Mathematical Methods for Identifying Representative Reserve Networks

Introduction Many countries have committed to conserving significant amounts of their native biodiversity (McNeely et al. 1990). Biodiversity includes the diversity of ecosystems and the diversity between and within species. Establishing reserve systems dedicated to nature conservation is the cornerstone of most national, regional and state conservation strategies (Soulé 1991). In this chapter, we explore the question of which parcels of land, henceforth termed sites, should be selected for reservation. Implicit in our analysis is a limit on the total size of the reserve system. From the perspective of nature conservation alone, one would attempt to have the largest reserve system possible; however, in reality, the extent of any reserve system will be limited by social and economic constraints. Thus, building a reserve network that will conserve biodiversity effectively is not a process of accumulating as much land as possible, but, rather, necessitates doing so as efficiently as possible within a constrained area. We focus on a particular class of reserve design problem where the goal is to achieve some minimum representation of biodiversity features for the smallest possible cost. In these problems the objective is to minimize costs and biodiversity enters as a constraint. For example, governments have agreed to conserve 15% of the pre-European extent of Australia’s regional forest types. This sets a constraint, creating an imperative to provide algorithms to minimize opportunity costs to the timber industry or maintenance costs of reserve management, while still satisfying the representation constraint. It is worth noting that there is no guarantee that such a reserve system is adequate – an issue that can only be assessed using explicit population models (see Chapters 7 to 13, this volume). To provide some perspective, we briefly review how reserves have been selected in the past before proceeding with specific examples.