Trait evolution with jumps: illusionary normality

TL;DR

This paper investigates the effects of incorporating jump components into phylogenetic models of trait evolution, highlighting how jumps can create an illusion of normality and exploring their asymptotic behavior through simulations.

Contribution

It extends previous models by adding extinction to OU processes with jumps and analyzes their asymptotic properties using simulations and the mvSLOUCH package.

Findings

Jumps can mask non-normal trait distributions in phylogenetic models

Adding extinction affects the convergence behavior of OU processes with jumps

Simulations demonstrate the impact of jumps and extinction on trait evolution modeling

Abstract

Phylogenetic comparative methods for real-valued traits usually make use of stochastic process whose trajectories are continuous. This is despite biological intuition that evolution is rather punctuated than gradual. On the other hand, there has been a number of recent proposals of evolutionary models with jump components. However, as we are only beginning to understand the behaviour of branching Ornstein-Uhlenbeck (OU) processes the asymptotics of branching OU processes with jumps is an even greater unknown. In this work we build up on a previous study concerning OU with jumps evolution on a pure birth tree. We introduce an extinction component and explore via simulations, its effects on the weak convergence of such a process. We furthermore, also use this work to illustrate the simulation and graphic generation possibilities of the mvSLOUCH package.