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A phylogenetic birth-and-death model is a probabilistic graphical model for aso-called phylogenetic profile, i.e., the size distribution for a homolog genefamily at the terminal nodes of a phylogeny. Profile datasets are used inbioinformatics analyses for the inference of evolutionary trees, and offunctional associations between gene families, as well as for thequantification of various processes guiding genome evolution. Here we describethe mathematical formalism for phylogenetic birth-and-death models. We alsopresent an algorithm for computing the likelihood in a gain-loss-duplicationmodel.

Mathematical Framework for Phylogenetic Birth-And-Death Models