Reading tree leaves: inferring speciation anfd extinction processes using phylogenies.

Abstract

The birth-death process (BDP) is widely used in evolutionary biology as a model for generating phylogenetic trees of species. The generalized birth-death process (GBDP) allows rate variation over time, with speciation and extinction rates to be arbitrary functions of time. Here we review the probability theory underpinning the GBDP as a model of cladogenesis and recent findings concerning its identifiability. The GBDP with arbitrary continuous rate functions has been shown to be non-identifiable from lineage-through-time data: even with species phylogenies of infinite size the parameters cannot be estimated. However, a restricted class of BDPs with piecewise-constant rates has been shown to be identifiable. We review and illustrate these results using simple examples and discuss their implications for biologists interested in inferring the past tempo and mode of evolution using reconstructed phylogenetic trees.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.