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In modern coexistence theory, species coexistence can either arise via strong niche differences or weak fitness differences. Having a common currency for interpreting these mechanisms is essential for synthesizing knowledge across different studies and systems. However, several methods for quantifying niche and fitness differences exist, with little guidance on how and why these methods differ. Here, we first organize the available methods into three groups and review their differences from a conceptual point of view. Next, we apply four methods to quantify niche and fitness differences to one simulated and one empirical data set. We show that these methods do not only differ quantitatively, but affect how we interpret coexistence. Specifically, the different methods disagree on how resource supply rates (simulated data) or plant traits (empirical data) affect niche and fitness differences. We argue for a better theoretical understanding of what connects and sets apart different methods and more precise empirical measurements to foster appropriate method selection in coexistence theory.

A scientific understanding of the biological world arises when ideas about how nature works are formalized, tested, refined, and then tested again. Although the benefits of feedback between theoretical and empirical research are widely acknowledged by ecologists, this link is still not as strong as it could be in ecological research. This is in part because theory, particularly when expressed mathematically, can feel inaccessible to empiricists who may have little formal training in advanced math. To address this persistent barrier, we provide a general and accessible guide that covers the basic, step-by-step process of how to approach, understand, and use ecological theory in empirical work. We first give an overview of how and why mathematical theory is created, then outline four specific ways to use both mathematical and verbal theory to motivate empirical work, and finally present a practical tool kit for reading and understanding the mathematical aspects of ecological theory. We hope that empowering empiricists to embrace theory in their work will help move the field closer to a full integration of theoretical and empirical research.

Reconstructing interactions from observational data is a critical need for investigating natural biological networks, wherein network dimensionality is usually high. However, these pose a challenge to existing methods that can quantify only small interaction networks. Here, we proposed a novel approach to reconstruct high-dimensional interaction Jacobian networks using empirical time series without specific model assumptions. This method, named "multiview distance regularised S-map," generalised the state space reconstruction to accommodate high dimensionality and overcome difficulties in quantifying massive interactions with limited data. When evaluating this method using time series generated from theoretical models involving hundreds of interacting species, estimated strengths of interaction Jacobians were in good agreement with theoretical expectations. Applying this method to a natural bacterial community helped identify important species from the interaction network and revealed mechanisms governing the dynamical stability of a bacterial community. The proposed method overcame the challenge of high dimensionality in large natural dynamical systems.

Understanding the mechanisms underlying spatial variability of exploited fish is critical for the sustainable management of fish stocks. Empirical studies suggest that size‐selective fishing can elevate fish population spatial variability (i.e., more heterogeneous distribution) through age truncation, making the population less resilient to changing environment. However, species differ in how their spatial variability responds to age truncation and the underlying mechanisms remain unclear.We hypothesize that age‐specific habitat preference, together with environmental carrying capacity and landscape structure, determines the response of population spatial variability to fishing‐induced age truncation. To test these hypotheses, we design an individual‐based model of an age‐structured fish population on a two‐dimensional landscape under size‐selective fishing. Individual fish reproduces and survives, and moves between habitats according to age‐specific habitat preference and density‐dependent habitat selection.Population spatial variability elevates with increasing age truncation, and the response is stronger for populations with stronger age‐specific habitat preference. On a gradient landscape, reducing carrying capacity elevates the relative importance of density dependence in habitat selection, which weakens the response of spatial variability to age truncation for populations with strong age‐specific habitat preference. On a fragmented landscape, both populations with strong and weak age‐specific habitat preferences are restricted at local optimal habitats, and reducing carrying capacity weakens the responses of spatial variability to age truncation for both populations. Synthesis and applications. We demonstrate that to track and predict the changes in population spatial variability under exploitation, it is essential to consider the interactive effects of age‐specific habitat preference, carrying capacity, and landscape structure. To improve spatial management in fisheries, it is crucial to enhance empirical and theoretical developments in the methodology to quantify age‐specific habitat preference of marine fish, and to understand how climatic change influences carrying capacity and landscape continuity., Using individual‐based model, we show that the interplay between age‐specific habitat preference, environmental carrying capacity, and landscapes structure determines the sensitivity of spatial variability to fishing‐induced age truncation. These findings provide important implications on spatial management in fisheries.

