On the use of the coefficient of variation to quantify and compare trait variation

Meaningful comparison of variation in quantitative trait requires controlling for both the dimension of the varying entity and the dimension of the factor generating variation. Although the coefficient of variation (CV; standard deviation divided by the mean) is often used to measure and compare variation of quantitative traits, it only accounts for the dimension of the former, and its use for comparing variation may sometimes be inappropriate. Here, we discuss the use of the CV to compare measures of evolvability and phenotypic plasticity, two variational properties of quantitative traits. Using a dimensional analysis, we show that contrary to evolvability, phenotypic plasticity cannot be meaningfully compared across traits and environments by mean-scaling trait variation. We further emphasize the need of remaining cognizant of the dimensions of the traits and the relationship between mean and standard deviation when comparing CVs, even when the scales on which traits are expressed allow meaningful calculation of the CV.