Minimum distance estimation of mutational parameters for quantitative traits.

Individual spontaneous mutations affecting the expression of quantitative traits cannot be systematically identified and, therefore, their effect on the trait cannot be measured. Thus, the rate of occurrence of such mutations and the moments of the probability distribution of the corresponding effects, which are important in evolutionary studies, remain unknown. Here we propose a method to estimate those mutational properties from the observed distribution of the trait mean in a set of independent inbred lines (all derived from the same homozygous base population) in which mutations had been allowed to accumulate randomly. It is based on the use of the well-known minimum distance method, i.e., on the minimization of a distance between the observed distribution and that expected on the basis of a genetic model. We analyze data for three morphological traits (wing length and abdominal and sternopleural bristle number) in Drosophila melanogaster. The method appears to be powerful, giving evolutionary coherent estimates of relevant mutational properties that had not been estimated previously. For all traits, mutational rates were low (smaller than 0.05). Most mutations affecting wing length or abdominal bristle number and negative effect, while almost half of those affecting sternopleural bristle number had positive effect. For each trait, results obtained from data on different generations are in qualitative agreement, although mutational effects seem to depend on generation-specific environmental factors. The method detected between-trait differences in the kurtosis coefficient of the distribution of mutational effects, which varied from values close to that of the normal distribution (wing length) to relatively high values (sternopleural bristle number). It reveals that an important proportion of the mutational input variance of each trait is due to mutations with absolute effect smaller than 0.5 environmental standard deviation units. For morphological traits undergoing weak direct selection, this suggests that large amounts of genetic variance due to genes segregating at intermediate frequencies can be present at the equilibrium.