Stochastic modeling of long-legged ant A. gracilipes locomotion in laboratory experiments

TL;DR

A combination of active Brownian and run-and-tumble models reproduces the trajectory statistics observed in experiments, both qualitatively and quantitatively, and finds good agreement between analytical predictions and quantities empirically measured from the trajectories.

Abstract

Stochastic modeling of movement behavior provides a valuable way to understand how complex motion can be generated from relatively simple building blocks. Ants demonstrate sophisticated social behavior ranging from foraging to nest relocation; while emphasis is often placed on the communication methods used to synchronize individuals, the movement paradigms of those individuals are of tantamount importance. Here, we apply a stochastic modeling approach to better understand the movement of isolated long-legged ant (A. gracilipes) specimens, informed by extensive laboratory tracking experiments. We find that a combination of active Brownian and run-and-tumble models reproduces the trajectory statistics observed in experiments, both qualitatively and quantitatively. We identify reproducible probability distributions for the turn angles, run times, and waiting times across specimens, and find good agreement between analytical predictions and quantities empirically measured from the trajectories. Having such a model allows for a better understanding and predictions of movement ecology from both simulations and analytics, and even can give insight into the underlying generative mechanisms of motion and the ants' sensory systems.

Figures (7)

• Figure 1: Overview of experiment to extract ant trajectories in a confined arena. Specimens are placed alone in an acrylic enclosure and recorded for 20 minutes. Ant position is tracked from videos using a neural network tracking approach (SLEAP), giving spatial trajectories.
• Figure 2: Trajectory analysis workflow. Original sampled trajectories are used to compute trajectory statistics like occupation maps and mean squared displacement, as well as to identify points when the ant changes direction and/or stops moving, generating a discretized trajectory. This allows for the extraction of the times spent moving in a straight line, $\tau_i$, the angle changes between these segments, $\Delta \theta_i$, the time spent waiting before each reorientation, $\gamma_i$, and the angle drift during each straight run, $D_{r,i}$. These values are used to derive statistics about the original trajectory using a Fokker-Planck equation, and to simulate new ant-like trajectories using a Langevin equation.
• Figure 3: Spatial and phase space occupation maps for ant motion. Average amount of time spent in each region of the experimental arena (left) and average amount of time spent in each region with a particular orientation (right). For phase space map, orange coloring represents time spent moving either up or down, and blue represents moving either left or right.
• Figure 4: Mean squared displacement (MSD) for ant motion. Blue, orange, and grey shading indicates regions where the displacement scales linearly with time (ballistic motion), with the square root of time (Brownian motion), and independently of time (finite-size effects). Regions are drawn as rough guides, not based on specific quantifications. Faint curves are the MSD for each individual trial; solid black line represents the pooled statistics for all trials, with standard deviations shown as error bars.
• Figure 5: Turn angle, run time, and wait time distributions for discretized ant motion. PDFs are created using pooled data from all ant trials. A single, representative choice of discretization parameters ($\theta_c = 45$°, $v_c = 5$mm/s) is shown here; for comparison with other parameter choices, see \ref{['fig:S3']}. Green dashed lines represent the median fit --- von Mises, exponential, and power law, respectively --- across the individual ant trials (in contrast to the pooled data shown in the curves with markers). Dashed vertical lines indicate the minimum value including in fitting.