Identification of ancestral genes untroducing incongruence between gene and species trees

The article introduces two novel approaches to detect potential incongruence between the protein family tree and the species tree. The first approach implements substitution of a known mapping of gene tree G into species tree S with somewhat analogous multivalued G-into-S "mapping". The second approach is based on elementary concepts from the fuzzy-set theory. Detailed description of the two corresponding algorithms is provided with demonstration of their performance on a model example and on three biological COGs.