Abstract
Genetic variation plays a fundamental role in all models of evolution. For phenotypes composed of multiple quantitative traits, genetic variation is best quantified as additive genetic variances and covariances, as these values determine the rate and trajectory of evolution. Additive genetic variances and covariances are often summarized conveniently in the G-matrix, which has additive genetic variances for each trait on the diagonal and additive genetic covariances as its off-diagonal elements. The evolution of the G-matrix is an interesting topic in its own right, because the processes that affect trait means also affect the distribution of standing genetic variation, which, in turn, feeds back to affect the rate of change of trait means. Theoretical studies of the G-matrix have profitably employed simulation-based models because the topic is often too complex to yield meaningful analytical results. Here, we present a series of G-matrix simulation software packages, which have emerged from about 15 years of research on this topic. These simulation models are useful for research and for building intuition regarding the evolution of the G-matrix under a wide variety of circumstances. A tutorial and source code also provide a foundation upon which future models can be built. These tools will be useful to students as well as researchers.