Emergent Shapes of Trait-Based Competition Functions from Resource-Based Models: A Gaussian Is Not Normal in Plant Communities

AbstractIn community ecology, it is widely assumed that organisms with similar traits compete more intensely with one another for resources. This assumption is often encoded into theory and empirical tests via a unimodal competition function, which predicts that per capita competitive effect declines with separation in traits. Yet it remains unknown how well this function represents the true effect of traits on competitive outcomes, especially for long-lived plant communities, where lifetime fitness is difficult to estimate. Here, we evaluate the shape of competition functions embedded in two resource-based (RB) models, wherein plants compete for shared, essential resources. In the first RB model individuals compete for two essential nutrients, and in the second they compete for light in a size-based successional setting. We compared the shapes of the competition functions that emerged from interactions within these RB models to the unimodal function and others shapes commonly applied. In few instances did the trait-based competition function emerging from the RB model even vaguely resemble any of the shapes previously used. The mismatch between these two approaches suggests that theory derived using fixed competition functions based on trait separation may not apply well to plant systems, where individuals compete for shared resources. The more promising path will be to model depletion of resources by populations in relation to their traits, with its consequences for fitness landscapes and competitive exclusion.

The mechanistic basis for higher-order interactions and non-additivity in competitive communities

Motivated by both analytical tractability and empirical practicality, community ecologists have long treated the species pair as the fundamental unit of study. This notwithstanding, the challenge of understanding more complex systems has repeatedly generated interest in the role of so-called higher-order interactions (HOIs) imposed by species beyond the focal pair. Here we argue that HOIs - defined as non-additive effects of density on per capita growth - are best interpreted as emergent properties of phenomenological models (e.g. Lotka-Volterra competition) rather than as distinct 'ecological processes' in their own right. Using simulations of consumer-resource models, we explore the mechanisms and system properties that give rise to HOIs in observational data. We demonstrate that HOIs emerge under all but the most restrictive of assumptions, and that incorporating non-additivity into phenomenological models improves the quantitative and qualitative accuracy of model predictions. Notably, we also observe that HOIs derive primarily from mechanisms and system properties that apply equally to single-species or pairwise systems as they do to more diverse communities. Consequently, there exists a strong mandate for further recognition of non-additive effects in both theoretical and empirical research.

Limiting Similarity? The Ecological Dynamics of Natural Selection among Resources and Consumers Caused by Both Apparent and Resource Competition

Much of ecological theory presumes that natural selection should foster species coexistence by phenotypically differentiating competitors so that the stability of the community is increased, but whether this will actually occur is a question of the ecological dynamics of natural selection. I develop an evolutionary model of consumer-resource interactions based on MacArthur's and Tilman's classic works, including both resource and apparent competition, to explore what fosters or retards the differentiation of resources and their consumers. Analyses of this model predict that consumers will differentiate only on specific ranges of environmental gradients (e.g., greater productivity, weaker stressors, lower structural complexity), and where it occurs, the magnitude of differentiation also depends on gradient position. In contrast to "limiting similarity" expectations, greater intraspecific phenotypic variance results in less differentiation among the consumers because of how phenotypic variation alters the fitness landscapes driving natural selection. In addition, the final structure of the community that results from the coevolution of these interacting species may be highly contingent on the initial properties of the species as the community is being assembled. These results highlight the fact that evolutionary conclusions about community structure cannot be based on ecological arguments of community stability or coexistence but rather must be explicitly based on the ecological dynamics of natural selection.

Generalizing clusters of similar species as a signature of coexistence under competition

Patterns of trait distribution among competing species can potentially reveal the processes that allow them to coexist. It has been recently proposed that competition may drive the spontaneous emergence of niches comprising clusters of similar species, in contrast with the dominant paradigm of greater-than-chance species differences. However, current clustering theory relies largely on heuristic rather than mechanistic models. Furthermore, studies of models incorporating demographic stochasticity and immigration, two key players in community assembly, did not observe clusters. Here we demonstrate clustering under partitioning of resources, partitioning of environmental gradients, and a competition-colonization tradeoff. We show that clusters are robust to demographic stochasticity, and can persist under immigration. While immigration may sustain clusters that are otherwise transient, too much dilutes the pattern. In order to detect and quantify clusters in nature, we introduce and validate metrics which have no free parameters nor require arbitrary trait binning, and weigh species by their abundances rather than relying on a presence-absence count. By generalizing beyond the circumstances where clusters have been observed, our study contributes to establishing them as an update to classical trait patterning theory.

Stability criteria for complex microbial communities

Competition and mutualism are inevitable processes in microbial ecology, and a central question is which and how many taxa will persist in the face of these interactions. Ecological theory has demonstrated that when direct, pairwise interactions among a group of species are too numerous, or too strong, then the coexistence of these species will be unstable to any slight perturbation. Here, we refine and to some extent overturn that understanding, by considering explicitly the resources that microbes consume and produce. In contrast to more complex organisms, microbial cells consume primarily abiotic resources, and mutualistic interactions are often mediated through the mechanism of crossfeeding. We show that if microbes consume, but do not produce resources, then any positive equilibrium will always be stable to small perturbations. We go on to show that in the presence of crossfeeding, stability is no longer guaranteed. However, positive equilibria remain stable whenever mutualistic interactions are either sufficiently weak, or when all pairs of taxa reciprocate each other's assistance.

