Using average autonomy to test whether behavioral syndromes constrain evolution

Genetic correlations between behaviors underlying a behavioral syndrome may constrain the capacity of a population to respond to selection on these behaviors. Average autonomy quantifies the extent in which estimated genetic (co)variances constrain the rate of evolutionary change of behavioral traits forming a syndrome when these traits are under selections in all possible directions of multivariate trait-space. However, it is not clear whether a calculated average autonomy value of an observed syndrome constitutes a significant evolutionary constraint or not. I here outline an approach for testing evolutionary constraint in a syndrome, which is based on comparing the observed genetic (co)variance structure to the one where the genetic covariances are assumed to be zero and taking onboard the uncertainty in the (co)variances between behaviors into the calculations of average autonomy. The approach can be implemented in the context of parametric bootstrap or Bayesian statistics, and I provide a worked example of the latter. I further highlight that when genetic (co)variances are unattainable, the between-individual (co)variances act as an interesting proxy, which is within reach for many behavioral studies. I provide R code for all calculations.