A New Fluctuating Asymmetry Index, or the Solution for the Scaling Effect?

作者：Pertoldi Cino^*; Kristensen Torsten Nygaard

来源：Symmetry-Basel, 2015, 7(2): 327-335.

DOI：10.3390/sym7020327

Two principal methods are commonly employed for the estimation of developmental instability at the population level. Some studies use variances of morphological traits (sigma(2)(p)), while others use fluctuating asymmetry (FA). In both cases, differences in the degree of developmental instability can be tested with an F-test, which is the most common way to compare variances. However, the variance is expected to scale proportionally to the square of the mean as there is a tendency in biological data for sigma(2)(p) to scale proportionally to the square of the mean
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, where xi is the scaling exponent, which is expected to be two for pure statistical reasons,
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is the mean of the trait and Z is a measure of individual-level variability. Because of this scaling effect, the fluctuating asymmetry will be affected, FA is estimated as the variance between the right and the left sides of a trait (sigma(2)(r) (-) (l) = sigma(2)(r) + sigma(2)(l) - 2r sigma(r)sigma(l)), where sigma(2)(r) and sigma(2)(l) are the variances of the right and the left trait values, respectively. In this paper, we propose a novel method that allows an exact correction of the scaling effect, which will enable a proper comparison of the degree of fluctuating asymmetry for a trait. The problem of the scaling of the FA with the trait size is quite crucial if FA is to be considered an indicator of fitness or an indicator of environmental or genetic stress, as different stresses or fitness levels are typically accompanied by a change of the traits'
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.

• 出版日期2015-6