Selection among site-dependent structurally constrained substitution models of protein evolution by approximate Bayesian computation

The selection among substitution models of molecular evolution constitutes an essential step in phylogenetic analyses. At the protein level, evolutionary analyses are traditionally based on empirical substitution models but these models make unrealistic assumptions and were surpassed by structurally constrained substitution (SCS) models. The SCS models often consider site-dependent evolution, a process that provides realism but complicates their implementation into likelihood functions like those traditionally used for substitution model selection. Here we present an alternative method to perform selection among site-dependent SCS and empirical substitution models of protein evolution based on the approximate Bayesian computation (ABC) approach and its implementation into a computational framework called ProteinModelerABC. The framework implements ABC with and without regression adjustments and includes diverse empirical and site-dependent SCS models of protein evolution. Using extensive simulated data, we found that it providesselection between empirical and SCS models with acceptable accuracy. As illustrative examples, we applied the framework to analyse a variety of protein families observing that SCS models fit them better than the traditional empirical substitution models. ProteinModelerABC is freely available from https://github.com/DavidFerreiro/ProteinModelerABC, can run in parallel and includes a user-friendly graphical user interface. The framework is also distributed with a detailed documentation and ready-to-use examples.