The scientific, political and societal debate on how to prevent the erosion of the world biodiversity has largely concentrated on the effects of two alternative types of agricultural production, land sparing (intensive farming leaving more land for natural spaces) and land sharing (extensive farming richer in biodiversity). For a given production target, Green et al. (2005) conclude in favor of land sparing if the relation between biodiversity and yield is decreasing and convex. Indeed, with a shift to extensive farming, biodiversity then increases little on already cultivated land, while it decreases strongly on newly cultivated land. According to these authors and to Phalan et al. (2011a), available empirical data are in favor of a land s...