Coexistence holes in ecological systems

Abstract: A central challenge of Ecology is to explain the enormous biodiversity of species that we find on Earth, from the diversity of plant and animal species that stably coexist in tropical forests to the variety of microbial species that coexist in our gut. Ecologists have focused on characterizing the "limits" of species coexistence ---that is, the maximum number of different species that can coexist under given constraints. Yet, little is known about the structure of species coexistence below such limits. Namely, is it possible to assemble an ecological system by adding one species at a time until reaching the coexistence limits? Or is it possible to find obstructions where species coexistence abruptly breaks before reaching the limits? To address these questions, we built a novel formalism based on hypergraphs and Algebraic Topology to show that, below its limits, species coexistence in ecological systems has ubiquitous obstructions that we call "coexistence holes". A coexistence hole occurs during an assembly process when a species collection does not coexist, although we can assemble it from sub-collections that coexist. Using theoretical and experimental ecological systems, we provide direct evidence showing that coexistence holes obey regularities. Namely, their diversity is constrained by the internal structure of species interactions, while their frequency can be explained by external factors acting on these systems. Overall, our work provides one of the first applications of Algebraic Topology to Ecology, unveiling how biodiversity is a discontinuous process driven by internal design constraints.

This is joint work with Aaron Kelley (IM-UNAM), Luis Montejano (IM-UNAM), Chuliang Song (McGill/Toronto University) and Serguei Saavedra (MIT).

References: [1] Angulo, Marco Tulio, et al. "Coexistence holes characterize the assembly and disassembly of multispecies systems." Nature Ecology & Evolution (2021): 1-11. [2] Letten, A. D. (2021). "Coexistence holes fill a gap in community assembly theory." Nature Ecology & Evolution, 1-2.

geometric topology

Audience: researchers in the topic

GEOTOP-A seminar

Series comments: Web-seminar series on Applications of Geometry and Topology