Quartile coefficient of variation is more robust than CV for traits calculated as a ratio

Abstract

Comparing within-species variations of traits can be used in testing ecological theories. In these comparisons, it is useful to remove the effect of the difference in mean trait values, therefore measures of relative variation, most often the coefficient of variation (CV), are used. The studied traits are often calculated as the ratio of the size or mass of two organs: e.g. specific leaf area (SLA) is the ratio of leaf size and leaf mass. Often the inverse of these ratios is also meaningful; for example, the inverse of SLA is often referred to as LMA (leaf mass per area). Relative variation of a trait and its inverse should not considerably differ. However, it is illustrated that using the coefficient of variation may result in differences that could influence the interpretation, especially if there are outlier trait values. The alternative way for estimating CV from the standard deviation of log-transformed data assuming log-normal distribution and Kirkwood's geometric coefficient of variation free from this problem, but they proved to be sensitive to outlier values. Quartile coefficient of variation performed best in the tests: it gives the same value for a trait and its inverse and it is not sensitive to outliers.