The Shape of Phylogenies Under Phase-Type Distributed Times to Speciation and Extinction

TL;DR

This paper introduces a flexible macroevolutionary model for phylogenetic trees using Coxian phase-type distributions for speciation and extinction times, improving fit to empirical data and extending tree shape analysis.

Contribution

It proposes a novel Coxian phase-type distribution model for phylogenetic tree shapes, extending existing statistics and providing likelihood-based goodness-of-fit tests.

Findings

Models with Coxian PH distributions fit empirical trees better.

Extended beta statistic reduces bias in tree shape analysis.

Likelihood expressions enable rigorous model testing.

Abstract

Phylogenetic trees are widely used to understand the evolutionary history of organisms. Tree shapes provide information about macroevolutionary processes. However, macroevolutionary models are unreliable for inferring the true processes underlying empirical trees. Here, we propose a flexible and biologically plausible macroevolutionary model for phylogenetic trees where times to speciation or extinction events are drawn from a Coxian phase-type (PH) distribution. First, we show that different choices of parameters in our model lead to a range of tree balances as measured by Aldous' $\beta$ statistic. In particular, we demonstrate that it is possible to find parameters that correspond well to empirical tree balance. Next, we provide a natural extension of the $\beta$ statistic to sets of trees. This extension produces less biased estimates of $\beta$ compared to using the median $\beta$ values from individual trees. Furthermore, we derive a likelihood expression for the probability of observing any tree with branch lengths under a model with speciation but no extinction. Finally, we illustrate the application of our model by performing both absolute and relative goodness-of-fit tests for two large empirical phylogenies (squamates and angiosperms) that compare models with Coxian PH distributed times to speciation with models that assume exponential or Weibull distributed waiting times. In our numerical analysis, we found that, in most cases, models assuming a Coxian PH distribution provided the best fit.