ϵ-Machine and ϵ-Transducer Analysis of Functional Differentiation in Ant Collectives

We investigate functional behavioural differentiation in genetically homogeneous animal collectives using the ϵ-machine and ϵ-transducer frameworks from symbolic dynamics. Long-term tracking of unmarked individuals in colonies of the clonally reproducing ant Pristomyrmex punctatus reveals two distinct movement modes-clustering within the group and solitary exploration outside it. Reconstructed individual ϵ-transducers expose a sharp asymmetry in computational structure between these modes: solitary explorers are described by a deterministic machine, whereas clustering ants require stochastic machines to capture their complex patterns of micro-movement. A population-level (universal) ϵ-transducer, inferred from pooled data, captures the shared behavioural repertoire across all individuals. Individual differences are parsimoniously explained as biased and partial traversals of a common state space rather than as distinct generative programs. We compare three predictive models: the ϵ-machine, which relies solely on an ant's own output history; a memoryful ϵ-transducer, which additionally conditions on changes in the local neighbour count as social input; and a memoryless ϵ-transducer, which uses this social input alone. The memoryful transducer matches the ϵ-machine in prediction accuracy despite requiring ten times as many states, while the memoryless transducer performs substantially worse. This shows that an ant's own behavioural history is the essential predictor of its future movement at the temporal resolution examined here. We argue, however, that this predictive redundancy does not entail the causal irrelevance of social input: the behavioural history itself accumulates the trace of past social encounters so that any role differentiation established through prior interactions is already inscribed in the output sequence that the ϵ-machine reads, and mode transitions-the moments at which social input most plausibly exerts causal influence-are rare events that contribute negligibly to aggregate one-step accuracy. Agent-based simulations driven by the universal ϵ-transducer reproduce basic motion statistics and transient aggregations but fail to generate the stable macroscopic clusters observed experimentally, pointing to the role of additional mechanisms such as longer-term memory or stigmergic coupling. Nevertheless, ants do respond to their social environment: an explorer encountering an increase in neighbours is absorbed into the cluster and ceases directed movement. Together, our results suggest a two-level organisation: within each behavioural mode, individual dynamics are self-sufficient for one-step prediction, while transitions between modes are environmentally triggered and represent switches between fundamentally different classes of dynamical organisation.