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arXiv · 2610.24865

A mechanism for collective foraging: percolating recruitment cascades coupled to a maximum-entropy

Galen J. Wilkerson
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Abstract

Foraging recruitment is a contagion: an agent that finds a resource triggers a linear-threshold cascade, the model built for rumour and adoption spread on social networks, now embedded in space. Because activation is degree-normalized, the same rule that spreads the cascade also stifles it as neighbourhoods crowd, so the swarm aggregates on a resource and then releases to explore again. The cascade runs on the communication network, but acting on it moves agents in physical space, and that motion rewires the network: network and space are one coupled system, and this feedback, not any tuning, makes the coordination self-limiting. Because recruitment chains along the graph rather than reaching near neighbours alone, whether a discovery stays local or spans the swarm is a question of percolation. The swarm holds itself in a cascade window that is locally near-critical though globally subcritical, a self-organized, self-limiting drive-release cycle, sandpile-like but non-conservative. Nothing is tuned, yet behaviours that foraging biology documents separately emerge together: recruitment to discoveries, marginal-value patch-leaving, and Levy search with a switch to local exploitation. These follow from one least-committal principle, the resource field and the search both as maximum entropy, with Levy search matched to the field's sparsity and recruitment to its clustering, so active-matter order and optimal foraging appear as one system seen in two domains. The gains are real but conditional: up to 7.6x the harvest of solitary search when resources are sparse and clustered, shrinking to nothing when search is already easy. That sparse, clustered field is also the generic one, because resources almost inevitably aggregate, so one untuned rule should recur widely.

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Galen J. Wilkerson. 2026-10-20. A mechanism for collective foraging: percolating recruitment cascades coupled to a maximum-entropy. https://arxiv.org/abs/2610.24865

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