Soil microbes can influence plant competitive outcomes by stabilizing plant community dynamics or mediating plant competitive hierarchies. Which effect dominates depends on whether microbial effects can extend beyond the focal conditioning individual. While it is well known that microbial effects can extend to other individuals through space, we lack an explicit theoretical understanding of the factors that regulate their spread to other individuals in subsequent generations. Here, we examine how the commonly assumed stabilizing effects of host-specific pathogens in fact depend on two factors that allow microbial effects to be cross-generational-which plant demographic vital rate is influenced by microbes and the conditioning and decay rates of soil microbial communities. With a novel patch occupancy model that incorporates the transition of soil states following plant colonization and mortality, we show that host-specific pathogens enable plant coexistence when they suppress conspecific plant colonization of empty patches but contribute to competitive hierarchies when they modify only the mortality and fecundity of the conditioning plant individual. In a series of model extensions, we further demonstrate that these latter microbial effects can still promote coexistence, but only when microbial communities decay slowly following plant death, thereby allowing microbial effects to be cross-generational. Our study calls for further empirical work quantifying the demographic rates most affected by soil microbes as well as the timescales of conditioning and decay.

Priority effects are commonly used to describe a broad suite of phenomena capturing the influence of species arrival order on the diversity, composition and function of ecological communities. Several studies have suggested reframing priority effects around the stabilizing and equalizing concepts of coexistence theory. We show that the only compatible priority effects are those characterized by positive frequency-dependence, irrespective of whether they emerge in equilibrium or non-equilibrium systems.

Understanding the origins and maintenance of biodiversity remains one of biology's grand challenges. From theory and observational evidence, we know that variability in environmental conditions through time is likely critical to the coexistence of competing species. Nevertheless, experimental tests of fluctuation-driven coexistence are rare and have typically focused on just one of two potential mechanisms, the temporal storage effect, to the neglect of the theoretically equally plausible mechanism known as relative nonlinearity of competition. We combined experiments and simulations in a system of nectar yeasts to quantify the relative contribution of the two mechanisms to coexistence. Resource competition models parameterized from single-species assays predicted the outcomes of mixed-culture competition experiments with 83% accuracy. Model simulations revealed that both mechanisms have measurable effects on coexistence and that relative nonlinearity can be equal or greater in magnitude to the temporal storage effect. In addition, we show that their effect on coexistence can be both antagonistic and complementary. These results falsify the common assumption that relative nonlinearity is of negligible importance, and in doing so reveal the importance of testing coexistence mechanisms in combination.

Organisms typically change their diets ontogenetically. Recent studies have shown that an ontogenetic diet shift undermines the resilience of stage-structured food webs. Here, we study the integration of stage-structured food-web theory into theory of hybrid community (i.e. mixture of different interaction types), considering that not only diet but also interaction type often changes because of ontogenetic niche shift (e.g. the metamorphosis of pollinating insects, in which juveniles and adults are herbivores and pollinators, respectively). We developed and mathematically analysed a one-consumer two-resource model in which juvenile and adult consumers utilise different resources as antagonists and mutualists, respectively. Model analyses illustrated that the consumer either goes extinct or coexists with the resources depending on the initial condition when the resources have low carrying capacities while their community dynamics always converge to a single steady state when the resources have high carrying capacities. These dynamic features are different from those of the corresponding purely antagonistic module in previous studies, in which the consumer always goes extinct for low resource carrying capacities while the dynamics converge to either juvenile-dominated or adult-dominated state depending on the initial conditions for high resource carrying capacities. Taken together, we can suggest that ontogenetic antagonism–mutualism coupling is stabilising in that it increases the potential for species coexistence in unproductive environments while improving community resilience in productive environments. Further, these effects are generally robust to interaction nonlinearity. Beyond the previous concern of the instability in stage-structured food-webs, our results suggest that antagonism–mutualism coupling can play a crucial role in stabilising stage-structured hybrid (e.g. plant–animal) communities under environmental changes. The present study represents an important first step in understanding how interaction type diversity can mediate the dynamics of stage-structured communities. This article is protected by copyright. All rights reserved.

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.

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.

Summary � Reciprocal interaction between plant and soil (plant–soil feedback, PSF) can determine plant community structure. Understanding which traits control interspecific variation of PSF strength is crucial for plant ecology. Studies have highlighted either plant-mediated nutrient cycling (litter-mediated PSF) or plant–microbe interaction (microbial-mediated PSF) as important PSF mechanisms, each attributing PSF variation to different traits. However, this separation neglects the complex indirect interactions between the two mechanisms. � We developed a model coupling litter- and microbial-mediated PSFs to identify the relative importance of traits in controlling PSF strength, and its dependency on the composition of root-associated microbes (i.e. pathogens and/or mycorrhizal fungi). � Results showed that although plant carbon: nitrogen (C : N) ratio and microbial nutrient acquisition traits were consistently important, the importance of litter decomposability varied. Litter decomposability was not a major PSF determinant when pathogens are present. However, its importance increased with the relative abundance of mycorrhizal fungi as nutrient released from the mycorrhizal-enhanced litter production to the nutrient-depleted soils result in synergistic increase of soil nutrient and mycorrhizal abundance. Data compiled from empirical studies also supported our predictions. � We propose that the importance of litter decomposability depends on the composition of root-associated microbes. Our results provide new perspectives in plant invasion and traitbased ecology.