Analytical Solutions to Trade‐Offs between Size of Protected Areas and Land‐Use Intensity | Soluciones Analíticas a las Ventajas y Desventajas entre el Tamaño de Áreas Protegidas y la Intensidad del Uso de Suelo

Land‐use change is affecting Earth's capacity to support both wild species and a growing human population. The question is how best to manage landscapes for both species conservation and economic output. If large areas are protected to conserve species richness, then the unprotected areas must be used more intensively. Likewise, low‐intensity use leaves less area protected but may allow wild species to persist in areas that are used for market purposes. This dilemma is present in policy debates on agriculture, housing, and forestry. Our goal was to develop a theoretical model to evaluate which land‐use strategy maximizes economic output while maintaining species richness. Our theoretical model extends previous analytical models by allowing land‐use intensity on unprotected land to influence species richness in protected areas. We devised general models in which species richness (with modified species‐area curves) and economic output (a Cobb–Douglas production function) are a function of land‐use intensity and the proportion of land protected. Economic output increased as land‐use intensity and extent increased, and species richness responded to increased intensity either negatively or following the intermediate disturbance hypothesis. We solved the model analytically to identify the combination of land‐use intensity and protected area that provided the maximum amount of economic output, given a target level of species richness. The land‐use strategy that maximized economic output while maintaining species richness depended jointly on the response of species richness to land‐use intensity and protection and the effect of land use outside protected areas on species richness within protected areas. Regardless of the land‐use strategy, species richness tended to respond to changing land‐use intensity and extent in a highly nonlinear fashion.