On the Structure of Reconciliations
In this paper we present an extended model related to reconciliation concepts. It is based on gene duplications, gene losses and speciation events. We define an evolutionary scenario (called a DLS-tree) which informally can represent an evolution of genes in species. We are interested in all scenarios – not only parsimonious ones. We propose a system of rules 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. Moreover, we present a classification of the scenarios and analyze their hierarchy. Finally, we prove that the tree in normal form could be easily transformed into the reconciled tree  in duplication-loss model. This solves some open problems stated in .
Keywordsmolecular evolution phylogenetic tree reconciliation gene duplication gene loss computational biology
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- 1.Arvestad, L., Berglund, A.-C., Lagergren, J., Sennblad, B.: Gene tree reconstruction and orthology analysis based on an integrated model for duplications and sequence evolution. In: RECOMB 2004 (2004)Google Scholar
- 4.Eulenstein, Vingron: On the equivalence of two tree mapping measures. DAMATH: Discrete Applied Mathematics and Combinatorial Operations Research and Computer Science 88 (1998)Google Scholar
- 6.Goodman, M., Czelusniak, J., Moore, G.W., Romero-Harrera, A.E., Matsuda, G.: Fitting the gene lineage into its species lineage. A parsimony strategy illustrated by cladograms constructed from globin sequences. Syst. Zool. 28, 132–163 (1979)Google Scholar
- 8.Ma, B., Li, M., Zhang, L.: On Reconstructing Species Trees from Gene Trees in Term of Duplications and Losses. In: RECOMB 1998, pp. 182–191 (1998)Google Scholar
- 10.Górecki, P.: Reconciliation problems for duplication, loss and horizontal gene transfer. In: RECOMB 2004, San Diego (2004)Google Scholar
- 11.Mirkin, B., Muchnik, I., Smith, T.F.: A biologically meaningful model for comparing molecular phylogenies. J. of Comput. Biol. 2, 492–507 (1995)Google Scholar
- 12.Page, R.D.M.: Maps between trees and cladistic analysis of historical associations among genes, organisms, and areas. Systematic Biology 43, 58–77 (1994)Google Scholar
- 13.Page, R.D.M., Charleston, M.A.: Reconciled trees and incogruent gene and species trees. Mathematical Hierarchies and Biology. DIMACS Series in Mathematics and Theoretical Computers Science, vol. 37(57–70) (1997)Google Scholar