  The Noah's Ark Problem (NAP) is an NP-Hard optimization problem with
relevance to ecological conservation management. It asks to maximize the
phylogenetic diversity (PD) of a set of taxa given a fixed budget, where each
taxon is associated with a cost of conservation and a probability of
extinction. NAP has received renewed interest with the rise in availability of
genetic sequence data, allowing PD to be used as a practical measure of
biodiversity. However, only simplified instances of the problem, where one or
more parameters are fixed as constants, have as of yet been addressed in the
literature. We present NAPX, the first algorithm for the general version of NAP
that returns a $1 - \epsilon$ approximation of the optimal solution. It runs in
$O(\frac{n B^2 h^2 \log^2n}{\log^2(1 - \epsilon)})$ time where $n$ is the
number of species, and $B$ is the total budget and $h$ is the height of the
input tree. We also provide improved bounds for its expected running time.
