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Abstract Most ecological models are based on the assumption that species interact in pairs. Diverse communities, however, can have higher‐order interactions, in which two or more species jointly impact the growth of a third species. A pitfall of the common pairwise approach is that it misses the higher‐order interactions potentially responsible for maintaining natural diversity. Here, we explore the stability properties of systems where higher‐order interactions guarantee that a specified set of abundances is a feasible equilibrium of the dynamics. Even these higher‐order interactions which lead to equilibria do not necessarily produce stable coexistence. Instead, these systems are more likely to be stable when the pairwise interactions are weak or facilitative. Correlations between the pairwise and higher‐order interactions, however, do permit robust coexistence even in diverse systems. Our work not only reveals the challenges in generating stable coexistence through higher‐order interactions but also uncovers interaction patterns that can enable diversity. 

Abstract Understanding how diversity is maintained in plant communities requires that we first understand the mechanisms of competition for limiting resources. In ecology, there is an underappreciated but fundamental distinction between systems in which the depletion of limiting resources reduces the growth rates of competitors and systems in which resource depletion reduces the time available for competitors to grow, a mechanism we call ‘competition for time’. Importantly, modern community ecology and our framing of the coexistence problem are built on the implicit assumption that competition reduces the growth rate. However, recent theoretical work suggests competition for time may be the predominant competitive mechanism in a broad array of natural communities, a significant advance given that when species compete for time, diversity‐maintaining trade‐offs emerge organically. In this study, we first introduce competition for time conceptually using a simple model of interacting species. Then, we perform an experiment in a Mediterranean annual grassland to determine whether competition for time is an important competitive mechanism in a field system. Indeed, we find that species respond to increased competition through reductions in their lifespan rather than their rate of growth. In total, our study suggests competition for time may be overlooked as a mechanism of biodiversity maintenance. 

Abstract When species simultaneously compete with two or more species of competitor, higher‐order interactions (HOIs) can lead to emergent properties not present when species interact in isolated pairs. To extend ecological theory to multi‐competitor communities, ecologists must confront the challenges of measuring and interpreting HOIs in models of competition fit to data from nature. Such efforts are hindered by the fact that different studies use different definitions, and these definitions have unclear relationships to one another. Here, we propose a distinction between ‘soft’ HOIs, which identify possible interaction modification by competitors, and ‘hard’ HOIs, which identify interactions uniquely emerging in systems with three or more competitors. We show how these two classes of HOI differ in their motivation and interpretation, as well as the tests one uses to identify them in models fit to data. We then show how to operationalise this structure of definitions by analysing the results of a simulated competition experiment underlain by a consumer resource model. In the course of doing so, we clarify the challenges of interpreting HOIs in nature, and suggest a more precise framing of this research endeavour to catalyse further investigations. 

A central assumption in most ecological models is that the interactions in a community operate only between pairs of species. However, two species may interactively affect the growth of a focal species. Although interactions among three or more species, called higher-order interactions, have the potential to modify our theoretical understanding of coexistence, ecologists lack clear expectations for how these interactions shape community structure. Here we analytically predict and numerically confirm how the variability and strength of higher-order interactions affect species coexistence. We found that as higher-order interaction strengths became more variable across species, fewer species could coexist, echoing the behavior of pairwise models. If interspecific higher-order interactions became too harmful relative to self-regulation, coexistence in diverse communities was destabilized, but coexistence was also lost when these interactions were too weak and mutualistic higher-order effects became prevalent. This behavior depended on the functional form of the interactions as the destabilizing effects of the mutualistic higher-order interactions were ameliorated when their strength saturated with species’ densities. Last, we showed that more species-rich communities structured by higher-order interactions lose species more readily than their species-poor counterparts, generalizing classic results for community stability. Our work provides needed theoretical expectations for how higher-order interactions impact species coexistence in diverse communities. 

Abstract Community ecology typically assumes that competitive exclusion and species coexistence are unaffected by evolution on the time scale of ecological dynamics. However, recent studies suggest that rapid evolution operating concurrently with competition may enable species coexistence. Such findings necessitate general theory that incorporates the coexistence contributions of eco‐evolutionary processes in parallel with purely ecological mechanisms and provides metrics for quantifying the role of evolution in shaping competitive outcomes in both modelling and empirical contexts. To foster the development of such theory, here we extend the interpretation of the two principal metrics of modern coexistence theory—niche and competitive ability differences—to systems where competitors evolve. We define eco‐evolutionary versions of these metrics by considering how invading and resident species adapt to conspecific and heterospecific competitors. We show that the eco‐evolutionary niche and competitive ability differences are sums of ecological and evolutionary processes, and that they accurately predict the potential for stable coexistence in previous theoretical studies of eco‐evolutionary dynamics. Finally, we show how this theory frames recent empirical assessments of rapid evolution effects on species coexistence, and how empirical work and theory on species coexistence and eco‐evolutionary dynamics can be further integrated.