The accuracy of Buffon's needle: a rule of thumb used by ants to estimate area

Colonies of the ant Leptothorax albipennis naturally inhabit flat rock crev ices. Scouts can determine, before initiating an emigration, if a nest has sufficient area to house their colony. They do so with a rule of thumb: the Buffon's needle algorithm. Based on a derivation from the classical statis tical geometry of Comte George de Buffon in the 18th century, it can be sho wn that it is possible to estimate the area of a plane from the frequency o f intersections between two sets of randomly scattered lines of known lengt hs. Our earlier work has shown that individual ants use this Buffon's needl e algorithm by laying individual-specific trail pheromones on a first visit to a potential nest site and by assessing the frequency at which they inte rsect that path on a second visit. Nest area would be inversely proportiona l to the intersection frequency. The simplest procedure would be for indivi dual ants to keep their first-visit path-length constant regardless of the size of the nest they are visiting. Here we show, for the first time, that this is the case. We also determine the potential quality of information th at individual ants might have at their disposal from their own path-laying and path-crossing activities. Hence, we can determine the potential accurac y of nest area estimation by individual ants. Our findings suggest that ant s using the Buffon's needle rule of thumb might obtain remarkably accurate assessments of nest area.