Connectivity in reserve selection: Mathematical questions.
Cerdeira, J. Orestes*,1, Gaston, Kevin J.2, Pinto, Leonor S.3, 1 Instituto Superior de Agronomia, Lisboa, Portugal2 University of Sheffield, Sheffield, England3 Instituto Superior de Economia, Lisboa, Portugal
ABSTRACT- A number of problems associated with the spatial structure in the design of networks of protected areas are not mathematically trivial, and solutions are not readily approximated intuitively. One such issue is that of designing networks so that the sites which they comprise respect some minimal level of adjacency or connectivity between areas. These spatial issues fit within the framework of graph theory. Connectivity has been addressed using a graph to describe the adjacency relationship between sites. However, in situations where different species require levels of adjacency that are quite dissimilar (e.g. through having different dispersal abilities), it may be more realistic to address connectivity on a species by species basis. Say that for each species there exist: (i) certain habitat sites, (ii) a target number indicating the number of sites considered adequate for its survival, and (iii) a graph describing adjacencies between pairs of habitats sites reflecting that species mobility. Feasible solutions are now subsets of sites that, for each species, include a connected network consisting of the required number of habitat sites. We consider these two types of connectivity from a mathematical point of view. We give integer linear formulations for the problem of designing minimum size networks that meet the connectivity requirements and the species representation targets. We develop integer cutting algorithms to solve this problem and report computational experiments.
Key words: graphs, algorithms, connectivity
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