Removing bias for fluctuating asymmetry in meristic characters

Abstract

Fluctuating asymmetry (FA) in meristic characters is a random difference in count of a character between the right and left sides of an organism. Although FA has been used as an index of developmental instability for more than 30 years, it has not been closely related to the intensity of factors commonly thought to induce instability. The poor relationship could be due to use of biased FA metrics based on differences in bilateral counts, bias introduced by counting errors, low sample sizes, or a truly low correspondence between FA and stressor intensity. I demonstrate why FA metrics based on count differences are inherently biased for meristic characters, develop an unbiased maximum likelihood metric for FA (\(\hat \sigma _A \)), and establish a general method to remove bias caused by counting errors. A likelihood ratio test based on the new metric is nearly as powerful as the F-test, and has a Type I statistical error closer to the nominal level. When applied to bilateral counts of sternopleural bristles in Drosophila, the new metric confirmed previous results based on count differences but removed the concern that the FA estimates were biased by the character mean. Apparent differences in pectoral fin ray FA between rainbow and cutthroat trout disappeared after correction for counting errors.