An ancestral process with selection in an ecological community. (English) Zbl 1411.92307
Summary: An ecological community is a geographical area composed of two or more species. The ancestral histories of individuals from the same and different species in an ecological community may be interconnected due to direct and indirect interactions. Here, we present a model of the ancestral history of an ecological community that is built upon the framework of coalescent and ancestral graph theory. The model includes selection, whereby the fitness of an ancestral lineage is a function of both its abiotic environment and interactions with individuals from its biotic environment. The model also allows for metacommunity structure. We first define a forward-time percolation process characterizing the evolution of an ecological community and then present its corresponding backward-time graphical model in the limit of large population sizes. Next, we present expectations of properties of phenotypes in the graph. These expectations give insight into the structure of phenotypic variation and trait-environment covariances across local communities, including the effects of drift, intra and inter-species genealogical structure and the sampling effects of selection. In addition, we derive expectations for multivariate phenotypic diversity in a community assuming neutrality and compare this to expectations with stabilizing selection.
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