Optimizing Species Richness in Mosaic Landscapes: A Probabilistic Model of Species-Area Relationships

Most landscapes are comprised of multiple habitat types differing in the biodiversity they contain. This is certainly true for human modified landscapes, which are often a mix of habitats managed with different intensity, semi-natural habitats and even pristine habitats. To understand fundamental questions of how the composition of such landscapes affects biodiversity conservation, and to evaluate biodiversity consequences of policies that affect the composition of landscapes, there is a need for models able to translate information on biodiversity from individual habitats to landscape-wide predictions. However, this is complicated by species richness not being additive. We constructed a model to help analyze and solve this problem based on two simple assumptions. Firstly, that a habitat can be characterized by the biological community inhabiting it; i.e., which species occur and at what densities. Secondly, that the probability of a species occurring in a particular unit of land is dictated by its average density in the associated habitats, its spatial aggregation, and the size of the land unit. This model leads to a multidimensional species-area relation (one dimension per habitat). If the goal is to maximize species diversity at the landscape scale (γ-diversity), within a fixed area or under a limited budget, the model can be used to find the optimal allocation of the different habitats. In general, the optimal solution depends on the total size of the species pool of the different habitats, but also their similarity (β-diversity). If habitats are complementary (high β), a mix is usually preferred, even if one habitat is poorer (lower α diversity in one habitat). The model lends itself to economic analyses of biodiversity problems, without the need to monetarize biodiversity value, i.e., cost-effectiveness analysis. Land prices and management costs will affect the solution, such that the model can be used to estimate the number of species gained in relation to expenditure on each habitat. We illustrate the utility of the model by applying it to agricultural landscapes in southern Sweden and demonstrate how empirical monitoring data can be used to find the best habitat allocation for biodiversity conservation within and between landscapes