Inference of functional divergence among proteins when the evolutionary process is non-stationary

Functional shifts during protein evolution are expected to yield shifts in substitution rate, and statistical methods can test for this at both codon and amino acid levels. Although methods based on models of sequence evolution serve as powerful tools for studying evolutionary processes, violating underlying assumptions can lead to false biological conclusions. It is not unusual for functional shifts to be accompanied by changes in other aspects of the evolutionary process, such as codon or amino acid frequencies. However, models used to test for functional divergence assume these frequencies remain constant over time. We employed simulation to investigate the impact of non-stationary evolution on functional divergence inference. We investigated three likelihood ratio tests based on codon models and found varying degrees of sensitivity. Joint effects of shifts in frequencies and selection pressures can be large, leading to false signals for positive selection. Amino acid-based tests (FunDi and Bivar) were also compromised when several aspects of the substitution process were not adequately modeled. We applied the same tests to a core genome "scan" for functional divergence between light-adapted ecotypes of the cyanobacteria Prochlorococcus, and carried out gene-specific simulations for ten genes. Results of those simulations illustrated how the inference of functional divergence at the genomic level can be seriously impacted by model misspecification. Although computationally costly, simulations motivated by data in hand are warranted when several aspects of the substitution process are either misspecified or not included in the models upon which the statistical tests were built.