Self-organised criticality in the evolution of a thermodynamic model of rodent thermoregulatory huddling

A thermodynamic model of thermoregulatory huddling interactions between endotherms is developed. The model is presented as a Monte Carlo algorithm in which animals are iteratively exchanged between groups, with a probability of exchanging groups defined in terms of the temperature of the environment and the body temperatures of the animals. The temperature-dependent exchange of animals between groups is shown to reproduce a second-order critical phase transition, i.e., a smooth switch to huddling when the environment gets colder, as measured in recent experiments. A peak in the rate at which group sizes change, referred to as pup flow, is predicted at the critical temperature of the phase transition, consistent with a thermodynamic description of huddling, and with a description of the huddle as a self-organising system. The model was subjected to a simple evolutionary procedure, by iteratively substituting the physiologies of individuals that fail to balance the costs of thermoregulation (by huddling in groups) with the costs of thermogenesis (by contributing heat). The resulting tension between cooperative and competitive interactions was found to generate a phenomenon called self-organised criticality, as evidenced by the emergence of avalanches in fitness that propagate across many generations. The emergence of avalanches reveals how huddling can introduce correlations in fitness between individuals and thereby constrain evolutionary dynamics. Finally, a full agent-based model of huddling interactions is also shown to generate criticality when subjected to the same evolutionary pressures. The agent-based model is related to the Monte Carlo model in the way that a Vicsek model is related to an Ising model in statistical physics. Huddling therefore presents an opportunity to use thermodynamic theory to study an emergent adaptive animal behaviour. In more general terms, huddling is proposed as an ideal system for investigating the interaction between self-organisation and natural selection empirically.Author summary: Huddling is an adaptive behavior that emerges from simple interactions between animals. Huddling is a particularly important self-organising system because the behavior that emerges at the level of the group directly impacts the fitness of the individual. The huddle insulates the group, allowing pups to thermoregulate at a reduced metabolic cost, however a huddle can only self-organise if pups in turn contribute heat. Contributing too much heat is costly but contributing too little compromises the ability of the huddle to self-organise. To investigate how the resulting tension between co-operation and competition in the huddle might affect natural selection, litters of simulated rodents were subjected to a simple evolutionary process. After interacting with its littermates, the individual that incurred the greatest metabolic cost for thermoregulation was iteratively replaced by another with random thermal properties. Simulations resulted in the emergence of a phenomenon called self-organised criticality. Criticality is a hallmark of complex systems, and is evidenced here by the emergence of a power-law distribution of thermal properties in the evolving composition of the group. The model therefore reveals how complexity can emerge in a well-defined biological system (thermoregulation), where experiments can be designed to investigate the interaction between self-organisation and natural selection.