  We studied the formation of trail patterns by Argentine ants exploring an
empty arena. Using a novel imaging and analysis technique we estimated
pheromone concentrations at all spatial positions in the experimental arena and
at different times. Then we derived the response function of individual ants to
pheromone concentrations by looking at correlations between concentrations and
changes in speed or direction of the ants. Ants were found to turn in response
to local pheromone concentrations, while their speed was largely unaffected by
these concentrations. Ants did not integrate pheromone concentrations over
time, with the concentration of pheromone in a 1 cm radius in front of the ant
determining the turning angle. The response to pheromone was found to follow a
Weber's Law, such that the difference between quantities of pheromone on the
two sides of the ant divided by their sum determines the magnitude of the
turning angle. This proportional response is in apparent contradiction with the
well-established non-linear choice function used in the literature to model the
results of binary bridge experiments in ant colonies (Deneubourg et al. 1990).
However, agent based simulations implementing the Weber's Law response function
led to the formation of trails and reproduced results reported in the
literature. We show analytically that a sigmoidal response, analogous to that
in the classical Deneubourg model for collective decision making, can be
derived from the individual Weber-type response to pheromone concentrations
that we have established in our experiments when directional noise around the
preferred direction of movement of the ants is assumed.
