Phenomenological models derived from negative binomial distribution and Taylor's law are commonly used in ecology to describe relationships of the occupancy, spatial mean, and spatial variance of species abundance. However, the theoretical properties of these models have not been investigated rigorously, which impedes gaining analytic understanding of the fitted abundance distribution. In addition, the scales, methods, and measures used in the model fitting and evaluation are often arbitrarily chosen, casting doubts on the validity of model comparison.
Results/Conclusions
We evaluated six phenomenological models of occupancy-mean-variance relationships empirically and analytically. Using 12 empirical data sets (eight interspecific and four intraspecific), we showed that Taylor's law, negative binomial, and He-Gaston model for variance were equally well in predicting variance, except when the models were fitted under arithmetic scale and assessed using root-mean-square error of untransformed values. When predicting occupancy, negative binomial and a unified negative binomial model performed equally well. Moreover, we proved analytically that the He-Gaston model for occupancy was theoretically incorrect since it mixed two mathematically independent mean-variance relationships of negative binomial distribution and Taylor's law. We provided recommendations for the use of phenomenological models in empirical works and discussed the ecological relevance of our theoretical finding.