How to compare fluctuating asymmetry of different traits

Abstract

Abstract Comparing fluctuating asymmetry (FA) between different traits can be difficult because traits vary at different scales. FA is generally quantified either as the variance of the difference between left and right (σ2L−R) or the mean of the absolute value of this difference (μ|R−L|). Corrections for scale differences are obtained by dividing by trait size mean. We show that a third index, one minus the correlation coefficient between left and right (1 − rL,R), is equivalent to σ2L−R standardized by trait size variance. The indices are compared with Monte-Carlo simulations. All achieve the expected correction for scale differences. High type I error rates (false indication of differences) occur only for σ2L−R and μ|R−L| if trait sizes close to or below 0 occur. 1 − rL,R with a bootstrap test has always low error rates. Recommendation of the index to be used should be based on whether standardization of FA by trait size mean or trait size variance is preferred. A survey of 36 traits in the Speckled Wood Butterfly (Pararge aegeria) indicated that σ2L−R is slightly higher correlated to trait size variance than to trait size mean. Thus 1 − rL,R seems to be the superior index and should be reported when FA of different traits is compared.