DLS-trees: A model of evolutionary scenarios

We present a model of evolution of gene trees in the context of species evolution. Its concept is similar to reconciliation models. We assume that the gene evolution is modelled by duplications and losses. Evolution of species is modelled by speciation events. We define an evolutionary scenario (called a DLS-tree) which can represent an evolution of genes in species. We are interested in all scenarios for a given species tree and a given gene tree--not only parsimonious ones. 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 normal form (i.e., non-reducible) is unique and minimal in the sense of the cost computed as the total number of gene duplications and losses (mutation cost). We present a classification of the scenarios and analyze their hierarchy. Finally, we prove that the reconciled tree can be easily transformed into DLS-tree in normal form. This solves some open problems for reconciled trees.

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