In the reconstruction of phylogenetic networks from a set of trees, the so-called minimum hybridization number is a popular measure to quantify the extent to which hybridization or horizontal gene transfer has had an impact on the evolutionary history of a set of species.

Computing this minimum number for two phylogenetic trees is an NP-hard optimization problem and a lot of effort has been put into the development of clever characterizations and algorithms for this two-tree problem. However, no characterization is known for a collection of more than two trees.

We considered a variation of the problem that imposes two biologically motivated time-constraints on hybridization and speciation events. While the problem remains NP-hard, we were able to give the first characterization for calculating the minimum hybridization number under these constraints for when the collection of trees is arbitrarily large. The characterization is in terms of cherries (two leaves in a tree that have a common parent) and the existence of a particular type of sequence.

**Paper:** P. J. Humphries, S. Linz, and C. Semple (2013). Cherry picking: a characterization of the temporal hybridization number for a set of phylogenies. *Bulletin of Mathematical Biology,* 75:1879-1890.

**Researcher: **Dr Simone Linz