The relationship between the pleiotropic phenotypic effects of a mutation fixed by selection

A pleiotropic model of mutation is presented that allows for correlations between the effects of a new mutation and for the distribution of mutational effects to vary from being leptokurtic to normally distributed. Using this model I quantify how selection transforms the correlation between the effects of a new (random) mutation into the correlation between the effects of a mutation that is fixed by selection and contributes to an adaptation. Results suggest that under most conditions the correlation between the effects of a fixed mutation is less than the correlation between the effects of a new mutation. I also generalize previous results that quantified the expected size of a fixed mutation's effect on a character given an observed effect of that mutation on another character. In agreement with previous results, work here suggests that as the observed effect becomes large and beneficial the expected effect on another character approaches the expected effect of a new (random) mutation given the observed effect. Lastly, these theoretical results are related to recent empirical work that found beneficial mutations had a positive correlation in their pleiotropic effects.