Scale collapse and the emergence of the power law speciesâ€“area relationship

Abstract

AbstractAimThe recently proposed maximum entropy theory of ecology predicts that all nested species–area relationships (SARs) will collapse to a single, universal curve that exhibits a decreasing log–log slope with increasing scale, suggesting that the power law form of the SAR is invalid at any scale. In this analysis we test the generality of this scale collapse behaviour and determine the scale at which approximate power law behaviour of the SAR is predicted to occur.LocationGlobal.MethodsWe use common SAR models to recursively upscale SARs to (1) look for scale collapse of SARs built from different community assumptions and (2) identify the scale at which approximate power law SARs are recovered. We explore four SAR models in which species abundance distributions and the spatial aggregation of species vary within and across scales according to observed patterns.ResultsWe show that scale collapse is a property of nested SARs, not of maximum entropy theory, and that many types of SARs can exhibit scale‐collapsed curves that follow the general pattern of empirical communities. Moreover, we use the scale‐collapsed curves to show that power law behaviour is not predicted to occur at the scale of most SAR studies and that variation in species spatial aggregation or the scaling of species abundance distributions are needed to produce power law SARs at realistic scales.Main conclusionsOur findings show that power law behaviour of nested SARs is rare and that communities displaying approximate power law SARs may exhibit predictable characteristics within and across scale, such as interspecific variation in aggregation. Our findings regarding the general rarity of power law behaviour suggests that careful consideration of the curvature of a SAR and the scale of an ecological community are necessary before using power law SARs to predict biodiversity across scales.