A graph theory approach for designing conservation reserve networks with minimal fragmentation

Habitat fragmentation is often cited as one of the most important factors that adversely affect species persistence and survival ability. Contiguity of habitat sites is usually desirable when designing a conservation reserve. If a contiguous reserve is not feasible, due to landscape characteristics or economic constraints, designing a reserve network with minimal fragmentation may be a viable strategy. This article presents a linear integer programming formulation of the problem using graph theory concepts. A graph is constructed where nodes correspond to individual sites and directed arcs are defined for pairs of nodes corresponding to adjacent sites. The model determines a minimal representative tree as a subgraph where each node in the tree corresponds to either a selected reserve site or a gap site. Reserve fragmentation is defined as the sum of gap sites, which is to be minimized. An important computational problem is the formation of cycles when determining the minimal representative tree. This problem is resolved using an iterative procedure that utilizes Dantzig-cuts when a cycle occurs in the solution. Arbitrarily generated data sets are used to explore the computational efficiency of this approach. Finally an empirical application of the model to a real data set involving 744 sites and 32 endangered/threatened bird species is presented.