This case study illustrates three key themes in current evolutionary quantitative genetics: the role of genetic associations in the evolutionary dynamics of selection, the insights gained from multivariate models, and the utility of a Bayesian Markov Chain Monte Carlo (MCMC) approach. This chapter presents a multivariate analysis of sexually selected weaponry, antlers in red deer, using data from a long-term study of a wild population of red deer. Using a Bayesian MCMC framework, the relationship between a component of fitness, male annual breeding success (ABS), and two antler traits (size (mass) and shape (the number of points, or form)) is estimated. Using a multivariate animal model to dissect these relationships revealed substantial positive environmental associations between each trait and ABS, presumably reflecting condition-dependence of both antler growth and the traits determining mating success. In contrast, a lack of genetic covariance between either trait and ABS suggested that neither would be predicted to evolve further via sexual selection. Furthermore, a significant difference between the genetic and the environmental multivariate gradients between antler form and fitness indicated a lack of causal effects on fitness. The analyses reveal a complex set of relationships not apparent at either a phenotypic or a univariate level, and suggest constraints to evolution despite the presence of genetic variance in the focal fitness component. This chapter also discusses advantages and problems associated with using multivariate quantitative genetic analyses to explore the process of selection in wild populations.
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