that mutation and selection leave in the molecules of life, namely DNA and proteins. One of the central problems of the branch of biology that is devoted to the systematics of the tree of all living things, molecular evolution, concerns the rate of adaptation of individual organisms and species. A precise understanding of molecular phylogeny requires accurate models of evolution and adaptation. In this contribution, we model the adaptation of chromosomes that do not undergo recombination, or more generally, the rate of adaptation of asexual organisms.

The main observation that we study here is that the rate of adaptation of asexual organisms, or of regions of low recombination in the genomes of sexual organisms, does not steadily increase with increasing rate of advantageous mutations. When two or more advantageous mutations appear in different organisms at approximately the same time, then only one of them can go to fixation, i.e., become shared by all members of the population, while the others will be lost. This loss of potentially beneficial mutations limits the rate of adaptation to the rate at which individual mutants can go to fixation. By contrast, in sexual organisms, several mutations can recombine and thus go to fixation together. 