The statistics of detecting positional fluctuating asymmetry

The detection of asymmetry can be difficult because the signals indicating right–left differences are frequently weak. When bilaterally symmetric organisms can be further inspected for positional asymmetry (differences between body sides in the placement of meristic traits) anterior–posterior allocation may provide additional evidence for fluctuating asymmetry. Statistical power comparisons were made for indices used to measure fluctuating (FA) and positional fluctuating asymmetry (PFA) in meristic traits. Monte Carlo simulations of developmental and random processes were used to generate null and alternative distributions of a hypothetical meristic trait (such as bristle counts). The counts were used to calculate the corresponding distributions of six indices used to detect fluctuating and positional fluctuating asymmetry. Power comparisons show that there is no single best index. If positional deviations are strong relative to bilateral errors then pfa1 is generally the most powerful, while fa, the G-statistic, and in some instances the procrustes-distance measure do best when there is little positional deviation relative to sideto-side deviations. The decision on what index is best is thus influenced by knowledge of the likely sources of error. As a consequence, all three indices (fa, G and pfa1) should be explored when little a priori knowledge is available. © 2002 The Linnean Society of London, Biological Journal of the Linnean Society , 2002, 77 , 491–498.