Redefining Fitness: Inference, Information and Phase Transitions in Evolutionary Dynamics
Evolution is the adaptation of populations to their environment expressed through the concept of fitness. Darwin did not define fitness but described evolution as the higher prevalence of lineages with advantages in survival and reproduction in changing environments, an implicitly statistical and relational notion. As evolutionary dynamics became more quantitative, however, fitness acquired a narrower meaning of relative reproductive success. Crucially, this narrower definition suffers from three fundamental difficulties, known as the circularity, mismatch, and prediction problems. We show that interpreting evolutionary dynamics in terms of inference resolves these three problems while also creating new productive analytical tools. This shift redefines fitness via a Bayesian likelihood, a predictive probability of the environment specific to each type. We show that averaging the growth rate over environmental histories connects selection to information as types with better environmental models are amplified. It follows that long-run evolutionary dynamics maximizes the mutual information between population structure and environmental statistics, establishing information maximization as the governing principle of natural selection. We illustrate this approach in several population dynamics problems including task switching, evolutionary games, and selection in group-structured populations. In each case, we derive phase diagrams as functions of environmental statistics and Hamilton-type rules for the emergence of cooperation, while also demonstrating the generality of the approach.