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A non-exchangeable coalescent arising in phylogenetics

Banff International Research Station for Mathematical Innovation and Discovery

A popular line of research in evolutionary biology is to use time-calibrated phylogenies in order to infer the underlying process of species diversification. Most models of diversification assume that species are exchangeable and lead to phylogenetic trees whose shape is the same in distribution as that of a Yule pure-birth tree. Here, we propose a non-exchangeable, individual-based, point mutation model of diversification where interspecific pairwise competition (rate d) is always weaker than intraspecific pairwise competition (rate c), and is only felt from the part of individuals belonging to younger species. The only important parameter in this model is d/c, which can also be seen as a selection coefficient. In the large population limit, the rescaled abundances of species are deterministic but the phylogeny itself is random, interpolating between the completely asymmetric tree (d/c<<1) and the Kingman coalescent (d/c close to 1).

Mathematics; Partial differential equations; Probability theory and stochastic processes; Mathematical biology

video/mp4

Author affiliation: UPMC Univ Paris 06

2017-02-06

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60454

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/