Collective Foraging and Behavioural Syndromes in Ants: First-Passage Statistics with Heterogeneous Walkers on a Honeycomb Lattice

TL;DR

This study models ant foraging behavior using a correlated random walk on a honeycomb lattice, linking individual movement heterogeneity to collective efficiency through first-passage time analysis, supported by experimental data.

Contribution

It introduces a novel theoretical framework combining heterogeneous random walks and first-passage processes to analyze ant foraging dynamics.

Findings

Heterogeneous movement strategies influence foraging success.

Ants may use both strict central place foraging and patch revisiting.

Model aligns with empirical observations of ant behavior.

Abstract

Behavioral heterogeneities in animals, also known as syndromes, play a crucial role in understanding how natural populations flexibly adapt to environmental changes. In ant species like \textit{Aphaenogaster senilis}, two key roles in collective foraging are commonly recognised: scouts, who discover food patches, and recruits, who exploit these patches and transport food back to the nest. These roles involve distinct movement patterns and exploratory behaviours. In this chapter, we develop a correlated random walk model on a bounded honeycomb lattice to interpret and replicate empirical observations of foraging ants in an enclosed arena with honeycomb tiling. We do so by extending the theory of first-passage processes for $\mathcal{N}$ random walkers when individuals belong to a heterogeneous population. We apply this theory to examine how individual behavioural heterogeneity in ants affects collective foraging efficiency, focusing on first-passage time statistics for nest-to-patch and patch-to-patch movements. With the combined use of the mathematical model and the controlled experimental setup we evaluate (i) the impact of distinct movement strategies by scouts and recruits on finding food items and (ii) whether ants practice strict central place foraging or utilise previously discovered patches as starting points for further exploration.