by‐site data (with or without environmental or trait data), and experimental manipulations of ‘stochastic’ species colonization order or relative densities and frequencies of competing species. We identify the fundamental limitations of each method with respect to its ability to allow inferences about stochastic community processes. Critical future needs include greater precision in articulating the link between results and ecological inferences, a comprehensive theoretical assessment of the interpretation of statistical analyses of observational data, and experiments focusing on community size and on natural variation in species colonization order. Synthesis Community structure and dynamics have often been described as being underlain by ‘stochastic’ or ‘neutral’ processes, but there is great confusion as to what exactly this means. We attempt to provide conceptual clarity by specifying precisely what focal ecological variable (e.g. species distributions, community composition, demography) is considered to be stochastic with respect to what other variables (e.g. other species' distributions, traits, environment) when using different empirical methods. We clarify what inferences can be drawn by different observational and experimental approaches, and we suggest future avenues of research to better understand the role of neutral stochasticity in community ecology.     

Demographic trade-offs determine species abundance and diversity

Aims Much recent theory has focused on the role of neutral processes in assembling communities, but the basic assumption that all species are demographically identical has found little empirical support. Here, we show that the framework of the current neutral theory can easily be generalized to incorporate species differences so long as fitness equivalence among individuals is maintained through trade-offs between birth and death.Methods Our theory development is based on a careful reformulation of the Moran model of metacommunity dynamics in terms of a non-linear one-step stochastic process, which is described by a master equation.Important findings We demonstrate how fitness equalization through demographic trade-offs can generate significant macroecological diversity patterns, leading to a very different interpretation of the relation between Fisher's α and Hubbell's fundamental biodiversity number. Our model shows that equal fitness (not equal demographics) significantly promotes species diversity through strong selective sieving of community membership against high-mortality species, resulting in a positive association between species abundance and per capita death rate. An important implication of demographic trade-off is that it can partly explain the excessively high speciation rates predicted by the neutral theory of the stronger symmetry. Fitness equalization through demographic trade-offs generalizes neutral theory by considering heterospecific demographic difference, thus representing a significant step toward integrating the neutral and niche paradigms of biodiversity.     

The structure and stability of model ecosystems assembled in a variable environment

To explore how environmental variability may create non‐random community structure, we simulated the assembly of model communities under varying levels of environmental variability. We assembled communities by creating a large pool of randomly constructed species, and then added species from this pool sequentially, allowing extinctions of invading and resident species to occur until the community became saturated. Because much current research on community structure focuses on single trophic levels, we constructed species pools consisting only of competitors. To compare with more realistic communities, we also created species pools with multiple trophic levels. For both types of communities, following assembly we calculated a variety of metrics of community structure, and five measures of community stability. Communities assembled under high environmental variability had fewer species, fewer and weaker interactions among species, and greater evenness in abundance of persisting species. For single trophic‐level communities, community size was dictated primarily by competitive exclusion. In contrast, for multiple trophic‐level communities, community size was increasingly limited by dynamical instabilities as environmental variability increased. Differences in community structure resulting from assembly under high environmental variability led to differences in community stability. According to two measures of stability related to population variability – the characteristic return rate to equilibrium and the coefficient of variation in individual species densities – stability increased for communities assembled under high environmental variability. In contrast, three additional measures of stability that are not directly related to population variability showed a variety of patterns, either increasing, decreasing, or remaining constant. Thus, communities assembled in highly variable environments are not necessarily generically more stable. Our results demonstrate that environmental variability can structure communities and affect their stability properties in non‐trivial ways. Thus, when making predictions about the response of communities to future extinctions or environmental degradation, account should be given to the forces responsible for community structure.     

Resources Alter the Structure and Increase Stochasticity in Bromeliad Microfauna Communities

Although stochastic and deterministic processes have been found to jointly shape structure of natural communities, the relative importance of both forces may vary across different environmental conditions and across levels of biological organization. We tested the effects of abiotic environmental conditions, altered trophic interactions and dispersal limitation on the structure of aquatic microfauna communities in Costa Rican tank bromeliads. Our approach combined natural gradients in environmental conditions with experimental manipulations of bottom-up interactions (resources), top-down interactions (predators) and dispersal at two spatial scales in the field. We found that resource addition strongly increased the abundance and reduced the richness of microfauna communities. Community composition shifted in a predictable way towards assemblages dominated by flagellates and ciliates but with lower abundance and richness of algae and amoebae. While all functional groups responded strongly and predictably to resource addition, similarity among communities at the species level decreased, suggesting a role of stochasticity in species-level assembly processes. Dispersal limitation did not affect the communities. Since our design excluded potential priority effects we can attribute the differences in community similarity to increased demographic stochasticity of resource-enriched communities related to erratic changes in population sizes of some species. In contrast to resources, predators and environmental conditions had negligible effects on community structure. Our results demonstrate that bromeliad microfauna communities are strongly controlled by bottom-up forces. They further suggest that the relative importance of stochasticity may change with productivity and with the organizational level at which communities are examined.     

