Bayesian analysis of split sex ratios: methods and application to the ant Aphaenogaster rudis

Objective: We develop the use of Bayesian logistic regression models for the analysis of sex ratio data for organisms with variable brood sizes. Background: Ant populations often exhibit ‘split sex ratios’, whereby most colonies produce strongly male-biased or female-biased broods. Furthermore, colony-level sex ratios may depend on brood size or other non-normally distributed covariates. The lack of fit of such data to the assumptions of traditional statistical models can produce inaccurate estimates of population sex ratios. Methods: Using the freeware program OpenBUGS, we demonstrate the Bayesian approach by analysing the effects of food supplements on sex ratio expression in the ant Aphaenogaster rudis. Posterior sampling facilitates model checking and improves the estimation of populationlevel sex ratios for non-standard models. Results: Bayesian logistic regression modelling with a random effects term is effective for analysing ant sex ratio data. The distribution of sex ratios among colonies of A. rudis was bimodal with larger broods tending to be more male-biased. Posterior sampling confirmed that a random-effects model is consistent with the observed split sex ratios. The population-level sex ratio was estimated taking into account that brood size was greater for colonies with male-biased sex ratios. The investment sex ratio was 0.80 (proportion female investment: 95% credibility interval = 0.69 to 0.88), consistent with worker control of the sex ratio. We found no evidence to suggest that experimental food supplements affected brood size or sex ratio expression.