Epistatic contributions promote the unification of incompatible models of neutral molecular evolution

We introduce a model of amino acid sequence evolution that accounts for the statistical behavior of real sequences induced by epistatic interactions. The model is refered as Sequence Evolution with Epistatic Contributions (SEEC). Known statistical properties such as overdispersion, heterotachy and Gamma-distributed rate-across-sites are shown to be emergent properties of this model while being consistent with neutral evolution theory, thereby unifying observations from previously disjointed evolutionary models of sequences.  The relationship between site restriction and heterotachy is characterized by tracking the effective alphabet dynamics of sites.  We also observe an evolutionary Stokes Shift in the fitness of sequences that have undergone evolution under our simulation.  In this dataset we include all the data used as input and output of the model connected with the publication "Epistatic contributions promote the unification of incompatible models of neutral molecular evolution".

Methods
We introduce a model called Sequence Evolution with Epistatic Constributions (SEEC). The model dynamics are based on parameters derived from Multiple Sequence Alignments analyzed using Direct Coupling Analysis methodology. The dataset contains formated aligments of protein families compiled from Pfam and processed in our manuscript. These aligments are the input to the global inference method called Direct Coupling Analysis (DCA).  The dataset also includes paramaters computed and required to run the evolutionary model developed in the paper.