A reduction algorithm for computing the hybridization number of two trees

Abstract

Hybridization is an important evolutionary process for many groups of species. Thus, confl icting signals in a data set may not be the result of sampling or modeling errors, but due to the fact that hybridization has played a signifi cant role in the evolutionary history of the species under consideration. Assuming that the initial set of gene trees is correct, a basic problem for biologists is to compute this minimum number of hybridization events to explain this set. In this paper, we describe a new reduction-based algorithm for computing the minimum number, when the initial data set consists of two trees. Although the two-tree problem is NP-hard, our algorithm always gives the exact solution and runs effi ciently on many real biological problems. Previous algorithms for the two-tree problem either solve a restricted version of the problem or give an answer with no guarantee of the closeness to the exact solution. We illustrate our algorithm on a grass data set. This new algorithm is freely available for application at either http://www.bi.uni-duesseldorf.de/~linz or http://www.math. canterbury.ac.nz/~cas83.