Fitness flux and ubiquity of adaptive evolution

Natural selection favors fitter variants in a population, but actual evolutionary processes may decrease fitness by mutations and genetic drift. How is the stochastic evolution of molecular biological systems shaped by natural selection? Here, we derive a theorem on the fitness flux in a population, defined as the selective effect of its genotype frequency changes. The fitness-flux theorem generalizes Fisher's fundamental theorem of natural selection to evolutionary processes including mutations, genetic drift, and time-dependent selection. It shows that a generic state of populations is adaptive evolution: there is a positive fitness flux resulting from a surplus of beneficial over deleterious changes. In particular, stationary nonequilibrium evolution processes are predicted to be adaptive. Under specific nonstationary conditions, notably during a decrease in population size, the average fitness flux can become negative. We show that these predictions are in accordance with experiments in bacteria and bacteriophages and with genomic data in Drosophila. Our analysis establishes fitness flux as a universal measure of adaptation in molecular evolution.