A simple model of the relationship between asymmetry and developmental stability

The relationship between developmental stability and morphological asymmetry is derived under the standard view that structures on each side of an individual develop independently and are normally distributed. I use developmental variance of sizes of parts, V_D, as the converse of developmental stability, and assume that V_D follows a gamma distribution. Repeatability of asymmetry, a measure of how informative asymmetry is about V_D, is quite insensitive to the variance in V_D, for example only reaching 20% when the coefficient of variation of V_D is 100%. The coefficient of variation of asymmetry, CV_FA, also increases very slowly with increasing population variation in V_D. CV_FA values from empirical data are sometimes over 100%, implying that developmental stability is sometimes more variable than any previously studied type of trait. This result suggests that alternatives to this model may be needed.