Building modern coexistence theory from the ground up: the role of community assembly

Abstract

Modern coexistence theory (MCT) is one of the leading methods to understand species coexistence. It uses invasion growth rates -- the average, per-capita growth rate of a rare species -- to identify when and why species coexist. Despite significant advances in dissecting coexistence mechanisms when coexistence occurs, MCT relies on a "mutual invasibility" condition designed for two species communities, but poorly defined for species rich communities. Here, we review well-known issues with this component of MCT and propose a solution based on recent mathematical advances. These advances highlight the inescapable link between invasion-based coexistence criteria and community assembly. We propose a clear framework for expanding MCT to species rich communities and for understanding invasion resistance as well as coexistence. Using two data-driven community models from the literature, we illustrate the utility of our framework and highlight the opportunities for bridging the fields of community assembly and species coexistence.

Partitioning the Impacts of Spatial-Temporal Variation in Demography and Dispersal on Metapopulation Growth Rates

“…This type of decomposition is conceptually similar to the low-density growth rate decompositions in the quantitative coexistence theory of Chesson [Chesson, 1994, 2000, 2018]. Applications of Chesson’s theory are used extensively to evaluate the relative importance of alternative coexistence factors in empirical systems [Adler et al, 2010, Ellner et al, 2016, 2018, Spaak and Schreiber, 2023]. It will be exciting to see whether similar applications of the metapopulation growth rate decomposition can play a similar role for understanding metapopulation persistence in nature.…”

Trophic tug‐of‐war: Coexistence mechanisms within and across trophic levels

“…Nevertheless, these methodologies remained restricted to communities with a relatively low number of species. To address this limitation, Spaak and Schreiber (2023b) further advanced the approach to analyse species-rich communities. Building upon the extended theoretical foundation, Spaak, Carpentier, and De Laender (2021) have shown that fitness difference, not niche difference, limits coexistence in a single trophic level.…”

“…Species without a positive invasion growth rate, as well as those that were excluded, were removed from the analysis. This simplification was necessary because computing niche and fitness differences in such complex communities is challenging (Spaak & Schreiber, 2023a). Specifically, 4 out of 115 species were removed in the summer community, and 3 out of 93 were removed in the winter community.…”

“…This renders invasion growth rate, consequently niche and fitness differences, ill-defined. Nonetheless, recent advancements in invasion graph theory hold potential for overcoming this challenge (Hofbauer & Schreiber, 2022;Serván & Allesina, 2021;Spaak & Schreiber, 2023b).…”

Higher‐order species interactions cause time‐dependent niche and fitness differences: Experimental evidence in plant‐feeding arthropods

“…Generally, niche and fitness differences are estimated to better understand coexistence and are, therefore, applied to the invasion growth rates (Carroll et al., 2011; Spaak & De Laender, 2020), as positive invasion growth rates of competing species typically imply coexistence (Spaak & Schreiber, 2023; Box 1). Additionally, the sign and magnitude of niche and fitness differences inform about the species interactions, both in quality (e.g.…”