A Self-Organising Model of Thermoregulatory Huddling

Endotherms such as rats and mice huddle together to keep warm. The huddle is considered to be an example of a self-organising system, because complex properties of the collective group behaviour are thought to emerge spontaneously through simple interactions between individuals. Groups of rodent pups display two such emergent properties. First, huddling undergoes a ‘phase transition’, such that pups start to aggregate rapidly as the temperature of the environment falls below a critical temperature. Second, the huddle maintains a constant ‘pup flow’, where cooler pups at the periphery continually displace warmer pups at the centre. We set out to test whether these complex group behaviours can emerge spontaneously from local interactions between individuals. We designed a model using a minimal set of assumptions about how individual pups interact, by simply turning towards heat sources, and show in computer simulations that the model reproduces the first emergent property—the phase transition. However, this minimal model tends to produce an unnatural behaviour where several smaller aggregates emerge rather than one large huddle. We found that an extension of the minimal model to include heat exchange between pups allows the group to maintain one large huddle but eradicates the phase transition, whereas inclusion of an additional homeostatic term recovers the phase transition for large huddles. As an unanticipated consequence, the extended model also naturally gave rise to the second observed emergent property—a continuous pup flow. The model therefore serves as a minimal description of huddling as a self-organising system, and as an existence proof that group-level huddling dynamics emerge spontaneously through simple interactions between individuals. We derive a specific testable prediction: Increasing the capacity of the individual to generate or conserve heat will increase the range of ambient temperatures over which adaptive thermoregulatory huddling will emerge.Author Summary: Maintaining a constant body temperature is crucial to the survival of many species, including mammals such as rodents. Temperature regulation can be achieved via internal physiological processes and by seeking warmth when cold or cold when hot, as, for example, when young rats and mice exchange body heat by huddling together. Huddling is considered by many to be an important example of self-organisation, where a complex and adaptive group behaviour emerges from simple interactions between individuals behaving without plan or instruction. However, it is difficult to rule out the possibility that a complex group behaviour is the result of equally complex individual behaviours. Our approach is therefore to determine the simplest set of rules of interaction from which group-level huddling can emerge. Recent experiments have shown that huddling switches on at low temperatures, and that individuals continually exchange positions from the cool periphery of the huddle to its warm core. We show in computer simulations that both group behaviours emerge spontaneously when individuals simply turn towards sources of preferred temperature whilst continually generating, losing, and exchanging heat. A mathematical model of the simulation results suggests that individuals together behave as a single organism that continually adapts its exposed surface area to regulate its temperature in a way that no individual can. We therefore suggest that thermoregulatory huddling is a true self-organising system, and we derive from the model specific predictions that will enable future experiments to test this theory.