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Soil microorganisms play a major role in shaping plant diversity, not only through their direct effects as pathogens, mutualists, and decomposers, but also by altering the outcome of plant interactions. In particular, previous research has shown that the soil community often generates frequency-dependent feedback loops among plants that can either stabilize or destabilize species interactions and thereby promote or hinder species coexistence. However, recent insights from modern coexistence theory have shown that microbial effects on plant coexistence depend not only on these stabilizing or destabilizing effects, but also on the degree to which they generate competitive fitness differences. While many previous experiments have generated the data necessary for evaluating microbially mediated fitness differences, these effects have rarely been quantified in the literature. Here, we present a meta-analysis of data from 50 studies, which we used to quantify the microbially mediated (de)stabilization and fitness differences derived from a classic plant-soil feedback model. We found that across 518 plant species pairs, soil microbes generated both stabilization (or destabilization) and fitness differences, but also that the microbially mediated fitness differences dominated. As a consequence, if plants are otherwise equivalent competitors, the balance of soil microbe–generated (de)stabilization and fitness differences drives species exclusion much more frequently than coexistence or priority effects. Our work shows that microbially mediated fitness differences are an important but overlooked effect of soil microbes on plant coexistence. This finding paves the way for a more complete understanding of the processes that maintain plant biodiversity.

Although observations of species-rich communities have long served as a primary motivation for research on the coexistence of competitors, the majority of our empirical and theoretical understanding comes from two-species systems. How much of the coexistence observed in species-rich communities results from indirect effects among competitors that only emerge in diverse systems remains poorly understood. Resolving this issue requires simple, scalable, and intuitive metrics for quantifying the conditions for coexistence in multispecies systems, and how these conditions differ from those expected based solely on pairwise interactions. To achieve these aims, we develop a structural approach for studying the set of parameter values compatible with n-species coexistence given the geometric constraints imposed by the matrix of competition coefficients. We derive novel mathematical metrics analogous to stabilizing niche differences and fitness differences that measure the range of conditions compatible with multispecies coexistence, incorporating the effects of indirect interactions emerging in diverse systems. We show how our measures can be used to quantify the extent to which the conditions for coexistence in multispecies systems differ from those that allow pairwise coexistence, and apply the method to a field system of annual plants. We conclude by presenting new challenges and empirical opportunities emerging from our structural metrics of multispecies coexistence.

We give a comprehensive review of Chesson's coexistence theory, summarizing, for the first time, all its fundamental details in one single document. Our goal is for both theoretical and empirical ecologists to be able to use the theory to interpret their findings, and to get a precise sense of the limits of its applicability. To this end, we introduce an explicit handling of limiting factors, and a new way of defining the scaling factors that partition invasion growth rates into the different mechanisms contributing to coexistence. We explain terminology such as relative nonlinearity, storage effect, and growth-density covariance, both in a formal setting and through their biological interpretation. We review the theory's applications and contributions to our current understanding of species coexistence. While the theory is very general, it is not well suited to all problems, so we carefully point out its limitations. Finally, we critique the paradigm of decomposing invasion growth rates into stabilizing and equalizing components: we argue that these concepts are useful when used judiciously, but have often been employed in an overly simplified way to justify false claims.

Modern coexistence theory is increasingly used to explain how differences between competing species lead to coexistence versus competitive exclusion. Although research testing this theory has focused on deterministic cases of competitive exclusion, in which the same species always wins, mounting evidence suggests that competitive exclusion is often historically contingent, such that whichever species happens to arrive first excludes the other. Coexistence theory predicts that historically contingent exclusion, known as priority effects, will occur when large destabilizing differences (positive frequency-dependent growth rates of competitors), combined with small fitness differences (differences in competitors’ intrinsic growth rates and sensitivity to competition), create conditions under which neither species can invade an established population of its competitor. Here we extend the empirical application of modern coexistence theory to determine the conditions that promote priority effects. We conducted pairwise invasion tests with four strains of nectar-colonizing yeasts to determine how the destabilizing and fitness differences that drive priority effects are altered by two abiotic factors characterizing the nectar environment: sugar concentration and pH. We found that higher sugar concentrations increased the likelihood of priority effects by reducing fitness differences between competing species. In contrast, higher pH did not change the likelihood of priority effects, but instead made competition more neutral by bringing both fitness differences and destabilizing differences closer to zero. This study demonstrates how the empirical partitioning of priority effects into fitness and destabilizing components can elucidate the pathways through which environmental conditions shape competitive interactions.

Although research on the role of competitive interactions during community assembly began decades ago, a recent revival of interest has led to new discoveries and research opportunities. Using contemporary coexistence theory that emphasizes stabilizing niche differences and relative fitness differences, we evaluate three empirical approaches for studying community assembly. We show that experimental manipulations of the abiotic or biotic environment, assessments of trait-phylogeny-environment relationships, and investigations of frequency-dependent population growth all suggest strong influences of stabilizing niche differences and fitness differences on the outcome of plant community assembly. Nonetheless, due to the limitations of these approaches applied in isolation, we still have a poor understanding of which niche axes and which traits determine the outcome of competition and community structure. Combining current approaches represents our best chance of achieving this goal, which is fundamental to conceptual ecology and to the management of plant communities under global change.

