Presentation Information
[SS08-01]Coexistence theory for species pools: tractable insight from the cavity method
*Joe Wan1, Po-Ju Ke1 (1. National Taiwan University (Taiwan))
Keywords:
species coexistence,cavity method,community assembly,invasion analysis,statistical mechanics
Understanding biological diversity is one of the central aims of ecology, yet the majority of our theoretical understanding of diversity is focused on only one aspect—species richness, or the number of species coexisting in a community. Despite the success of quantitative frameworks such as modern coexistence theory (MCT) for understanding the maintenance of species richness, these frameworks do not address community structure because they do not predict the abundance of species within a community. Furthermore, in contrast to the astonishing diversity of many real systems, most empirical and theoretical studies using such frameworks are limited to a few species due to the challenges of parameterizing and analyzing highly multispecies systems. Here, we show how the cavity method, a powerful tool from statistical physics that has recently been applied to ecological systems, can resolve these two challenges.
Reviewing the multispecies cavity solution to classic competition models, we discuss key assumptions and generalizable techniques from this approach, and discuss why such approaches are not more frequently applied by community ecologists. In particular, we draw attention to the procedure for calculating species abundance, which can be viewed as an extension of the invasion analysis applied elsewhere in community ecology. Furthermore, we highlight a quantity measuring feedbacks between an invader species and the rest of the community, closely analogous to the niche overlap metric ρ² from modern coexistence theory.
Moving forward, we take advantage of these connections in order to synthesize the cavity method and modern coexistence theory. Our theoretical framework treats coexistence metrics as statistical properties of the species pool. Accordingly, we use analytical calculations and simulation-based approaches to quantify invasion growth rates, invader–resident feedbacks, and community-level stabilization of coexistence as tractable multispecies analogs of the fitness and niche metrics of modern coexistence theory. This in turn allows us to accurately quantify coexistence (species richness) and community structure (species abundance) in highly diverse communities. In doing so, we call for continued conceptual synthesis between community ecology and new theoretical approaches from statistical physics, and illustrate a path forward for understanding the structure and function of highly diverse communities.
Reviewing the multispecies cavity solution to classic competition models, we discuss key assumptions and generalizable techniques from this approach, and discuss why such approaches are not more frequently applied by community ecologists. In particular, we draw attention to the procedure for calculating species abundance, which can be viewed as an extension of the invasion analysis applied elsewhere in community ecology. Furthermore, we highlight a quantity measuring feedbacks between an invader species and the rest of the community, closely analogous to the niche overlap metric ρ² from modern coexistence theory.
Moving forward, we take advantage of these connections in order to synthesize the cavity method and modern coexistence theory. Our theoretical framework treats coexistence metrics as statistical properties of the species pool. Accordingly, we use analytical calculations and simulation-based approaches to quantify invasion growth rates, invader–resident feedbacks, and community-level stabilization of coexistence as tractable multispecies analogs of the fitness and niche metrics of modern coexistence theory. This in turn allows us to accurately quantify coexistence (species richness) and community structure (species abundance) in highly diverse communities. In doing so, we call for continued conceptual synthesis between community ecology and new theoretical approaches from statistical physics, and illustrate a path forward for understanding the structure and function of highly diverse communities.