Evolvability and Pleiotropic Constraint
Evolvability is a population's ability to change its underlying genetic makeup through natural selection, to evolve. Most measures of short-term evolvability relate genetic change to the abundance and geometry of standing genetic variation, making the additional assumption that this structure is captured by the genetic variance-covariance matrix G; G applies in only the multivariate normal scenario. Because we observe non-normality in natural distributions and are often unable to verify statistically whether a particular distribution is normal, we propose an alternate approach to discussing the short-term evolvability of general populations. Changes in the underlying genetic makeup of a population are observed as changes in the relative frequency of the population's traits. This is fundamentally a change in distribution, and is best quantified using an information-theoretical approach. The resulting measure of evolvability and its constraints apply to any well-behaved distribution and are for normally distributed traits a function of G; we suggest that existing measures may be placed within our general formulation. Comparing the total constraint to the sum of univariate constraints on individual traits we quantify the constraint due to multivariate trait interactions; we propose this as an appropriate measure of pleiotropic constraint. We find that pleiotropic constraint is highly dependent on the total correlation information, and to advance towards a suitable null hypothesis for tests of pleiotropy we derive the distribution of this quantity under multivariate normal independence. For large system sizes this relates to the Marchenko-Pasteur distribution, and is approximately normal, obeying Lyapunov's central limit theorem. We demonstrate the unique theoretical and practical advantages of a distribution-level approach to evolvability using both simulated and real data from Drosophila. In line with intuition, incorrectly assuming an absence of non-normality in the distribution of phenotypic traits leads to underestimation of the evolutionary constraint.
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