Are fluctuating asymmetry studies adequately sampled? Implications of a new model for size distribution.

Previous work on fluctuating asymmetry (FA) has highlighted its controversial relationship with environmental stress and genetic architecture. While size-based measures of FA have been assumed to have half-normal distributions within populations, studies of model developmental mechanisms have suggested other plausible distributions for FA. We investigated the distribution of FA in large empirical data sets of wing shape and wing size asymmetry from three species of insects (cotton aphid Aphis gossipyii Glover, honeybee Apis mellifera, and long-legged fly Chrysosoma crinitus). Regardless of measurement method, FA was best described by a double Pareto-lognormal (DPLN) distribution or one of its limiting functional forms. To investigate convergence of mean sample FA to the population mean at various sample sizes, we sampled repeatedly under a DPLN distribution using parameter values that best fitted our data. Sample variances are much larger, and hence, convergence is slowed considerably with univariate or multivariate size-based measures of FA in contrast to a multivariate shape-based measure of FA. We suggest that much of the past work on FA may be undersampled, and we recommend using multivariate shape-based approaches or collecting larger data sets in future studies. We also discuss the implications of the DPLN distribution for understanding the developmental mechanisms underlying FA.