A Magnetic-like Model for Chemotactic Navigation in Ants

TL;DR

This study frames ant chemotaxis along pheromone trails as a magnetic-like navigation problem and develops an Inertial Spin Model (ISM) that couples velocity to the chemical gradient via ferromagnetic-like and DM-like interactions. Under near-trail approximations, the model reduces to a stochastic damped oscillator for the orientation, yielding an analytical form for the perpendicular velocity correlations $C_{v_y}(t)$ that predict underdamped oscillations with parameters $\\gamma$ and $\\omega_0$. Experimental trajectories (156 paths) following an oval pheromone trail are well-described by the model, with fits showing robust oscillatory behavior and parameter trends: $\\gamma$ is largely independent of mean speed while $\\omega_0^2+\\gamma^2$ scales with speed as $D p v_0/\\chi$. These results demonstrate that a physics-based, magnet-like framework can capture essential mechanistic features of chemotactic navigation in ants and offer a basis for exploring the interplay of gradient-driven torques and inertia in biological motion.

Abstract

We propose a physical framework for ant navigation of chemical trails. For this, we use controlled experiments in which individuals follow narrow pheromone trails, for which ants display oscillatory motion, as previously reported in the literature. We model this behavior by treating chemotaxis as an effective magnetic interaction between the ant velocity and the local chemical gradient. Under suitable approximations, the model yields an analytical expression for the velocity correlations in the direction perpendicular to the trail, predicting an underdamped oscillatory decay. This theoretical prediction is in qualitative agreement with our experimental measurements, indicating that the model captures the essential dynamical features of ant trail following. We fit the model parameters to individual trajectories in order to assess the consistency of the underlying assumptions, finding the same parameter relationship in both theory and experiment. Our results contribute to the characterization of chemotactic navigation in ants and illustrate how physical modeling can provide mechanistic insights into complex biological dynamics.

Figures (5)

• Figure 1: a) Experimental plate in the frame of a given experiment. b) Heatmap of ant occupancy in the arena, previous to data processing, including data from the $20$ daily experiments described in the main text. c) Trajectories of three different ants in the region near the pheromone trail, highlighted in a white rectangle in panel b). The horizontal gray line indicates the position of the center of the pheromone trail. d) Velocity signal of the three trajectories plotted in panel c), showing separately the velocity components along the trail direction ($v_x$) in dashed lines and the perpendicular direction ($v_y$) in dotted lines. In solid lines, we plot the total speed $v=\vert \vec{v} \vert$. e) Velocity component $v_y$ distribution (dashed purple line) after integrating all $156$ trajectories and individual mean velocity $\left< v_y\right>_i$ distribution (solid pink line). The inset shows a zoom of the central region. f) Velocity component $v_x$ (dashed light-blue line) and speed $v$ (dashed orange line) distribution after integrating all $156$ trajectories and individual mean velocity $\left< v_x\right>_i$ (yellow solid line) and individual mean speed $\left< v \right>$ (purple solid line) distributions.
• Figure 2: a) Velocity correlations in the y-direction (perpendicular to the trail) for the $156$ experimental trajectories. Lines are shown up to half the duration of each trajectory. The three experiments shown in Figure \ref{['fig:ex_traj']} have been highlighted in light-blue, orange, and yellow colors. b) and c) Probability density distribution of the obtained parameters $\gamma$ (b) and $\omega_0$ (c) from individually fitting each of the $156$ trajectories. The colored bars highlight the parameter values corresponding to the fits in d). d) Velocity correlations of the highlighted experiments (in solid lines) and the best fit for each of them according to equation \ref{['eq:corr']} (in dashed lines). e) and f) The grey points represent the fitted values of $\gamma$ (e), and $\omega_0^2 +\gamma^2$ (f) as a function of the characteristic mean speed $\left<v\right>$ of each trajectory. The purple squared points correspond to an average of $20$ points, grouping them according to their $\left< v \right>$ value. The purple line corresponds to the best fit of the purple squared points to $\gamma=\eta/2\chi$ in (e) and to $\omega_0^2+\gamma^2=Dpv_0/\chi$ in (f), where $\left<v\right>$ takes the role of $v_0$. The value $r$ corresponds to the correlation coefficient of the gray points.
• Figure B.1: Example frame of the the trajectories detected during processing. All detected ants are boxed in red, with their mid point plotted in light green, which is the $(x,y)$ coordinates of our trails. In the plot we also present the full trajectories of the ants present in the frame.
• Figure E.1: a) Histogram of the adjusted $R^2_a$. b) Histogram of the Root Mean Squared Error. In both cases, the dotted line represents the median of the distribution. b) Fitted damping parameter $\gamma$ as a function of the trajectory length $t$. c) Fitted frequency $\omega_0$ as a function of the trajectory length $t$. The value $r$ represents the correlation coefficient.
• Figure F.1: Fitted values of $\omega_0$ as a function of the characteristic mean speed $\left<v\right>$ of each trajectory. The purple squared points correspond to an average of the $20$ points, grouping them according to their $\left< v \right>$ value. The value $r$ represents the correlation coefficient.