Coexistence holes characterize the assembly and disassembly of multispecies systems
Angulo et al., 2021
A central goal of ecological research has been to understand the limits on the maximum number of species that can coexist under given constraints. However, we know little about the assembly and disassembly processes under which a community can reach such a maximum number, or whether this number is in fact attainable in practice. This limitation is partly due to the challenge of performing experimental work and partly due to the lack of a formalism under which one can systematically study such processes. Here, we introduce a formalism based on algebraic topology and homology theory to study the space of species coexistence formed by a given pool of species. We show that this space is characterized by ubiquitous discontinuities that we call coexistence holes (that is, empty spaces surrounded by filled space). Using theoretical and experimental systems, we aprovide direct evidence showing that these coexistence holes do not occur arbitrarily—their diversity is constrained by the internal structure of species interactions and their frequency can be explained by the external factors acting on these systems. Our work suggests that the assembly and disassembly of ecological systems is a discontinuous process that tends to obey regularities.
Coexistence holes characterize discontinuities in assembly and disassembly processes. a, A hypothetical pool of S = 3 species. b, When each of the 2S − 1 = 7 different species collection is assembled, it can either coexist (blue background) or not (white background). In this hypothetical example, species survive in isolation and coexist when assembled in pairs. However, the three species cannot coexist when assembled together. The corresponding assembly hypergraph is H =[[1], [2], [3], [1, 2], [2, 3], [3, 1]]. c, When embedded into a two-dimensional space (that is, a plane), the assembly hypergraph reveals the assembly hole h = [1, 2, 3]. d, The assembly hole reveals that coexistence abruptly brakes: in all assembly processes to obtain [1, 2, 3], all of the intermediate species collections coexist, but in the final step coexistence does not occur. e, In these hypothetical coexistence outcomes, only species 1 survives in isolation and coexistence is possible only if the species are assembled in a trio. The corresponding assembly hypergraph is H =[[1], [1, 2, 3]]. f, The associated disassembly hypergraph is D(H)=[[1], [2], [3], [1, 2], [2, 3], [3, 1]], calculated from the missing boundary of H. Each hyperedge of D is a sub-community that does not coexist, despite it having been disassembled from the species collection [1, 2, 3] that coexists. When embedded into the plane, D(H) uncovers the disassembly hole [1, 2, 3]. g, The disassembly hole reveals that coexistence abruptly brakes: despite [1, 2, 3] coexisting, in all disassembly processes starting from [1, 2, 3], not a single intermediate species collection with more than one species coexists.
.
No hay comentarios:
Publicar un comentario