A mathematical synthesis of niche and neutral theories in community ecology

The debate between niche-based and neutral community theories centers around the question of which forces shape predominantly ecological communities. Niche theory attributes a central role to niche differences between species, which generate a difference between the strength of intra- and interspecific interactions. Neutral theory attributes a central role to migration processes and demographic stochasticity. One possibility to bridge these two theories is to combine them in a common mathematical framework. Here we propose a mathematical model that integrates the two perspectives. From a niche-based perspective, our model can be interpreted as a Lotka-Volterra model with symmetric interactions in which we introduce immigration and demographic stochasticity. From a neutral perspective, it can be interpreted as Hubbell's local community model in which we introduce a difference between intra- and interspecific interactions. We investigate the stationary species abundance distribution and other community properties as functions of the interaction coefficient, the immigration rate and the strength of demographic stochasticity.     

Why equalising trade-offs aren't always neutral

Equalising trade-offs, such as seed mass vs. number, have been invoked to reconcile neutral theory with observed differences between species. This is an appealing explanation for the dramatic seed size variation seen within guilds of otherwise similar plants: under size-symmetric competition, where resource capture is proportional to mass, the outcome of competition should be insensitive to whether species produce many small seeds or few large ones. However, under this assumption, stochastic variation in seed rain leads to exclusion of all but the smallest-seeded species. Thus stochasticity in seed arrivals, a process that was previously thought to generate drift, instead results in deterministic competitive exclusion. A neutral outcome is possible under one special case of a more general equalising framework, where seed mass affects survival but not competition. Further exploration of the feasibility of neutral trade-offs is needed to understand the respective roles of neutrality and niche structure in community dynamics.     

How variation between individuals affects species coexistence

Although the effects of variation between individuals within species are traditionally ignored in studies of species coexistence, the magnitude of intraspecific variation in nature is forcing ecologists to reconsider. Compelling intuitive arguments suggest that individual variation may provide a previously unrecognised route to diversity maintenance by blurring species‐level competitive differences or substituting for species‐level niche differences. These arguments, which are motivating a large body of empirical work, have rarely been evaluated with quantitative theory. Here we incorporate intraspecific variation into a common model of competition and identify three pathways by which this variation affects coexistence: (1) changes in competitive dynamics because of nonlinear averaging, (2) changes in species’ mean interaction strengths because of variation in underlying traits (also via nonlinear averaging) and (3) effects on stochastic demography. As a consequence of the first two mechanisms, we find that intraspecific variation in competitive ability increases the dominance of superior competitors, and intraspecific niche variation reduces species‐level niche differentiation, both of which make coexistence more difficult. In addition, individual variation can exacerbate the effects of demographic stochasticity, and this further destabilises coexistence. Our work provides a theoretical foundation for emerging empirical interests in the effects of intraspecific variation on species diversity.     

The risk of competitive exclusion during evolutionary branching: Effects of resource variability, correlation and autocorrelation

Evolutionary branching has been suggested as a mechanism to explain ecological speciation processes. Recent studies indicate however that demographic stochasticity and environmental fluctuations may prevent branching through stochastic competitive exclusion. Here we extend previous theory in several ways; we use a more mechanistic ecological model, we incorporate environmental fluctuations in a more realistic way and we include environmental autocorrelation in the analysis. We present a single, comprehensible analytical result which summarizes most effects of environmental fluctuations on evolutionary branching driven by resource competition. Corroborating earlier findings, we show that branching may be delayed or impeded if the underlying resources have uncorrelated or negatively correlated responses to environmental fluctuations. There is also a strong impeding effect of positive environmental autocorrelation, which can be related to results from recent experiments on adaptive radiation in bacterial microcosms. In addition, we find that environmental fluctuations can lead to cycles of repeated branching and extinction.