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 fitnessflux 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. A daptive processes have taken center stage in molecular evolutionary biology. Deep sequencing of populations opens unprecedented opportunities to trace the genomic basis of adaptation in population-genetic studies within and across species as well as in time series of evolution experiments. Various methods are used to infer natural selection from such data; however, their results lack a common gauge and are sometimes difficult to compare. This paper develops the concept of fitness flux in a population as a generic measure of adaptation applicable to molecular data. Whereas fitness characterizes the state of a population at a given point in time, fitness flux can be accumulated in a population's history over a period (a precise definition of this quantity will be given below). Fitness flux, not fitness, turns out to be the right variable to show that adaptive evolution is a generic state of natural populations. The notion of fitness flux is already implicitly contained in Fisher's fundamental theorem of natural selection (1), which states that any fitness difference within a population leads to adaptation in an evolution process governed by natural selection alone. The fitness flux of this deterministic process equals the (additive) fitness variance in the population. Hence, the flux is positive when adaptation occurs and zero otherwise.Generalizing this picture to realistic processes of molecular evolution has been a long-standing problem (2-8). The solution presented here involves a number of important conceptual steps. First, molecular processes are always stochastic because of genetic drift and mutations, and we include these forces into a stochastic theory of fitness flux. Second, we extend the observation of this dynamics to the time scales of genomic data, describing populations by histories of genotype composition and demography that may extend beyond their ...