In gregarious species, rates of foraging behaviour are often positively related to group size while there is simultaneously a negative relation between group size and vigilance. Although the mechanisms underlying these behavioural patterns are still incompletely understood, decreased predation risk or increased foraging competition in larger groups have been put forward as two possible explanations. Since most empirical tests of these two hypotheses have used manipulative experiments, they have mainly been limited to small-bodied species or to animals in captivity. Here we suggest a time-budget model to test for the causal effects of predation risk and foraging competition that does not necessitate manipulative approaches. We used this method on two species of gregarious antelope, blesbok (Damaliscus pygargus phillipsi) and impala (Aepyceros melampus). We suggest that increased foraging competition in large groups drives the negative relationship between vigilance and group size in these species. This study shows that observational data can be used to test explicit hypotheses on species that are logistically unsuitable for manipulative experiments, and also render support for hypotheses suggesting that factors unrelated to predation risk are involved in shaping the differences in vigilance rates over different group sizes in gregarious species.