Directional asymmetry and the measurement of developmental instability

Abstract

Three widely used methods of estimating fluctuating asymmetry may yield serious overestimates if directional asymmetry is present. When two sides of a bilateral trait grow at different rates, then the asymmetry variance (Var[l-r]) increases with size, even when developmental noise is nil. But the residual variance around a population's mean developmental trajectory is invariant with respect to size. Thus, it can be used as a measure of developmental instability. We introduce a measure of developmental instability, the residual variance (s(delta)(2)), obtainable from either a major axis regression: which is equivalent to a principal component analysis on l and r, or a general structural model. This residual variance can be estimated from directionally asymmetric or even antisymmetric traits. We present examples of developmental instability estimated from directionally asymmetric mandibles (house mouse) and leaves (soybean), and antisymmetric flaws (fiddler crab). (C) 1998 The Linnean Society of London