Evolutionary rates across gradients

1. A key question in the fields of macroecology and evolution is how rates of evolution vary across gradients, be they ecological (e.g. temperature, rainfall, net primary productivity), geographic (e.g. latitude, elevation), morphological (e.g. body mass), etc. Evolutionary rates across gradients (EVORAG 2.0) is a new software package provided as open source in the R language (and available from CRAN) that tests whether rates of trait evolution vary continuously across such continuous gradients. 2. The approach uses quantitative trait data for a series of sister-pair contrasts (i.e. sister species or other types of sister taxa) and applies Brownian Motion and Ornstein Uhlenbeck models in which parameter (evolutionary rate and constraint) values vary as a function of discrete variables (e.g. male vs. female) and/or continuous variables (e.g. latitude, temperature, body size). 3. We used simulation to test performance of the models in EvoRAG. Our gradient models accurately estimate parameter values, have very low levels of bias, and low rates of model misspecification. 4. The modelling framework developed here provides great flexibility in designing models that test how rates of evolution vary across gradients. We provide an example where both discrete (songbird vs. suboscine) and continuous (latitude) effects on evolutionary rate in avian song were simultaneously estimated.