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Mathematic methods and models for comparative analysis of large sets of protein phylogenies are described. Processes of gene duplication, loss, gain and horizontal transfer are modeled. Underlying evolutionary events are inferred with original algorithms of reconciliation of gene and species tree topologies. The methods performance is illustrated with biological data and computer simulations. Original algorithms are described to advance stages of phylogenetic analysis. In complex with conventional approaches those are used to construct the dataset of 51 orthologs representing 11 metazoan (animal) phyla for the purpose of inferring a reliable phylogeny of the Metazoa.