A bootstrap comparison of genetic covariance matrices

An important problem in evolutionary biology is how population bottlenecks affect additive genetic variance (V-A). When only additive effects are present, a decrease in V-A is predicted, whereas with many forms of nonadditive interactions, an increase is predicted. We present an analysis of the changes in variance that occur as a result of a bottleneck in a population of the red flour beetle Tribolium castaneum. In this experiment, the additive genetic covariance matrix for four traits in two sexes was measured in the ancestral population. The population then went through a bottleneck and the genetic covariance matrix was again measured. These data were analyzed by first examining the univariate estimates for V-A and, second, examining the covariance matrices. For the univariate measures, the statistic we used was the change in V-A. For the multivariate comparisons, we used three measures: the difference in rank (the difference in the number of positive eigenvalues) to test changes in the number of heritable traits, a multivariate equivalent of Bartlett's statistic to test changes in the size of the matrices, and a modification of Mantel's correlation to test for changes in the correlation structure of the matrices. Because the distribution of all of these measures is complex and dependent on the specifics of the particular matrices being compared, we chose to use a bootstrap analysis to test for significance. For females, we found that, following the population bottleneck, V-A was significantly decreased and that the correlation structure of the matrix was significantly changed. For males, we found that, following the population bottleneck, V-A significantly increased but that the correlation structure was unchanged.