Are Fluctuating Asymmetry Studies Adequately Sampled? Implications of a New Model for Size Distribution

Abstract

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.

How accurate is the phenotype? – An analysis of developmental noise in a cotton aphid clone

“…Under the conditions of this experiment, the aphid wing was found to be a highly developmentally unstable trait, by comparison to levels of FA usually observed in the wings of other insects (see Figure 3), exhibiting nearly four times the level of FA that is typical of other insects [29]. This was clearly not the result of directional asymmetry possibly inflating the overall FA measured in this study.…”

“…See Babbit et al [29], Babbit [30] and Reed and Jorgensen [38] for further explanation of this distribution type. Similar distributional patterns are observed within temperatures (not shown) as that observed across temperatures (Figure 3).…”

“…Because of probable under-sampling in the Lake Alfred clone (see [29]) the results presented here are from the Gainesville clone. Mean centroid size FA (Figure 4) and development time (Figure 2) follow a nearly identical pattern, decreasing rapidly at first then slowing with increased temperature.…”

“…The culture was maintained on cotton seedlings ( Gossipium ) grown at different temperatures (12.5°C, 15°C, 17°C, 19°C, 22.5°C and 25°C with n = 677 total or about 100+ per treatment) under artificial grow lights (14L:10D cycle). Because of potential under-sampling caused by a non-normal distribution of FA (see [29]), a second monoclonal population collected from Gainesville, FL in June 2004 was reared similarly, but in much larger numbers at 12.5°C, 15°C, 17°C, 19°C, and 25°C (n = 1677 or about 300+ per treatment).…”

“…However, Leamy and Klingenberg [28] rationalize that molecular noise could scale to the level of tissue when developmentally important molecules exist in very small quantities (e.g., regulated transcript or protein), and therefore FA actually may represent a stochastic component of developmental gene expression. The temporal variation in cell cycle that this could cause is also implicated by the observation of high kurtosis (or, more specifically, in this case a non-normal distribution due to power law scaling in the tails) often observed in FA data [25,29]. Babbitt [30] has also linked increased scaling phenomena (and kurtosis) to increased genetic heterogeneity in a population.…”