Aim What factors set species' range edges? One general hypothesis, often attributed to Darwin and MacArthur, is that interspecific competition prevents species from inhabiting the warmest portions along geographic gradients (i.e., low latitudes or low elevations). A prediction arising from this Darwin–MacArthur hypothesis is that lower elevation species are better competitors than related higher elevation species. An alternative prediction is that higher elevation animal taxa will tend to be better competitors because they will tend to be larger (Bergmann's rule). Here, I test these opposing predictions. Location Global. Time period 1971–2019. Major taxa studied Birds, mammals, amphibians, fishes. Methods I conducted a meta‐analysis of studies that measured pairwise behavioural aggression between species‐pairs of closely related animals where the two species inhabit divergent elevational distributions. Results I found that (a) interspecific aggression appears to be a reliable indicator of interspecific competition; (b) elevational position was not consistently linked to interspecific aggression—while lower elevation songbird species in the tropics showed stronger interspecific aggression in response to playback experiments, higher elevation species showed stronger interspecific aggression in direct observations of interspecific aggression across a range of taxa and latitudes; (c) body size was a good predictor of pairwise interspecific aggression and (d) there was limited evidence for Bergmann's rule. Main conclusions My results do not support the longstanding prediction that lower elevation animals are generally better competitors than their higher elevation relatives. Instead, patterns of interspecific aggression are linked to body size, with larger animals showing more aggression towards smaller relatives than vice versa. Hence, a trait—body size—that is idiosyncratically related to elevational position appear to determine the outcome of pairwise behavioural interactions. Last, I consider these results in the context of the hypothesis that behavioural interactions may impact rates of upslope range shifts associated with recent warming.