Data on adult female Dall's sheep, Ovis nalli dalli, were used to assess how predation risk factors combine to affect vigilance. An interactive factors hypothesis was proposed, and whether predation risk factors have interactive (or multiplicative) effects on vigilance was tested. Because most studies have implicitly assumed additivity, for illustrative purposes the alternative but less plausible independent factors hypothesis, in which predation risk factors have independent (or additive) effects on vigilance, was also tested. It was predicted that natural selection would favour interactive relationships because, rather than making redundant investments in anti-predator behaviour, animals that are already 'safe enough' can make greater investments in foraging (i.e. an animal in a very large group need not have a strong vigilance response to increasing distance to refuge). Results supported the interactive model and did not support the independent model. Sheep became less vigilant as group size increased, but this relationship became weaker as they got closer to cliffs. Sheep also became more vigilant as distance to cliffs increased, but this relationship became weaker as group size increased. Finally, a posteriori analysis suggested that when sheep were within 20 m from obstructive cover, the interaction between group size and distance to cliffs affected vigilance more strongly than when sheep were further from obstructive cover. Rather than implicitly assuming that predation risk factors have additive effects, as most previous studies have done, generating predictions with the interactive factors hypothesis may be a more realistic approach for understanding vigilance and other anti-predator behaviours. (C) 1997 The Association for the Study of Animal Behaviour.