The phylogenetic effective sample size and jumps

TL;DR

This paper investigates the phylogenetic effective sample size in models where traits can jump at speciation, revealing a non-trivial limit influenced by the Ornstein-Uhlenbeck process parameters.

Contribution

It extends the understanding of phylogenetic effective sample size to models with trait jumps at speciation, highlighting new asymptotic behaviors.

Findings

Non-trivial limit exists as jump effects increase

Limit depends on the Ornstein-Uhlenbeck drift parameter

Numerical results support theoretical insights

Abstract

The phylogenetic effective sample size is a parameter that has as its goal the quantification of the amount of independent signal in a phylogenetically correlated sample. It was studied for Brownian motion and Ornstein-Uhlenbeck models of trait evolution. Here, we study this composite parameter when the trait is allowed to jump at speciation points of the phylogeny. Our numerical study indicates that there is a non-trivial limit as the effect of jumps grows. The limit depends on the value of the drift parameter of the Ornstein-Uhlenbeck process.