The conditioned reconstructed process

TL;DR

This paper derives the distribution and expectations of speciation times in a conditioned birth-death process, providing a complete characterization of reconstructed phylogenetic trees useful for dating phylogenies.

Contribution

It offers the first analytic results for speciation times in conditioned birth-death trees, extending understanding beyond tree shape distributions.

Findings

Derived the distribution of speciation times in conditioned trees

Calculated expectations of speciation times analytically

Provided tools for dating phylogenies using reconstructed trees

Abstract

We investigate a neutral model for speciation and extinction, the constant rate birth-death process. The process is conditioned to have $n$ extant species today, we look at the tree distribution of the reconstructed trees-- i.e. the trees without the extinct species. Whereas the tree shape distribution is well-known and actually the same as under the pure birth process, no analytic results for the speciation times were known. We provide the distribution for the speciation times and calculate the expectations analytically. This characterizes the reconstructed trees completely. We will show how the results can be used to date phylogenies.