Identifying robustness in the regulation of collective foraging of ant colonies using an interaction-based model with backward bifurcation

Abstract

Collective behaviors in social insect societies often emerge from simple local rules. However, little is known about how these behaviors are dynamically regulated in response to environmental changes. Here, we use a compartmental modeling approach to identify factors that allow harvester ant colonies to regulate collective foraging activity in response to their environment. We propose a set of di↵erential equations describing the dynamics of: (1) available foragers inside the nest, (2) active foragers outside the nest, and (3) successful returning foragers, to understand how colony-specific parameters, such as baseline number of foragers, interactions among foragers, food discovery rates, successful forager return rates, and foraging duration might influence collective foraging dynamics, while maintaining functional robustness to perturbations. Our analysis indicates that the model can undergo a forward (transcritical) bifurcation or a backward bifurcation depending on colony-specific parameters. In the former case, foraging activity persists when the average number of recruits per successful returning forager is larger than one. In the latter case, the backward bifurcation creates a region of bistability in which the size and fate of foraging activity depends on the distribution of the foraging workforce among the model's compartments. We validate the model with experimental data from harvester ants (Pogonomyrmex barbatus) and perform sensitivity analysis. Our model provides insights on how simple, local interactions can achieve an emergent and robust regulatory system of collective foraging activity in ant colonies.

Modeling ant foraging: A chemotaxis approach with pheromones and trail formation

“…We make no attempt to model the mechanics of recruitment which take place in the nest or near its entrance, by which returning ants recruit other ants, often by antenna contact or by physically pushing them in the direction of the trail. See [17, p.279] for a description of some species' intricate dynamics near the nest, and [47] for a model of these dynamics, with an analysis of the measure in which they may influence foraging.…”

“…The paper [38] contains an overview of the chemical study of pheromones. Concerning the trail-laying behavior of ants, and foraging in general, we refer to [5,8,10,11,12,36,37,42,43,47,49,48,50,55,56,57], and the references therein, although of course many other papers could be cited.…”

Same length, different shapes: ants collectively choose a straight foraging path over a bent one

“…The question arises, therefore, to what extent this system is robust to navigational traps and errors [7,8], particularly how the orientation and the ability to return to the nest are affected by various environmental conditions. It has already been shown that the successful foragers' return rates positively influence the outgoing flow of foragers [9,10] but the link between the nestbound travel durations and the resulting collective decisionmaking is poorly understood. In this paper, we investigate the collective choice of ants in a binary choice set-up in which individuals could follow two equal length paths leading to two identical food sources (figure 1a).…”

Dynamical Models of Task Organization in Social Insect Colonies

“…Differential equations provide a promising tool for analyzing the mechanisms underlying colony-level patterns and dynamics such as division of labor, task allocation, and generate testable predictions about how multiple components of colony organization interact in changing environments. These models have been successfully applied to insect societies in colony population dynamics (e.g., [69]), colony organization (e.g., [75,52]), foraging (e.g., [109,114,124]), colony metabolic scaling (e.g., [54]), optimal decision-making in social insect colonies (e.g., [81]) and social parasitism (e.g., [70]). The power of these models lies in their simple mathematical formalism for describing how different interested components interact and change through time.…”