Empirical comparison of G matrix test statistics: finding biologically relevant change

A central assumption of quantitative genetic theory is that the breeder's equation (R=GP(-1)S) accurately predicts the evolutionary response to selection. Recent studies highlight the fact that the additive genetic variance-covariance matrix (G) may change over time, rendering the breeder's equation incapable of predicting evolutionary change over more than a few generations. Although some consensus on whether G changes over time has been reached, multiple, often-incompatible methods for comparing G matrices are currently used. A major challenge of G matrix comparison is determining the biological relevance of observed change. Here, we develop a "selection skewers"G matrix comparison statistic that uses the breeder's equation to compare the response to selection given two G matrices while holding selection intensity constant. We present a bootstrap algorithm that determines the significance of G matrix differences using the selection skewers method, random skewers, Mantel's and Bartlett's tests, and eigenanalysis. We then compare these methods by applying the bootstrap to a dataset of laboratory populations of Tribolium castaneum. We find that the results of matrix comparison statistics are inconsistent based on differing a priori goals of each test, and that the selection skewers method is useful for identifying biologically relevant G matrix differences.