Mean-field methods in evolutionary duplication-innovation-loss models for the genome-level repertoire of protein domains

We present a combined mean-field and simulation approach to different models describing the dynamics of classes formed by elements that can appear, disappear, or copy themselves. These models, related to a paradigm duplication-innovation model known as Chinese restaurant process, are devised to reproduce the scaling behavior observed in the genome-wide repertoire of protein domains of all known species. In view of these data, we discuss the qualitative and quantitative differences of the alternative model formulations, focusing in particular on the roles of element loss and of the specificity of empirical domain classes.