LB 9-96 - You keep using Coefficient of Variation; I do not think it means what you think it means (Inigo Montoya suggests variance partitioning, instead)

Variability–statistically, variance, the second data moment–is an important ecological property, often more consequential for understanding ecosystem processes than the first statistical moment, the mean. But variability can be an abstract concept, and there is understandable incentive to apply simple measures when describing it. A popular metric in the ecology literature is Coefficient of Variation (CV=standard deviation /mean ⋅100). The objective of this study is to address issues that arise when ecologists try to describe multiple components of variability and demonstrate variance partitioning as a spatially-explicit alternative. We are particularly concerned about comparisons of local (alpha) variability across broad gradients that effect differences in mean values (gamma variability), and present examples of CV changing more with precipitation or land use intensity gradients that inherently drive differences in mean biomass. Our approach is to revisit Kotliar & Wien’s description of spatial heterogeneity as patch contrast and apply variance partitioning regression models to measure and compare multiple sources of variability in a spatially-explicit manner. Here we show, using data simulations, firstly the errors introduced to CV when calculated across environmental gradients that effect differences in mean and standard deviation, and secondly, the sensitivity of variance partitioning to patch contrast across broad gradients of data moments (ranges of mean and variance). In conclusion, this study demonstrates the fatal errors introduced when using CV to describe variability across environmental gradients and the additional information obtained with variance partitioning.