Abstract
In this paper, we present a model of evolution of genes in the context of evolution of species. The concept is based on reconciliation models. We assume that the gene evolution is modeled by macro-evolutionary events like gene duplications, losses and horizontal gene transfers (HGTs) while the evolution of species is shaped by speciation events. We define an evolutionary scenario (called an H-tree) which will represent the common evolution of genes and species. We propose a rewrite system for transforming the scenarios. We prove that the system is confluent, sound and strongly normalizing. We show that a scenario in a normal form (that is, non-reducible) is unique and minimal in the sense of the cost computed as the total number of gene duplications, losses and HGTs (mutation cost). We present a classification of the scenarios and analyze their hierarchies.