Explaining nature’s biodiversity is a key challenge for science. To persist, populations must be able to grow faster when rare, a feature called negative frequency dependence and quantified as ‘niche differences’ (scriptN) in modern coexistence theory. Here, we first show that available definitions of scriptN differ in how scriptN link to species interactions, are difficult to interpret and often apply to specific community types only. We then present a new definition of scriptN that is intuitive and applicable to a broader set of (modelled and empirical) communities than is currently the case, filling a main gap in the literature. Given scriptN, we also redefine fitness differences (scriptF) and illustrate how scriptN and scriptF determine coexistence. Finally, we demonstrate how to apply our definitions to theoretical models and experimental data, and provide ideas on how they can facilitate comparison and synthesis in community ecology.

There has been considerable focus on the impacts of environmental change on ecosystem function arising from changes in species richness. However, environmental change may affect ecosystem function without affecting richness, most notably by affecting population densities and community composition. Using a theoretical model, we find that, despite invariant richness, (1) small environmental effects may already lead to a collapse of function; (2) competitive strength may be a less important determinant of ecosystem function change than the selectivity of the environmental change driver and (3) effects on ecosystem function increase when effects on composition are larger. We also present a complementary statistical analysis of 13 data sets of phytoplankton and periphyton communities exposed to chemical stressors and show that effects on primary production under invariant richness ranged from À75% to +10%. We conclude that environmental protection goals relying on measures of richness could underestimate ecological impacts of environmental change.

We propose the niche and fitness differences map, a tool that simplifies the comparison of results across modern coexistence theory. Importantly, it allows to compare communities with very different underlying structure, such as competitive, mutualistic, multi-species or even multi-trophic communities. This generality will help us to unify formerly distant research areas into one combined framework, the N-F map. The N-F map consists of nine different regions that give insight into the underlying mechanism affecting each species. This gives us a visual tool to quickly and easily compare different species from different communities. SynthesisModern coexistence theory (MCT) holds the potential to study the ability of species to avoid extinction (i.e. to persist) across community types but is rarely applied beyond pairs of competing species. Here, we show that this limitation can be overcome by mapping species according to their niche (  i ) and fitness differences (  i ). This application provides three main benefits to study processes of multispecies persistence across trophic levels. First, N F mapping introduces a novel categorization of species and communities according to the high-level processes at play: frequency dependence (negative or positive), the occurrence of positive species interactions (facilitation and mutualism) and whether persistence is possible without the presence of other species because of trophic interactions, such as herbivory or predation. Therefore, this mapping can be seen as a toolbox to describe how species persistence depends on species interactions. Second, N F mapping facilitates studying how species persistence responds to environmental changes that shift intrinsic growth rates and the strength and sign of species interactions. Third, N F mapping has the potential to foster synthesis across community types because it can accommodate co-occurrence of positive, negative and neutral interactions between species. We, therefore, argue that N F mapping can promote collaboration across sub-fields, as it provides a common concept to link disparate ecological communities.

AbstractExplaining nature’s biodiversity is a key challenge for science. To persist, populations must be able to grow faster when rare, a feature called negative frequency dependence and quantified as ‘niche differences’ (𝒩) in coexistence theory. Here, we first show that available definitions of 𝒩 differ in how 𝒩 link to species interactions, are difficult to interpret, and often apply to specific community types only. We then present a new definition of 𝒩 that is intuitive and applicable to a broader set of (modelled and empirical) communities than is currently the case, filling a main gap in the literature. Given 𝒩, we also re-define fitness differences (ℱ) and illustrate how 𝒩 and ℱ determine coexistence. Finally, we demonstrate how to apply our definitions to theoretical models and experimental data, and provide ideas on how they can facilitate comparison and synthesis in community ecology.

Trait diversity is traditionally seen as promoting species richness and ecosystem function. Species with dissimilar traits would partition available resources, increasing niche differences, facilitating coexistence and increasing ecosystem function. Here we first show, using theory and simulations for light‐limited phytoplankton, that combing photosynthetic pigments is indeed a necessary condition for coexistence and stimulates ecosystem function. However, pigment richness does mostly not permit the coexistence of more than two species, and increases productivity at most 40% compared to single‐pigment communities. That is because blending in more pigments leads to coexistence of species with many pigments and therefore flat absorption spectra, which equalizes their fitness but decreases their niche differences. Similarly, seeding species with more variable size leads to an excess of large‐celled species, which does not only decrease fitness differences but also niche differences. Empirical data and additional simulations suggest that pigment richness effects can be stronger during transient dynamics but inevitably weaken with time, that is, pigment richness effects on species richness and function are likely short‐lived. Synthesis. Our results highlight the need to apply coexistence theory to understand the long‐term effects of trait diversity on biodiversity and ecosystem function.

A key question in ecology is what limits species richness. Coexistence theory presents the persistence of species amidst heterospecifics as a balance between niche differences and fitness differences that favour and hamper coexistence, respectively. With most applications focusing on species pairs, we know little about how niche and fitness differences respond to species richness, i.e. what constraints richness most. We present analytical proof that, in absence of higher-order interactions, the average fitness difference increases with richness, while the average niche difference stays constant. Analysis of a simple model with higher-order interactions, extensive simulations that relaxed all assumptions, and analyses of empirical data, confirmed these results. Our work thus shows that fitness differences, not niche difference, limit species richness. Our results contribute to the expansion of coexistence theory towards multi-species communities.

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The niche and fitness differences of modern coexistence theory separate mechanisms into stabilizing and equalizing components. Although this decomposition can help us predict and understand species coexistence, the extent to which mechanistic inference is sensitive to the method used to partition niche and fitness differences remains unclear. We apply two alternative methods to assess niche and fitness differences to four well known community models. We show that because standard methods based on linear approximations do not capture the full community dynamics, they can sometimes lead to incorrect predictions of coexistence and misleading interpretations of stabilizing and equalizing mechanisms. Conversely, a more recently developed method to decompose niche and fitness differences, that accounts for the full nonlinear dynamics of competition, consistently identifies the correct contribution of stabilizing and equalizing components. This approach further reveals that when the true complexity of the system is taken into account, essentially all mechanisms comprise both stabilizing and equalizing components. Amidst growing interest in the role of non-additive and higher-order interactions in regulating species coexistence, we propose that the effective decomposition of niche and fitness differences will become increasingly reliant on methods that account for the inherent non-linearity of community dynamics.