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Collective vigilance is the surveillance supplied by a group of animals, for example when attention by any member can reveal an approaching predator. Group coverage and each individual's time spent vigilant are different quantities. Several members can jointly provide substantial coverage even if each watches for only part of the time.

An original independent-attention model makes that distinction precise. Suppose each of $n$ individuals is vigilant at a randomly chosen instant with probability $p$, independently of the others. The probability that at least one is vigilant isFor $p=0.2$, one individual gives0.2 coverage, while five give $1-0.8^5=0.67232$. The model specifies attention, not guaranteed detection: visibility, sensory ability and information transfer still matter.

Independence is a substantive assumption. If every individual watches during exactly the same20percent of instants, coverage remains0.2 however large the group. In an ideal five-member schedule with perfectly nonoverlapping20-percent attention intervals, coverage can instead be one. Thus group size and individual attention fractions alone do not determine the collective result.

A field study of Dolichotis patagonum found that larger communal warrens had more adult attendance and greater total vigilance despite less sitting-alert time per pair. The reported portion of the day with at least one vigilant pair reached90percent at larger crèches. This supplied an observational example of individual and group measures changing in different directions.^[ref]

The field comparison does not randomize warren membership or establish that the independent-attention model describes those animals. Simultaneous behavioral observations and records of predation risk can test which temporal correlations and detection mechanisms actually produce group coverage.

David W. Macdonald is a researcher in wildlife conservation and animal behaviour. His institutional WildCRU profile identifies David Macdonald with publications using the D. W. Macdonald byline. His research includes the 1992 study of mara communal breeding with Andrew B. Taber.^[ref][ref]

An illuminating result concerned collective vigilance. Larger breeding groups could have more total coverage even though each pair spent less time sitting alert. The group-level readout was whether at least one pair was vigilant, a different variable from the alert fraction of a particular pair.^[ref]

A toy probability model explains how this can happen. If $n$ pairs each have alert probability $p$ at a sampled instant, and their alert states are independent events, thenTwo pairs with $p=0.40$ give $1-0.60^2=0.64$. Six pairs with $p=0.20$ give $1-0.80^6\approx 0.738$. In this constructed model, individual alert probability falls while group coverage increases. These values are not the study's data.

Independence is essential to that calculation. If all pairs became alert in perfect synchrony, group coverage would equal $p$, regardless of how many pairs were present. Field measurements of timing and coordination are therefore needed to choose between such models.

The mara work illustrates how an ecological explanation can connect individual behavior to an emergent group outcome while keeping their measurement definitions distinct.