When defending resources, animals need to reliably detect and identify potential competitors. Animals that live at high population densities would be expected to be efficient in this aspect of resource defence since the time lost in false alarms could be substantial and the failure of identifying a competitor could be very costly. How does an animal decide whether another animal is or is not a threat to a resource or a territory? Fiddler crabs [Uca vomeris (McNeill)] operate from burrows that they guard and defend vigorously against other crabs. The crabs live in dense populations, with many animals inhabiting one square metre of mudflat. We describe here the behavioural responses of foraging crabs to repeated presentations of small crab-like dummies approaching their burrows. We explore the relationship between the probability and the timing of burrow defence responses, the crab's behavioural state, and the visual appearance and direction of approach of the dummies. We find that the probability of response of resident crabs is independent of the relative position of crab and dummy but is strongly affected by the dummy's position and movement direction relative to the crab's burrow. The critical stimuli are the dummy's distance from the crab's burrow and whether the dummy is moving towards the burrow or not. The response distance (dummy-burrow distance) increases with the crab's own distance from the burrow, indicating that the crabs modify their assessment of threat depending on their own distance away from the burrow. Differences in dummy size and brightness do not affect the probability or the timing of the response. We discuss these results in the context of fiddler crab social life and, in a companion paper, identify the visual and non-visual cues involved in burrow defence.