Knowledge of the genetic and environmental influences on a character is pivotal for understanding evolutionary changes in quantitative traits in natural populations. Dominance and aggression are ubiquitous traits that are selectively advantageous in many animal societies and have the potential to impact the evolutionary trajectory of animal populations. Here we provide age- and sex-specific estimates of additive genetic and environmental components of variance for dominance rank and aggression rate in a free-living, human-habituated bird population subject to natural selection. We use a long-term data set on individually marked greylag geese (Anser anser) and show that phenotypic variation in dominance-related behaviours contains significant additive genetic variance, parental effects and permanent environment effects. The relative importance of these variance components varied between age and sex classes, whereby the most pronounced differences concerned non-genetic components. In particular, parental effects were larger in juveniles of both sexes than in adults. In paired adults, the partner's identity had a larger influence on male dominance rank and aggression rate than in females. In sex- and age-specific estimates, heritabilities did not differ significantly between age and sex classes. Adult dominance rank was only weakly genetically correlated between the sexes, leading to considerably higher heritabilities in sex-specific estimates than across sexes. We discuss these patterns in relation to selection acting on dominance rank and aggression in different life history stages and sexes and suggest that different adaptive optima could be a mechanism for maintaining genetic variation in dominance-related traits in free-living animal populations.