Long-range Hill-Robertson effect in adapting populations with recombination and standing variation

In sexual populations, closely-situated genes have linked evolutionary fates, while genes spaced far in genome are commonly thought to evolve independently due to recombination. In the case where evolution depends essentially on supply of new mutations, this assumption has been confirmed by mathematical modeling. Here I examine it in the case of pre-existing genetic variation, where mutation is not important. A haploid population with N genomes, L loci, a fixed selection coefficient, and a small initial frequency of beneficial alleles f0 is simulated by a Monte-Carlo algorithm. The results demonstrate the existence of extremely strong linkage effects, including clonal interference and genetic background effects, that depend neither on the distance between loci nor on the average number of recombination crossovers. When the number of loci, L, is larger than 4log2(Nf0), beneficial alleles become extinct at most loci. The substitution rate varies broadly between loci, with the fastest rate exceeding the one-locus model prediction. All observables and the transition to the independent-locus limit are controlled by single composite parameter log2(Nf0)/L. The potential link between these findings and the emergence of new Variants of Concern of SARS CoV-2 is discussed.