Revisiting the minimum set cover, the maximal coverage problems and a maximum benefit area selection problem to make climate-change-concerned conservation plans effective

Informed decisions for the selection of protected areas (PAs) are grounded in two general problems in Operations Research: the minimum set covering problem (minCost), where a set of ecological constraints are established as conservation targets and the minimum cost PAs are found, and the maximal coverage problem (maxCoverage) where the constraint is uniquely economic (i.e. a fixed budget) and the goal is to maximize the number of species having conservation targets adequately covered. We adjustminCostandmaxCoverageto accommodate the dynamic effects of climate change on species' ranges. The selection of sites is replaced by the selection of time-ordered sequences of sites (climate change corridors), and an estimate of the persistence of each species in corridors is calculated according to the expected suitability of each site in the respective time period and the capacity of species to disperse between consecutive sites along corridors. In these problems, conservation targets are expressed as desired (and attainable) species persistence levels. We also introduce a novel problem (minShortfall) that combinesminCostandmaxCoverage. Unlike these two problems,minShortfallallows persistence targets to be missed and minimizes the sum of those gaps (i.e. target shortfalls), subject to a limited budget. We illustrate the three problems with a case study using climatic suitability estimates for 10 mammal species in the Iberian Peninsula under a climate change scenario until 2080. We compare solutions of the three problems with respect to species persistence and PA costs, under distinct settings of persistence targets, number of target-fulfilled species and budgets. The solutions from different problems differed with regard to the areas to prioritize, their timings and the species whose persistence targets were fulfilled. This analysis also allowed identifying groups of species sharing corridors in optimal solutions, thus allowing important financial savings in site protection. We suggest that enhancing species persistence is an adequate approach to cope with habitat shifts due to climate change. We trust the three problems discussed can provide complementary and valuable support for planners to anticipate decisions in order that the negative effects of climate change on species' persistence are minimized.