Non-hereditary Minimum Deep Coalescence trees

One of the goals of phylogenetic research is to find the species tree describing the evolutionary history of a set of species. But the trees derived from geneti data with the help of tree inference methods are gene trees that need not coincide with the species tree. This can for example happen when so-called deep coalescence events take place. It is also known that species trees can differ from their most likely gene trees. Therefore, as a means to find the species tree, it has been suggested to use subtrees of the gene trees, for example triples, and to puzzle them together in order to find the species tree. In this paper, we will show that this approach may lead to wrong trees regarding the minimum deep coalescence criterion (MDC). In particular, we present an example in which the optimal MDC tree is unique, but none of its triple subtrees fulfills the MDC criterion. In this sense, MDC is a non-hereditary tree reconstruction method.