Abstract
Two principal methods are commonly employed for the estimation of developmental instability at the population level. Some studies use variances of morphological traits (σ2p), 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 σ2p to scale proportionally to the square of the mean ( ): σ2p = Z ξ, where ξ is the scaling exponent, which is expected to be two for pure statistical reasons, 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 (σ2r − l = σ2r + σ2l − 2rσrσl), where σ2r and σ2l 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’ .
Highlights
IntroductionThe development of a trait in a given environment is disturbed by random processes that cause it to deviate from its expected phenotype
The method proposed in this paper can be utilized to make an exact correction for differences in means between samples that are compared
Even with this correction we should be aware of confounding factors, such as the standard error of the variance and the presence of mixtures due to environmental variability, which can produce platykurtic or leptokurtic distributions of the (r − l) values [35,36,37,38,39,40]
Summary
The development of a trait in a given environment is disturbed by random processes that cause it to deviate from its expected phenotype. It is believed that an individual’s ability to buffer its development against these random perturbations is influenced by genotype, environment and/or genotype-environment interactions [1,2,3,4]. Developmental instability (DI) results when stress affects the buffering capacity of the processes that provide stability to an organism’s development [5]. Empirical studies supporting its general adequacy for monitoring species or populations are generally lacking or contradictory [4,13,14,15,16]
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