1. A quantitative approach to species coexistence based on the invasibility criterion has led to an appreciation of coexistence mechanisms in terms of stabilizing and equalizing components, but major challenges are the need to consider general multispecies settings, interactions beyond competition, and multiple scales of space and time. Moreover, two essential concepts, species-level average fitness and scaling factors, have not had clear definitions. 2. A general approach to defining average fitnesses and scaling factors is given, along with the origin of stabilizing mechanisms as deviations from a reference model where no coexistence is possible. Illustrations are general Lotka-Volterra models, models accounting specifically for resource use and natural enemies, and models with temporal fluctuations. 3. Community averages of stabilizing mechanisms reveal overall opportunities for coexistence, and define mechanisms more precisely through their formulae. Average fitnesses adjusted for the presence of coexistence mechanisms provide a better definition of equalizing mechanisms. While these ideas apply to the components of invasion rates, permanence theory and stochastic persistence theory show how invasion rates can be used to demonstrate species coexistence in complex settings. 4. Although species coexistence has often focused on competition, detailed models of the roles of natural enemies provide a new perspective on the opportunities for coexistence in nature. The concept of apparent competition recognizes the essential symmetry between density-dependence from resource depletion and from supporting natural enemies. Natural enemy partitioning is the natural analogue of resource partitioning and has an equivalent role in promoting coexistence. Rather than reinforcing each other, however, the strength of coexistence is often intermediate between that implied by resource partitioning alone and that implied by natural enemy partitioning alone, as elucidated by recent LotkaVolterra theory. 5. Synthesis. Although there are alternative approaches for understanding coexistence in multispecies settings, ideas based on stabilizing and equalizing mechanisms continue to provide new insights. Multiple species and multiple trophic levels are naturally challenging, but the new theories of permanence and stochastic persistence support the critical role of invasion rates in species coexistence, and thus support the understanding to be derived by partitioning invasion rates into average fitness differences and stabilizing components.

Modern coexistence theory and contemporary niche theory represent parallel frameworks for understanding the niche's role in species coexistence. Despite increasing prominence and shared goals, their compatibility and complementarity have received little attention. This paucity of overlap not only presents an obstacle to newcomers to the field, but it also precludes further conceptual advances at their interface. Here, we present a synthetic treatment of the two frameworks. We review their main concepts and explore their theoretical and empirical relationship, focusing on how the resource supply ratio, impact niche, and requirement niche of contemporary niche theory translate into the stabilizing and equalizing processes of modern coexistence theory. We show, for a general consumer-resource model, that varying resource supply ratios reflects an equalizing process; varying impact niche overlap reflects a stabilizing process; and varying requirement niche overlap may be both stabilizing and equalizing, but has no qualitative effect on coexistence. These generalizations provide mechanistic insight into modern coexistence theory, while also clarifying the role of contemporary niche theory's impacts and requirements in mediating coexistence. From an empirical perspective, we recommend a hierarchical approach, in which quantification of the strength of stabilizing mechanisms is used to guide more focused investigation into the underlying niche factors determining species coexistence. Future research that considers alternative assumptions, including different forms of species interaction, spatiotemporal heterogeneity, and priority effects, would facilitate a more complete synthesis of the two frameworks.

