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.

This is an introductory review on how genes interact to produce biological functions. Transcriptional interactions involve the binding of proteins to regulatory DNA. Specific binding sites can be identified by genomic analysis, and these undergo a stochastic evolution process governed by selection, mutations, and genetic drift. We focus on the links between the biophysical function and the evolution of regulatory elements. In particular, we infer fitness landscapes of binding sites from genomic data, leading to a quantitative evolutionary picture of regulation.

Evolution is a quest for innovation. Organisms adapt to changing natural selection by evolving new phenotypes. Can we read this dynamics in their genomes? Not every mutation under positive selection responds to a change in selection: beneficial changes also occur at evolutionary equilibrium, repairing previous deleterious changes and restoring existing functions. Adaptation, by contrast, is viewed here as a non-equilibrium phenomenon: the genomic response to time-dependent selection. Our approach extends the static concept of fitness landscapes to dynamic fitness seascapes. It shows that adaptation requires a surplus of beneficial substitutions over deleterious ones. Here, we focus on the evolution of yeast and Drosophila genomes, providing examples where adaptive evolution can and cannot be inferred, despite the presence of positive selection