Disentangling dispersion from mean reveals true heterogeneity-diversity relationships.

Abstract

Understanding the effect of heterogeneity is fundamental to numerous fields. In community ecology, classical theory postulates that habitat heterogeneity determines niche dimensionality and drives biodiversity. However, disparate heterogeneity-diversity relationships have been empirically observed, generating increasingly complex theoretical developments. Here we show that spurious heterogeneity-diversity relationships and subsequent theories arise as artifacts of heterogeneity measures that are mean-biased for bounded continuous variables. To solve this, we derive an alternative mean-independent measure of heterogeneity for beta and gamma distributed variables that disentangles statistical dispersion from mean. Using the mean-independent measure of heterogeneity, true monotonic positive heterogeneity-diversity relationships, consistent with classical theory, are revealed in data previously presented as evidence for both hump-shaped heterogeneity-diversity relationships and theories of an area-heterogeneity trade-off for biodiversity. This work sheds light on the source of conflicting results that have hindered understanding of heterogeneity relationships in broader ecology and numerous other fields. The mean-independent measure of heterogeneity is provided as a solution, essential for understanding true mean-independent heterogeneity relationships in wider research.