On the accuracy and theoretical underpinnings of the multiple variance Brownian motion approach for estimating variable rates and inferring ancestral states

Abstract

In a recent contribution, Griffin & Yapuncich (2016) (‘G&Y’) report on purported inaccuracies and lack of theoretical underpinnings of our recently proposed ancestral estimation procedure. Our method is designed to provide a good overall fit with the data when different branches may be subject to different rates of change (multiple variance Brownian motion, or ‘mvBM’). Here we demonstrate that G&Y’s theoretical concerns stem from a misinformed account of basic statistical concepts and procedures, a misinterpretation of the primary literature and a circular adherence to a restrictive model of evolution (standard Brownian motion, or ‘standard BM’) whose usefulness has long been considered inappropriate for modelling branch-specific evolutionary patterns. We further apply a series of simple tests that falsify G&Y’s claims on every account. Finally, we show that including a range of sample sizes (from 4 through 100) to G&Y’s own suggested simulation procedure further substantiates what they purport to falsify: the validity of mvBM when modelling potential deviations from standard BM in trait evolution.