Introgression under linear selection on continuous genomes

We model the introgression of a small block that carries many weakly selected linked loci into a large homogeneous population, under the simple assumption that a block of introduced genome has a selective effect proportional to its map length. Using a diffusion approximation, we compute the probability that some part of the initial block survives the initial phase of the introgression and give the typical length of the surviving blocks. Our results quantify the effect of recombination on selection and drift during an introgression and indicate that the fate of the block depends on the strength of selection relative to recombination. When selection is positive some parts of the block are able to survive at large times, but large blocks can only persist if selection is stronger than recombination. Surprisingly, the probability of such a successful introgression is independent of the strength of recombination and is the same as that for a single beneficial allele. (This is not true of other quantities.) Conversely, a deleterious or neutral block is eventually lost, but at a much slower rate than a single allele with the same selective effect. In this case, surviving blocks are very small. We also consider the introgression of a block of genome made of a single beneficial allele linked to a deleterious background and compute the amount of deleterious material that hitchhikes during fixation.