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

Abstract

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.

How large spatially-explicit optimal reserve design models can we solve now? An exploration of current models’ computational efficiency

“…The models of Önal and Briers (2006) and Jafari and Hearne (2013) completed only two runs in 2 hours in, respectively, three and two population settings (for Önal and Briers (2006) model, these settings are p=100, 150 and 200 and for Jafari and Hearne (2013) model, the settings are p=100 and 150). The models of Önal and Wang (2008) and Conrad et al (2012) are better in the sense that they completed more runs in most population settings.…”

A heuristic for the maximum value region problem in raster space

“…Major applications include site selection (Brookes 1997, Cova andChurch 2000), land-use allocation (Wright et al 1983, Gilbert et al 1985, Diamond and Wright 1988, Tomlin and Johnston 1990, Eastman et al 1998, Aerts and Heuvelink 2002, Aerts et al 2003, Ligmann-Zielinska et al 2008, and conservation reserve design (McDonnell et al 2002, Church et al 2003, Nalle et al 2003, Cerdeira et al 2005, Ö nal and Briers 2005, Ö nal and Wang 2008. Solution of these problems generally requires two kinds of tasks: evaluation and allocation of space.…”

Designing a multi-species spatially explicit nature reserve network construction framework based on extinction probability: A case study of Wuyishan city

“…In recent years, a broad range of approaches has been proposed to accommodate spatial consideration in reserve selection. These approaches deal with some spatial design criteria as either constraints or objectives, such as performing adjacent rule (Lombard et al, 1997;Briers, 2002;Fuller et al, 2006;Zafra-Calvo et al, 2010), minimizing the boundary length or a linear combination of boundary length and total reserve area (Fischer and Church, 2003;Onal and Briers, 2003;McDonnell et al, 2002;Cabeza et al, 2004a), minimizing the maximum intersite distance or the sum of pairwise distances between all planning sites (Onal and Briers, 2002), measuring the total distance between neighboring sites (Onal and Briers, 2005;Onal and Wang, 2008) and the summed distance to mandatory sites (Alagador and Cerdeira, 2007), maximizing the sum of the inverse distances between pairs of sites (Rothley, 1999), enforcing buffers surrounding selected critical sites (Williams and ReVelle, 1998), keeping sites occurring within the stated proximity distance or the dispersal range of species (Briers, 2002;Van Langevelde et al, 2002;Williams, 2008;Cerdeira et al, 2010) and maximizing connectivity (Briers, 2002;Siitonen et al, 2003;Van Langevelde et al, 2002;Cerdeira et al, 2005;Fuller et al, 2006;Onal and Briers, 2006;Moilanen and Cabeza, 2002;Cabeza, 2003;Moilanen et al, 2005;Van Teeffelen et al, 2006;Rayfield et al, 2009;Bauer et al, 2010). By doing so, selected reserve networks are assumed to capture the optimal configurations that will ensure species' long-term survival while satisfying defined representation goals.…”