Place prioritization for biodiversity conservation using probabilistic surrogate distribution data

We analyse optimal and heuristic place prioritization algorithms for biodiversity conservation area network design which can use probabilistic data on the distribution of surrogates for biodiversity. We show how an Expected Surrogate Set Covering Problem (ESSCP) and a Maximal Expected Surrogate Covering Problem (MESCP) can be linearized for computationally efficient solution. For the ESSCP, we study the performance of two optimization software packages (XPRESS and CPLEX) and five heuristic algorithms based on traditional measures of complementarity and rarity as well as the Shannon and Simpson indices of alpha-diversity which are being used in this context for the first time. On small artificial data sets the optimal place prioritization algorithms often produced more economical solutions than the heuristic algorithms, though not always ones guaranteed to be optimal. However, with large data sets, the optimal algorithms often required long computation times and produced no better results than heuristic ones. Thus there is generally little reason to prefer optimal to heuristic algorithms with probabilistic data sets.