Quantifying hybridization in realistic time

Abstract

Recently, numerous practical and theoretical studies in evolutionary biology aim at calculating the extent to which reticulation-for example horizontal gene transfer, hybridization, or recombination-has influenced the evolution for a set of present-day species. It has been shown that inferring the minimum number of hybridization events that is needed to simultaneously explain the evolutionary history for a set of trees is an NP-hard and also fixed-parameter tractable problem. In this paper, we give a new fixed-parameter algorithm for computing the minimum number of hybridization events for when two rooted binary phylogenetic trees are given. This newly developed algorithm is based on interleaving-a technique using repeated kernelization steps that are applied throughout the exhaustive search part of a fixed-parameter algorithm. To show that our algorithm runs efficiently to be applicable to a wide range of practical problem instances, we apply it to a grass data set and highlight the significant improvements in terms of running times in comparison to an algorithm which has previously been implemented.