Faller Beáta (University of Canterbury, New Zealand): Combinatorial and probabilistic methods in biodiversity theory



Abstract: Phylogenetic diversity (PD) is a measure of species biodiversity that describes how much of an evolutionary tree is spanned by a subset of species. We study optimization problems that aim to find species sets with maximum PD in different scenarios, and examine random extinction models under various assumptions to predict the PD of species that will still be present in the future.

The first part of the talk studies PD maximization problems. Here, we analyze the computational complexity of the problem ‘optimizing PD with ecological constraints’ and use the approach of integer linear programming to find exact solutions to real instances of this problem. We then introduce a maximization problem that is based on a more general biodiversity measure. We discuss the complexity and the approximability properties of this problem.

In the second part, we consider three species extinction models. We discuss the asymptotic distribution of future phylogenetic diversity under the ‘generalized field of bullets model’ (g-FOB). We then compare the expected loss of PD under the ‘state-based field of bullets model’ (s-FOB) to that under the associated g-FOB model, using the classical FKG inequality and the four functions theorem. We further generalize the s-FOB model and compare the expected future PD obtained for the resulting trait-dependent field of bullets model (t-FOB) to that for the associated g-FOB model.