WHAT DO WE KNOW ABOUT THE HERITABILITY OF DEVELOPMENTAL INSTABILITY? ANSWERS FROM A BAYESIAN MODEL

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Abstract
In spite of over half a century of research, little is known about the genetic basis of developmental instability (DI). The estimation of the heritability of DI is seriously hampered by the fact that fluctuating asymmetry-FA, that is, the observable outcome of DI-only poorly reflects DI. This results in an underestimation of the heritability of DI. Current methods transforming heritabilities in FA into those of DI fail to take all sources of variation into account and yield incorrect confidence bands that are usually based on unrealistic assumptions. Therefore, a Bayesian latent variable model is developed and explored. Simulations show that with sample sizes currently applied in empirical studies, extremely wide posterior distributions are obtained and data do not allow to distinguish between high (0.5) and low (0.1) heritabilities of DI at all. Even sample sizes of 5000 result in very wide posteriors in many cases. Furthermore, for smaller samples (250 and 1250), up to 70% of the estimates of the heritability of DI were below the mean expected value because of the high skewness of its distribution. Knowing that in only one study, sample sizes were above 5000, there is a need for larger studies to evaluate the evolutionary potential of DI. Designs with relatively low numbers of sires (1-2% of total number of offspring) appear most efficient. Because such high sample sizes are hard to obtain for many study organisms, more insights are required about how data from different traits can be combined in a single analysis. In addition, new designs and methods, such as QTL analyses and micro-array techniques, should be applied to gain a better understanding of the genetic basis of DI.