= Collective vigilance
<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 is
$$
V_n=1-(1-p)^n.
$$
For $p=0.2$, 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.<Communal breeding in the mara, Dolichotis patagonum by A. B. Taber and D. W. Macdonald>[Primary Abstract: adult attendance, sitting-alert behavior and collective coverage]{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.
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