Hybridization Networks

Reticulate evolution is a fundamental process in the evolution of certain groups of taxa. Consequently, conflicting signals in a data set may not be the result of sampling or modelling errors, but due to the fact that reticulation has played a role in the evolutionary history of the species under consideration. However, despite its occurrence, such processes are still relatively rare, and so, assuming our initial data set is correct, a fundamental problem is to compute the minimum number of reticulation events that explains this set. In this chapter, we focus our attention on this problem for when the initial set consists of two rooted binary phylogenetic trees. This may seem rather special, but there are several reasons for this. Firstly, the problem is NP-hard even when the initial set consists of two such trees. Secondly, we are interested in finding a general solution rather than one that is restricted in some way. Lastly, the problem for when the initial set consists of binary sequences can be interpreted as a sequence of two-tree problems.