Fluctuating Asymmetry Analyses Revisited

In spite of a decade of furious activity and an increasingly bewildering array of analytical methods, essential requirements for a robust study of fluctuating asymmetry have not changed: judicious choice of traits, meticulous attention to measurement precision, visual inspection and tests for dubious data, appropriate tests and corrections for size-dependence, confirmation that subtle deviations from symmetry both exceed those expected due to measurement error and meet the criteria for ideal fluctuating asymmetry, and an open mind about alternative hypotheses. We review these requirements and try to clarify why they are so essential. Studies of fluctuating asymmetry face a number of serious challenges: a) random phenotypic variation arises for reasons other than developmental instability, b) all descriptors of FA estimate a variance and variances are estimated with much lower confidence than means (i.e., repeatability is lower), c) subtle departures from symmetry are typically so minute they are exceedingly difficult to measure reliably, d) measurement error and trait size interact in complex and mischievous ways, and e) tests for departures from normality are uncomfortably weak for small to modest sample sizes. We outline the foundations of these challenges and some of the ways they may be addressed. Persistent efforts to improve analytical tools nonetheless have yielded some useful advances: a) log transformations help remove the size-dependence of subtle asymmetries and the heterogeneity of variance that can arise from this size-dependence, b) proper critical values for the kurtosis statistic provide more reliable statistical tests, c) indexes that combine information from multiple traits yield more reliable estimates of individual developmental instability, and d) a generalization of Levene's test improves both the ease and the power of analyses testing for differences in fluctuating asymmetry among individuals, traits or groups. Finally, as an appendix, we provide a detailed worked example, with commentary, of a complete FA analysis. It outlines how care and common sense in preliminary analyses greatly improve the rigor of the final results. This appendix, and the data files for the analyses, are available as web supplements. Rev. 5/13/01 Palmer & Strobeck -3-