The multivariate distribution of genetic variance is key to understanding two fundamental and interrelated processes in evolution; the ability of populations to respond to selection, and the balance of forces that maintain the genetic variance that such a response is based upon. In this thesis, I develop an analytical framework for characterizing the multivariate distribution of genetic variance and how it evolves. I then apply this framework to explore the evolution of genetic variance in multiple sexually-selected traits under artificial selection using the Drosophila serrata experimental system. An analytical framework for characterizing the multivariate distribution of genetic variance and how it evolves: First, I present a method from the statistical literature to establish the statistical dimensionality of genetic variance in a suite of traits. I evaluate the ability of this and two other methods to predict the correct number and orientation of dimensions of genetic variance by conducting a simulation study for a suite of eight traits. Second, I present a method from the materials science literature that uses multi-linear algebra to characterize the variation among matrices. I show how variation in the multivariate distribution of genetic variance among populations can be analyzed by constructing a fourth-order genetic variance-covariance tensor, and how the spectral decomposition of this tensor reveals independent aspects of change in genetic variance. I use the tensor to explore the variation in the genetic variance of eight traits among nine populations of D. serrata, and show how this variation can be associated with variation in selection pressures to determine whether selection may have affected genetic variance within populations. The evolution of genetic variance in sexually-selected traits under artificial selection: Female D. serrata display a strong preference for a particular combination of male cuticular hydrocarbons (CHCs). Individually, these pheromones display substantial genetic variance, but the genetic variance is not distributed equally among all phenotypic dimensions. In the specific CHC combination preferred by females, genetic variance is low. This is compatible with the expectation that selection will deplete genetic variance, but is contrary to the typical observation of high levels of genetic variance in individual sexually-selected traits. By artificially selecting on the trait combination preferred by females, I show that male mating success can successfully respond to selection, but the evolution of the combination of CHCs preferred by females is constrained. I then show that a key prediction of mutation-selection balance (MSB) models that has rarely been observed holds for these traits. Under MSB, genetic variance is expected to be maintained by rare alleles with large effects. Therefore, when a trait that is usually under stabilizing selection is subjected to directional artificial selection, the genetic variance is predicted to increase. I show that genetic variance increases in the CHC combination preferred by females under artificial selection, but not when another combination of the same traits with greater genetic variance is artificially selected. Complex segregation analysis indicated that the observed increase in genetic variance was a consequence of at least one allele of major effect increasing in frequency. This experiment demonstrates the importance of the past history of selection on the nature of genetic variance. General conclusion: Mutation-selection balance (MSB) is appealing as an explanation for the maintenance of genetic variance because it is simple and intuitive: the total mutation rate must be sufficiently high to replenish the variation eliminated by selection. However, MSB models seem unable to adequately explain the coexistence of the observed levels of genetic variance and strength of selection on individual traits. I contend that the failure of MSB models to explain these data is not a failure of MSB theory itself; rather it is the data that has been used to evaluate MSB models that may not be appropriate. It is now clear that there are fewer genetically independent traits than measured phenotypes, and that selection gradients measured for individual traits do not adequately reflect the nature of selection on combinations of traits. In other words, it is not possible to understand the relationship between genetic variance and selection by simply associating median levels of genetic variance and selection collated across studies as levels of genetic variance are likely to be much lower in trait combinations associated with stronger selection. Together, these observations suggest that we should be looking at the distribution of genetic variance in suites of traits and pattern of correlated selection on those same traits if we are to understand MSB.

No description available.