  Phylogenetic Diversity (PD) is a measure of the overall biodiversity of a set
of present-day species (taxa) within a phylogenetic tree. In Maximize
Phylogenetic Diversity (MPD) one is asked to find a set of taxa (of bounded
size/cost) for which this measure is maximized. MPD is a relevant problem in
conservation planning, where there are not enough resources to preserve all
taxa and minimizing the overall loss of biodiversity is critical. We consider
an extension of this problem, motivated by real-world concerns, in which each
taxon not only requires a certain amount of time to save, but also has an
extinction time after which it can no longer be saved. In addition there may be
multiple teams available to work on preservation efforts in parallel; we
consider two variants of the problem based on whether teams are allowed to
collaborate on the same taxa. These problems have much in common with machine
scheduling problems, (with taxa corresponding to tasks and teams corresponding
to machines), but with the objective function (the phylogenetic diversity)
inspired by biological considerations. Our extensions are, in contrast to the
original MPD, NP-hard, even in very restricted cases. We provide several
algorithms and hardness-results and thereby show that the problems are
fixed-parameter tractable (FPT) when parameterized the target phylogenetic
diversity, and that the problem where teams are allowed to collaborate is FPT
when parameterized the acceptable loss of diversity.
