How Can We Maximize Phylogenetic Diversity? Parameterized Approaches for Networks
M.E.L. Jones (TU Delft - Discrete Mathematics and Optimization)
Jannik Schestag (TU Delft - Discrete Mathematics and Optimization, Friedrich Schiller University Jena)
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Abstract
Phylogenetic Diversity (PD) is a measure of the overall biodiversity of a set of present-day species (taxa) within a phylogenetic tree. We consider an extension of PD to phylogenetic networks. Given a phylogenetic network with weighted edges and a subset S of leaves, the all-paths phylogenetic diversity of S is the summed weight of all edges on a path from the root to some leaf in S. The problem of finding a bounded-size set S that maximizes this measure is polynomial-time solvable on trees, but NP-hard on networks. We study the latter from a parameterized perspective. While this problem is W[2]-hard with respect to the size of S (and W[1]-hard with respect to the size of the complement of S), we show that it is FPT with respect to several other parameters, including the phylogenetic diversity of S, the acceptable loss of phylogenetic diversity, the number of reticulations in the network, and the treewidth of the underlying graph.
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