A Minimal yet Flexible Likelihood Framework to Assess Correlated Evolution

An evolutionary process is reflected in the sequence of changes of any trait (e.g., morphological or molecular) through time. Yet, a better understanding of evolution would be procured by characterizing correlated evolution, or when two or more evolutionary processes interact. Previously developed parametric methods often require significant computing time as they rely on the estimation of many parameters. Here, we propose a minimal likelihood framework modeling the joint evolution of two traits on a known phylogenetic tree. The type and strength of correlated evolution are characterized by a few parameters tuning mutation rates of each trait and interdependencies between these rates. The framework can be applied to study any discrete trait or character ranging from nucleotide substitution to gain or loss of a biological function. More specifically, it can be used to 1) test for independence between two evolutionary processes, 2) identify the type of interaction between them, and 3) estimate parameter values of the most likely model of interaction. In the current implementation, the method takes as input a phylogenetic tree with discrete evolutionary events mapped on its branches. The method then maximizes the likelihood for one or several chosen scenarios. The strengths and limits of the method, as well as its relative power compared to a few other methods, are assessed using both simulations and data from 16S rRNA sequences in a sample of 54 $\gamma$-enterobacteria. We show that, even with data sets of fewer than 100 species, the method performs well in parameter estimation and in evolutionary model selection. [Correlated evolution; maximum likelihood; model.].