A probabilistic model of reserve design

We develop a probabilistic approach to optimum reserve design based on the species–area relationship. Specifically, we focus on the distribution of areas among a set of reserves maximizing biodiversity. We begin by presenting analytic solutions for the neutral case in which all species have the same colonization probability. The optimum size distribution is determined by the local-to-regional species richness ratio k. There is a critical k t ratio defined by the number of reserves raised to the scaling exponent of the species–area relationship. Below k t , a uniform area distribution across reserves maximizes biodiversity. Beyond k t , biodiversity is maximized by allocating a certain area to one reserve and uniformly allocating the remaining area to the other reserves. We proceed by numerically exploring the robustness of our analytic results when departing from the neutral assumption of identical colonization probabilities across species.