Emergent niche structuring leads to increased differences from neutrality in species abundance distributions

Species abundance distributions must reflect the dynamic processes involved in community assembly, but whether and when specific processes lead to distinguishable signals is not well understood. Biodiversity and species abundances may be shaped by a variety of influences, but particular attention has been paid to competition, which can involve neutral dynamics, where competitor abundances are governed only by demographic stochasticity and immigration, and dynamics driven by trait differences that enable stable coexistence through the formation of niches. Key recent studies of the species abundance patterns of communities with niches employ simple models with pre-imposed niche structure. These studies suggest that species abundance distributions are insensitive to the relative contributions of niche and neutral processes, especially when diversity is much higher than the number of niches. Here we analyze results from a stochastic population model with competition driven by trait differences. With this model, niche structure emerges as clumps of species that persist along the trait axis, and leads to more substantial differences from neutral species abundance distributions than have been previously shown. We show that heterogeneity in "between-niche" interaction strength (i.e., in the strength of competition between species in different niches) plays the dominant role in shaping the species abundances along the trait axis, acting as a biotic filter favoring species at the centers of niches. Furthermore, we show that heterogeneity in "within-niche" interactions (i.e., in the competition between species in the same niche) counteracts the influence of heterogeneity in "between-niche" interactions on the SAD to some degree. Our results suggest that competitive interactions that produce niches can also influence the shapes of SADs.

Experimentally testing and assessing the predictive power of species assembly rules for tropical canopy ants

Understanding how species assemble into communities is a key goal in ecology. However, assembly rules are rarely tested experimentally, and their ability to shape real communities is poorly known. We surveyed a diverse community of epiphyte-dwelling ants and found that similar-sized species co-occurred less often than expected. Laboratory experiments demonstrated that invasion was discouraged by the presence of similarly sized resident species. The size difference for which invasion was less likely was the same as that for which wild species exhibited reduced co-occurrence. Finally we explored whether our experimentally derived assembly rules could simulate realistic communities. Communities simulated using size-based species assembly exhibited diversities closer to wild communities than those simulated using size-independent assembly, with results being sensitive to the combination of rules employed. Hence, species segregation in the wild can be driven by competitive species assembly, and this process is sufficient to generate observed species abundance distributions for tropical epiphyte-dwelling ants.

General relationships between consumer dispersal, resource dispersal and metacommunity diversity

One of the central questions of metacommunity theory is how dispersal of organisms affects species diversity. Here, we show that the diversity-dispersal relationship should not be studied in isolation of other abiotic and biotic flows in the metacommunity. We study a mechanistic metacommunity model in which consumer species compete for an abiotic or biotic resource. We consider both consumer species specialised to a habitat patch, and generalist species capable of using the resource throughout the metacommunity. We present analytical results for different limiting values of consumer dispersal and resource dispersal, and complement these results with simulations for intermediate dispersal values. Our analysis reveals generic patterns for the combined effects of consumer and resource dispersal on the metacommunity diversity of consumer species, and shows that hump-shaped relationships between local diversity and dispersal are not universal. Diversity-dispersal relationships can also be monotonically increasing or multimodal. Our work is a new step towards a general theory of metacommunity diversity integrating dispersal at multiple trophic levels.

Limiting similarity, species packing, and the shape of competition kernels

A traditional question in community ecology is whether species' traits are distributed as more-or-less regularly spaced clusters. Interspecific competition has been suggested to play a role in such structuring of communities. The seminal theoretical work on limiting similarity and species packing, presented four decades ago by Robert MacArthur, Richard Levins and Robert May, has recently been extended. There is now a deeper understanding of how competitive interactions influence community structure, for instance, how the shape of competition kernels can determine the clustering of species' traits. Competition is typically weaker for greater phenotypic difference, and the shape of the dependence defines a competition kernel. The clustering tendencies of kernels interact with other effects, such as variation in resource availability along a niche axis, but the kernel shape can have a decisive influence on community structure. Here we review and further extend the recent developments and evaluate their importance.

Asymmetric and frequency-dependent pollinator-mediated interactions may influence competitive displacement in two vernal pool plants

A plant species immigrating into a community may experience a rarity disadvantage due to competition for the services of pollinators. These negative reproductive interactions have the potential to lead to competitive displacement or exclusion of a species from a site. In this study, we used one- and two-species arrays of potted plants to test for density and frequency dependence in pollinator-mediated and above-ground intraspecific and interspecific competition between two species of Limnanthes that have overlapping ranges, but rarely occur in close sympatry. There were asymmetric competitive effects; the species responded differently to their frequency within 16-plant replacement series arrays. Limnanthes douglasii rosea experienced stronger reductions in lifetime and per-flower fertility, likely due to pollinator-mediated competition with Limnanthes alba. This effect may be linked to asymmetrical competition through heterospecific pollen transfer. This study demonstrates that pollinator-mediated competition may discourage establishment of L. d. rosea in sites already occupied by its congener.

