Individual Rules for Trail Pattern Formation in Argentine Ants (Linepithema humile)

Abstract

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.

A common rule for decision making in animal collectives across species

“…Ants′ choices to turn left and right have been recorded by Perna et al (24), and we found that they have choice probabilities well described by Eq. 3, except that experimental probabilities do not reach values as close to 0 or 1 as the theory.…”

“…For a high number of animals, both theory and data show Weber behavior, corresponding in this logarithmic plot to a straight line with slope −1 (Fig. 3D, black line) (24). Interestingly, for low numbers of animals, the theoretical prediction of a deviation from Weber behavior corresponds to the data.…”

“…This line obeys for high number of animals that n y ≈ k n x . This is a Weber law (23,24), according to which the justnoticeable difference between two groups is proportional to the total number of individuals. Indeed, if we substitute n y ≈ k n x into ΔN=N ≡ ðn x − n y Þ=ðn x + n y Þ we obtain a constant of value ðk − 1Þ=ðk + 1Þ.…”

Adversity magnifies the importance of social information in decision-making

“…A simple and widespread decision rule is to choose options according to the ratio of predicted qualities [28,30,[32][33][34][35][36][37][38][39][40][41]. Then, the probability of choosing option y (P y ) is a monotonically increasing function of the ratio of the estimated probabilities,…”

“…Examples range from bacteria to humans, including rules such as Weber's Law (which depends on the relative difference between qualities (Q y 2 Q x )/(Q y þ Q x )), probability matching (which depends on Q y /(Q x þ Q y )), direct ratio rules (Q y /Q x ) and others [28,30,[32][33][34][35][36][37][38][39][40][41]. All these rules share the condition that…”