Understanding the evolution of binary traits, which affects the birth and survival of species and also the rate of molecular evolution, remains challenging. In this work, we present a probabilistic modeling framework for binary trait, random species trees, in which the number of species and their traits are represented by an asymmetric, two-type, continuous time Markov branching process. The model involves a number of different parameters describing both character and molecular evolution on the so-called 'reduced' tree, consisting of only extant species at the time of observation. We expand our model by considering the impact of binary traits on dN/dS, the normalized ratio of nonsynonymous to synonymous substitutions. We also develop mechanisms which enable us to understand the substitution rates on a phylogenetic tree with regards to the observed traits. The properties obtained from the model are illustrated with a phylogeny of outcrossing and selfing plant species, which allows us to investigate not only the branching tree rates, but also the molecular rates and the intensity of selection.
Keywords: Binary traits; Branching processes; Irreversible transitions; Mutation rates; Phylogenetic trees.
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