Spatial heterogeneity: Evolved behaviour or mathematical artefact?

For more than a century ecologists have sought to explain the spatial heterogeneity of plants and animals¹, but progress has been hampered by measurement bias². A measure thought to be an unbiased index of spatial heterogeneity³ is b, the fitted exponent in the empirical relationship s² = aM^b, where s² is the variance and M the average of randomly placed replicate population estimates ⁴. This index is widely accepted because of the impressive correlation between s² and M and because it requires no inter-organism distance measures. Theoretical models, based on migratory behaviour⁵ or demographic factors⁶, have been proposed to account for the relationship between s² and M. These models disagree regarding the effect of environment on b and the divergence of b values shown by different species. Here I report data showing that species-specific b varies among environments and that different species often show similar b values, favouring the demographic model. Analysis of these data shows that different levels of replication and sampling coverage lead to biased b values, casting doubt on the use of b for the deduction of cause of spatial variance relationships or the comparative measurement of spatial heterogeneity.