Persistence of high diversity in non-equilibrium ecological communities: implications for modern and fossil ecosystems

Explaining the origin and maintenance of biodiversity is critical for understanding the potential consequences of present-day environmental change on ecological communities, as well as the evolutionary history of ecosystems in the Earth's past. Much effort in theoretical ecology has focused on identifying mechanisms that promote stable coexistence of species at equilibrium. However, in a consumer-resource model of competition along an environmental gradient, high-diversity assemblages have the potential to persist in non-equilibrium states for millions of generations with very little species loss. Species' populations in such competitively accommodated communities show slow drift; if disrupted, they rapidly reorganize into alternative persistent states. Fossil examples of prolonged ecological stability lasting 1-5 Myr punctuated by rapid reorganization (e.g. brachiopods from the Permian Reef of west Texas) suggest that some palaeocommunities represent a record of periodically disrupted transient states rather than stable equilibria. The similarity between the theoretical results reported here and palaeontological data suggests that the maintenance of high-diversity communities, both in the past and present, may reflect long-duration, non-equilibrium transient dynamics. If so, this has implications for the response of such communities to present-day environmental change, as well as for the evolution of lineages in such systems.

Niche and fitness differences relate the maintenance of diversity to ecosystem function

The frequently observed positive correlation between species diversity and community biomass is thought to depend on both the degree of resource partitioning and on competitive dominance between consumers, two properties that are also central to theories of species coexistence. To make an explicit link between theory on the causes and consequences of biodiversity, we define in a precise way two kinds of differences among species: niche differences, which promote coexistence, and relative fitness differences, which promote competitive exclusion. In a classic model of exploitative competition, promoting coexistence by increasing niche differences typically, although not universally, increases the "relative yield total", a measure of diversity's effect on the biomass of competitors. In addition, however, we show that promoting coexistence by decreasing relative fitness differences also increases the relative yield total. Thus, two fundamentally different mechanisms of species coexistence both strengthen the influence of diversity on biomass yield. The model and our analysis also yield insight on the interpretation of experimental diversity manipulations. Specifically, the frequently reported "complementarity effect" appears to give a largely skewed estimate of resource partitioning. Likewise, the "selection effect" does not seem to isolate biomass changes attributable to species composition rather than species richness, as is commonly presumed. We conclude that past inferences about the cause of observed diversity-function relationships may be unreliable, and that new empirical estimates of niche and relative fitness differences are necessary to uncover the ecological mechanisms responsible for diversity-function relationships.

Determining the functional form of density dependence: deductive approaches for consumer-resource systems having a single resource

Consumer-resource models are used to deduce the functional form of density dependence in the consumer population. A general approach to determining the form of consumer density dependence is proposed; this involves determining the equilibrium (or average) population size for a series of different harvest rates. The relationship between a consumer's mortality and its equilibrium population size is explored for several one-consumer/one-resource models. The shape of density dependence in the resource and the shape of the numerical and functional responses all tend to be "inherited" by the consumer's density dependence. Consumer-resource models suggest that density dependence will very often have both concave and convex segments, something that is impossible under the commonly used theta-logistic model. A range of consumer-resource models predicts that consumer population size often declines at a decelerating rate with mortality at low mortality rates, is insensitive to or increases with mortality over a wide range of intermediate mortalities, and declines at a rapidly accelerating rate with increased mortality when mortality is high. This has important implications for management and conservation of natural populations.

Adaptive changes in prey vulnerability shape the response of predator populations to mortality

Simple models are used to explore how adaptive changes in prey vulnerability alter the population response of their predator to increased mortality. If the mortality is an imposed harvest, the change in prey vulnerability also influences the relationship between harvest effort and yield of the predator. The models assume that different prey phenotypes share a single resource, but have different vulnerabilities to the predator. Decreased vulnerability is assumed to decrease resource consumption rate. Adaptive change may occur by phenotypic changes in the traits of a single species or by shifts in the abundances of a pair of coexisting species or morphs. The response of the predator population is influenced by the shape of the predator's functional response, the shape of resource density dependence, and the shape of the tradeoff between vulnerability and food intake in the prey. Given a linear predator functional response, adaptive prey defense tends to produce a decelerating decline in predator population size with increased mortality. Prey defense may also greatly increase the range of mortality rates that allow predator persistence. If the predator has a type-2 response with a significant handling time, adaptive prey defense may have a greater variety of effects on the predator's response to mortality, sometimes producing alternative attractors, population cycles, or increased mean predator density. Situations in which there is disruptive selection on prey defense often imply a bimodal change in yield as a function of harvesting effort, with a minimum at intermediate effort. These results argue against using single-species models of density dependent growth to manage predatory species, and illustrate the importance of incorporating anti-predator behavior into models in applied population ecology.