AIM. Biodiversity loss, measured as count of extinction events, is a key component of biodiversity change, and can significantly impact ecosystem services. However, estimation of the loss has focused mostly on per-species extinction rates measured over limited numbers of spatial scales, with no theory linking small-scale extirpations with global extinctions. Here we provide such link by introducing the relationship between area and per-species probability of extinction (PxAR) and between area and count of realized extinction events in that area (NxAR). We show theoretical and empirical forms of these relationships, and we discuss their role in perception and estimation of the current extinction crisis. LOCATION. USA, Europe, Czech Republic, Barro Colorado Island METHODS. We derived the expected forms of PxAR and NxAR from a range of theoretical frameworks based on theory of island biogeography, neutral models, and species-area relationships. We constructed PxAR and NxAR in five empirical datasets on butterflies, plants, trees and birds, collected over range of spatial scales. RESULTS. Both the theoretical arguments and empirical data support monotonically decreasing PxAR, i.e. per-species extinction probability decreasing with increasing area; however, we also report a rare theoretical possibility of locally increasing PxAR. In contrast, both theory and data revealed complex NxAR, i.e. counts of extinction events follow variety of relationships with area, including nonlinear unimodal, multimodal and U-shaped relationships, depending on region and taxon. MAIN CONCLUSIONS. The uncovered wealth of forms of NxAR can explain why biodiversity change (the net outcome of losses and gains) also appears scale-dependent. Furthermore, the complex scale dependence of PxAR and NxAR means that global extinctions indicate little about local extirpations, and vice versa. Hence, effort should be made to understand and report extinction crisis as a scale-dependent problem. In this effort, estimation of scaling relationships such as PxAR and NxAR should be central.

Extinction rate has a complex and non-linear relationship with area