High variation in developmental instability under non-normal developmental error: a Bayesian perspective.

The developmental mechanisms behind developmental instability (DI) are only poorly understood. Nevertheless, fluctuating asymmetry (FA) is often used a surrogate for DI. Based on statistical arguments it is often assumed that individual levels of FA are only weakly associated with the underlying DI. Patterns in FA therefore need to be interpreted with caution, and should ideally be transformed into patterns in DI. In order to be able to achieve that, assumptions about the distribution of developmental errors must be made. Current models assume that errors during development are additive and independent such that they yield a normal distribution. The observation that the distribution of FA is often leptokurtic has been interpreted as evidence for between-individual variation in DI. This approach has led to unrealistically high estimates of between-individual variation in DI, and potentially incorrect interpretations of patterns in FA, especially at the individual level. Recently, it has been suggested that the high estimates of variation in DI may be biased upward because either developmental errors are log-normal or gamma distributed and/or low measurement resolution of FA. A proper estimation of the amount (and shape) of heterogeneity in DI is crucial for the interpretation of patterns in FA and their transformation into patterns in DI. Yet, incorrect model assumptions may render misleading inferences. We therefore develop a statistical model to evaluate the sensitivity of results under the normal error model against the two alternative distributions as well as to investigate the importance of low measurement resolution. An analysis of simulated and empirical data sets indicated that bias due to misspecification of the developmental error distribution can be substantial, yet, did not appear to reduce estimates of variation in DI in empirical data sets to a large extent. Effects of low measurement resolution were neglectable. The importance of these results are discussed in the context of the interpretation of patterns in FA.