The tangled link between β- and γ-diversity: a Narcissus effect weakens statistical inferences in null model analyses of diversity patterns

Understanding the structure of and spatial variability in the species composition of ecological communities is at the heart of biogeography. In particular, there has been recent controversy about possible latitudinal trends in compositional heterogeneity across localities (β-diversity). A gradient in the size of the regional species pool alone can be expected to impose a parallel gradient on β-diversity, but whether β-diversity also varies independently of the size of the species pool remains unclear. A recently suggested methodological approach to correct latitudinal β-diversity gradients for the species pool effect is based on randomization null models that remove the effects of gradients in α- and γ-diversity on β-diversity. However, the randomization process imposes constraints on the variability of α-diversity, which in turn force γ- and β-diversity to become interdependent, such that any change in one is mirrored in the other. We argue that simple null model approaches are inadequate to discern whether correlations between α-, β- and γ-diversity reflect processes of ecological interest or merely differences in the size of the species pool among localities. We demonstrate that this kind of Narcissus effect may also apply to other metrics of spatial or phylogenetic species distribution. We highlight that Narcissus effects may lead to artificially high rejection rates for the focal pattern (Type II errors) and caution that these errors have not received sufficient attention in the ecological literature.