The coefficient of variation of body mass (and other traits)

Mirjam Borger , Klaus Reinhold

Variation is a fundamental property of populations and provides the raw material upon which evolutionary processes can act. The coefficient of variation, defined as the standard deviation divided by the arithmetic mean, is widely used in evolutionary biology to quantify relative variation, for example to draw conclusions about the strength of selection. However, comparing coefficients of variation among traits can be problematic, because traits of higher dimensionality (e.g. volume) may exhibit greater variation as a mathematical consequence of their dependence on the variation in multiple underlying traits (e.g. length, width, height), independent of any biologically relevant difference in variation between higher- and lower-dimensional traits. Some interpreted this as the need for a correction factor before an honest comparison can be made and e.g. divide coefficients of variation of body mass by three to make it comparable with length measures. Here, we provide three arguments, why this procedure might be misleading. 1). Body mass is not a proxy of volume, as it is also caused by density in living organisms, and therefore should be treated as at least four dimensional. 2). As previously argued, correction factors are extremely difficult to use correctly, as their value depends on the coefficients of variation of, and the correlations between, all underlying traits, which often are difficult or even impossible to measure. 3). Dimensionality in this context refers not exclusively to physical dimensions but instead represents the number of underlying sources of variation contributing to the variation in higher-order traits. This broader interpretation is relevant to traits such as behaviour, for which the underlying causes of variation may be numerous and difficult to identify, or for traits like condition, that have abstract meaning. We therefore recommend caution when comparing coefficients of variation among traits, particularly when their underlying causes of variation differ, or are unknown.