Computing the minimum number of hybridisation events for a consistent evolutionary history
It is now well-documented that the structure of evolutionary relationships between a set of present-day species is not necessarily tree-like. The reason for this is that reticulation events such as hybridisations mean that species are a mixture of genes from different ancestors. Since such events are relatively rare, a fundamental problem for biologists is to determine the smallest number of hybridisation events required to explain a given (input) set of data in a single (hybrid) phylogeny. The main results of this paper show that computing this smallest number is both NP-hard and APX-hard in the case the input is a collection of phylogenetic trees on sets of present-day species. This answers a problem which was raised at a recent conference. As a consequence of these results, we also correct a previously published NP-hardness proof in the case the input is a collection of binary sequences, where each sequence represents the attributes of a particular present-day species. The NP and APX-hardness of these problems mean that it is unlikely that there is an efficient algorithm for either computing the result exactly, or approximating it to any arbitrary degree of accuracy.
SubjectsField of Research::01 - Mathematical Sciences::0102 - Applied Mathematics::010202 - Biological Mathematics
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