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This paper presents a model of reconciling a species tree and a gene tree in an extended duplication-loss model. In the first part the definition of a model is introduced. In the second the horizontal transfer is defined and a new polynomial reconciliation algorithm is presented. We prove NP-completeness of the important problem related to the reconstruction of the species relationships with transfers from a given set of gene family trees. Some new problems are stated. We present a simple biological example.
Paweł Górecki (Thu,) studied this question.