ensuring that we do not exceed our budget. Unused
budget from one time step does not carry over to the
next time step. For clarity of presentation, here we
consider the setting where conservation recommendations are made on a faster timescale than the patch
dynamics. Thus, the goal is to plan the recommendation of patches to protect such that the final
reserve maximizes the persistence objective.
Formally, we are interested in a policy that speci-
fies which patches to recommend at time t, given
knowledge of the already selected patches, a fixed set
of patches to choose from, and a certain budget to
spend. What is a good policy? One natural (albeit
extremely optimistic) benchmark is a clairvoyant
policy that gets to know precisely which patches and
how much budget are available at any given point in
time (that is, gets to know this aspect of the future),
Even for a single time step, selecting the set of patch-
es that maximizes the survival probability is an NP-
hard optimization problem. Despite this hardness, in
the following, we present an efficient policy that
exploits adaptive submodularity.
In particular, we prove that if species do not colonize between separate patches, then we can guarantee near-optimal solutions. Under this assumption,
the patch dynamics for a given patch depend only on
Figure 3. The Conservation Planning Case Study.
Top: Endangered taxa considered. From left to right: Streaked Horned Lark, Taylor Checkerspot, Mazama Pocket Gopher (photo credits: Rod
Gilbert, Derek Stinson, Kim Flotlin). Bottom Left: A map consists of parcels, which are grouped into patches (one example marked in red).
Our model captures uncertain colonization and survival across parcels within a patch. Bottom right: A candidate solution to the (static)
reserve design problem consists of a set of selected patches (marked in red; map shows the show the South Puget Sound region). See Golovin
et al. (2011) for details.
Photographs courtesy (left to right) Rod Gilbert, Derek Stinson, and Kim Flotlin.