Coexistence between plant species is well known to depend on the outcomes of species interactions within an environmental context. The incorporation of environmental variation into empirical studies of coexistence are rare, however, due to the complex experiments needed to do so and the lack of feasible modelling approaches for determining how environmental factors alter specific coexistence mechanisms. In this article, we present a simple modelling framework for assessing how variation in species interactions across environmental gradients impact on niche overlap and fitness differences, two core determinants of coexistence. We use a novel formulation of an annual plant population dynamics model that allows for competitive and facilitative species interactions and for variation in the strength and direction of these interactions across environmental gradients. Using this framework, we examine outcomes of plant–plant interactions between four commonly co‐occurring annual plant species from Western Australian woodlands. We then determine how niche overlap and fitness differences between these species vary across three environmental gradients previously identified as important for structuring diversity patterns in this system: soil phosphorus, shade and water. We found facilitation to be a widespread phenomenon and that interactions between most species pairs shift between competitive and facilitative across multiple environmental gradients. Environmental conditions also altered the strength, direction and relative variation of both niche overlap and fitness differences in nonlinear and unpredictable ways. Synthesis. We provide a simple framework for incorporating environmental heterogeneity into explorations of coexistence mechanisms. Our findings highlight the importance of the environment in determining the outcome of species interactions and the potential for pairwise coexistence between species. The prevalence of facilitation in our system indicates a need to improve current theoretical frameworks of coexistence to include noncompetitive interactions and ways of translating these effects into explicit predictions of coexistence. Our study also suggests a need for further research into determining which factors result in consistent responses of niche overlap and fitness differences to environmental variation. Such information will improve our ability to predict outcomes of coexistence, invasion events and responses of whole communities to future environmental change. Foreign Language 环境因素的变动将影响物种之间的互动,进而决定它们的共存。但是,环境变数甚少被包括在实验性研究内,因为这需要复杂的实验设计以及适用的统计模型。 我们运用了一个新颖的一年生植物种群模型以探索环境变数如何影响物种之间的互动,进而影响它们之间的生态位重叠度和适应度差距。这种群模型可接纳竞争性与辅助性的物种互动,也能探测环境因素如何影响这些互动的强度和正负方向。在澳洲西部的木林内,此模型被用于探索环境因素(光量、土壤磷含量和水份)的变异如何影响四个草本植物物种之间的互动,以及物种之间的生态位相似度和适应度差距。 研究结果显示辅助性互动是个非常普遍的现象。在不同的环境下,物种的互动可在竞争性和辅助性之间交替,但是环境条件对生态位相似度和适应度差距的强度和正负方向所造成的影响是非直线性以及难以预测的。 总结. 我们提供了一个能容纳环境异质性的研究框架以了解物种之间的共存机制。我们的研究结果显示环境是一个决定物种互动和成对共存的重要因素。除了竞争性的物种互动,未来的研究和预测模型也必需含盖极为普遍的辅助性互动。我们也建议研究者发掘更多其他可以影响生态位相似度和适应度差距的环境因素,以促使我们更加了解物种共存、侵植过程和群落对未来环境变化的反应。 We provide a simple framework for incorporating environmental heterogeneity into explorations of coexistence mechanisms. We show that niche overlap and fitness differences change along three environmental gradients, including tree canopy cover (shown above in left panel, with the black line showing niche overlap and the gray line showing fitness differences for W. acuminata and H. glabra, two common annual wildflowers from our Western Australia woodland system). These changes have the potential to drive substantial shifts in coexistence outcomes in natural communities (shown theoretically in the right panel above). Our findings highlight the importance of the environment in determining the outcome of species interactions and coexistence outcomes in heterogeneous natural environments. We also found a prevalence of facilitation in our system that points to a need to improve current theoretical frameworks of coexistence to include noncompetitive interactions and ways of translating these effects into explicit predictions of coexistence. Results from our study represent a step forward, towards improving our ability to predict outcomes of coexistence, invasion events and responses of whole communities to future environmental change.

Growing evidence shows that soil microbes affect plant coexistence in a variety of systems. However, since these systems vary in the impacts microbes have on plants and in the ways plants compete with each other, it is challenging to integrate results into a general predictive theory. To this end, we suggest that the concepts of niche and fitness difference from modern coexistence theory should be used to contextualize how soil microbes contribute to plant coexistence. Synthesizing a range of mechanisms under a general plant–soil microbe interaction model, we show that, depending on host specificity, both pathogens and mutualists can affect the niche difference between competing plants. However, we emphasize the need to also consider the effect of soil microbes on plant fitness differences, a role often overlooked when examining their role in plant coexistence. Additionally, since our framework predicts that soil microbes modify the importance of plant–plant competition relative to other factors for determining the outcome of competition, we suggest that experimental work should simultaneously quantify microbial effects and plant competition. Thus, we propose experimental designs that efficiently measure both processes and show how our framework can be applied to identify the underlying drivers of coexistence. Using an empirical case study, we demonstrate that the processes driving coexistence can be counterintuitive, and that our general predictive framework provides a better way to identify the true processes through which soil microbes affect coexistence.

1. Climate change is predicted to have profound consequences for multispecies coexistence, and thus, patterns of biological diversity. These consequences will be mediated by direct and indirect impacts of environmental change on species' vital rates and interactions. While the impacts of environmental change on individual species has received much attention to date, the consequences for coexistence mediated by changes in the strength and direction of multispecies interactions are not as well understood. 2. To investigate how coexistence dynamics may be sensitive to environmental change, we conducted a field experiment in a diverse semi-arid annual plant system. We imposed a water manipulation treatment in two sites that vary in aridity and associated rainfall. Focusing on four common annual plant species in these sites, we quantified the fecundity (seed production) of individuals in response to a gradient of intra-and interspecific competitor densities and aridity. We then used these fecundities to parameterize an annual plant population model and examine the influence of aridity and species identity on resultant coexistence dynamics (as a function of stabilizing niche differences and fitness inequalities). 3. While the responses of some vital rates and competitive impacts to watering varied somewhat predictably across sites, coexistence metrics encapsulating changes in these vital rates and interaction strengths did not. Fitness inequalities among our focal species were driven largely by differences in sensitivity to competition, which were almost always much greater than the magnitude of stabilizing niche differences. These findings were surprising given observational evidence suggesting that these species do coexist at local scales in these natural communities. 4. Synthesis. Our study is one of the first to explicitly consider the influence of environmental variation on the individual components of coexistence outcomes. We show that environmental change has the ability to influence coexistence not only through direct pathways (i.e., vital rates), but also indirect pathways (i.e., species interactions). Despite the consistency of many of the responses of these individual components to environmental variation, their combined influence on predictions of both current and future coexistence remains unclear.