Conjugate Natural Selection

Evolution describes how distributions change. Specifically, evolution provides a model for how a population's distribution of traits or strategies (hereafter hypotheses) changes over time as an environment modulates reproduction rates (i.e., of individuals or of hypotheses; Lloyd, 2020): Hypotheses that have higher fitness are "selected" by the environment and, in expectation, become more popular with time. The replicator equation is a formal, analytic model of evolution and is indispensable to biology (Sinervo and Calsbeek, 2006; Queller, 2017). In the replicator equation, the absolute fitness (in this paper, the negative loss L) of hypotheses h H is identified with its rate of replication: exponential growth (or decline) in a population where different hypotheses compete for relative frequency ρ(h) [0, 1]. For probability distributions over hypothesis space H, this equation induces replicator dynamics, selecting hypotheses with lower than average loss.