Statistical physics of molecular evolution across scales

A venerable question in evolutionary biology is: if the tape of life was replayed, would the outcome be the same? We do not know how evolutionary predictability relates to molecular scales, ranging from genotypes to molecular phenotypes and function. I discuss universal properties of molecular phenotypes, encoded by high-dimensional genotypes, which allow for the predictive description of their evolution. I introduce a non-equilibrium framework for adaptation of populations in time-dependent environments. I present strong evidence that environmental fluctuations drive the evolution of gene expression levels in Drosophila. Co-evolving populations reciprocally affect the fitness of each other, acting as time-dependent environments with feedback. I show evidence of co-adaptation between interacting cellular populations of HIV and the antibody repertoire of a patient during infection.