Adaptive evolution is governed by various forces: Mutations occur randomly in the genome and generate variability in the individuals’reproductive success; natural selection shifts this variability in the population towards individuals with high fitness; genetic drift introduces random fluctuations in the number of offspring of an individual and affects weakly selected or neutral mutations. On top of these, genetic linkage can be an important evolutionary force. Linkage generates interference interactions, by which simultaneously occurring mutations affect each other’s chance of fixation. Here, we develop a comprehensive model of adaptive evolution in linked genomes, which integrates interference interactions between multiple beneficial and deleterious mutations into a unified framework. By an approximate analytical solution, we predict the fixation rates of these mutations, as well as the probabilities of beneficial and deleterious alleles at fixed genomic sites. We find that interference interactions generate a regime of emergent neutrality: all genomic sites with selection coefficients smaller in magnitude than a characteristic threshold have nearly random fixed alleles, and both beneficial and deleterious mutations at these sites have nearly neutral fixation rates. We show that this dynamics limits not only the speed of adaptation, but also a population’s degree of adaptation in its current environment. We apply the model to different scenarios: stationary adaptation in a time-dependent environment, and approach to equilibrium in a fixed environment. In both cases, the analytical predictions are in good agreement with numerical simulations. Our results suggest that interference can severely compromise biological functions in an adapting population, which sets viability limits on adaptive evolution under linkage. We furthermore develop a likelihood-based inference method for genomic data, which explicitly takes into account genetic linkage. Tests with simulated datasets show that our method correctly predicts the amount of positive selection in linked sequence. In contrast, many existing tests falsely interpret traces from linkage as spurious positive selection. We apply our method to fruit fly genome data (Drosophila melanogaster), and find that a substantial fraction of sequence differences between two related fly species is in fact caused by linkage instead of natural selection
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