Palmer, A. R. and C. Strobeck. 1992. Fluctuating asymmetry as a measure of developmental stability: Implications of non-normal distributions and power of statistical tests. Acta Zoologica Fennica 191:55-70.

ABSTRACT: Fluctuating asymmetry (FA) is a widely used measure of developmental stability. Nearly all FA indexes estimate the variance of the frequency distribution of right-minus-left (R-L) for a given bilateral character. Differences in these indexes among samples are usually interpreted as reflecting differences in the level of developmental stability. If developmental stability is the ability to correct for small, random developmental perturbations of exclusively environmental origin, then a distribution of R-L, which may include both genetically and environmentally caused asymmetries, may not be a good measure of developmental stability. R-L distributions that depart significantly from the statistical criteria for ideal FA (mean of zero, normal distribution) are unsuitable as descriptors of developmental stability because a fraction of the asymmetry variation may have a genetic basis. Broad-peaked or bimodal (platykurtic) distributions of R-L, which reveal the presence of antisymmetry, also imply genetically based asymmetries and thus seem inappropriate as descriptors of developmental stability.

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Figure 1. A graphical illustration of variation in fruit fly wing lengths (a,b) and ideal fluctuating asymmetry (c), illustrating the conventional interpretation of fluctuating asymmetry. Ri = size of a trait on the right side, Li = size of the bilaterally paired trait on the left side. Here and in later figures we use a convention to represent genetic and environmental components of bilateral variation that requires some explanation. Red portions of the frequency distributions represent genetically induced variation, and stippled frequency distributions represent total phenotypic variation (including developmental noise). The remaining region under the curve is intended to represent environmentally induced variation only. Two aspects of these curves, however, are not technically correct. First, the area under each should be the same (the area under any frequency distribution is one). Second, if environmental variation is added to underlying genetic variation, the combined distribution should be broader with a lower peak. We use this heuristic convention a) because we wish to emphasize that some subset of the total phenotypic variation has a genetic basis, and b) because it avoids introducing potentially distracting elements to the figures.

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Figure 2. Three "pure" forms of bilateral asymmetry: a) fluctuating asymmetry, b) directional asymmetry, and c) antisymmetry. See Fig. 1 for an explanation of the convention for representing genetic and environmental variation.

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