The fitness of an introgressing haplotype changes over the course of divergence and depends on its size and genomic location.

The genomic era has made clear that introgression, or the movement of genetic material between species, is a common feature of evolution. Examples of both adaptive and deleterious introgression exist in a variety of systems. What is unclear is how the fitness of an introgressing haplotype changes as species diverge or as the size of the introgressing haplotype changes. In a simple model, we show that introgression may more easily occur into parts of the genome which have not diverged heavily from a common ancestor. The key insight is that alleles from a shared genetic background are likely to have positive epistatic interactions, increasing the fitness of a larger introgressing block. In regions of the genome where few existing substitutions are disrupted, this positive epistasis can be larger than incompatibilities with the recipient genome. Further, we show that early in the process of divergence, introgression of large haplotypes can be favored more than introgression of individual alleles. This model is consistent with observations of a positive relationship between recombination rate and introgression frequency across the genome; however, it generates several novel predictions. First, the model suggests that the relationship between recombination rate and introgression may not exist, or may be negative, in recently diverged species pairs. Furthermore, the model suggests that introgression that replaces existing derived variation will be more deleterious than introgression at sites carrying ancestral variants. These predictions are tested in an example of introgression in Drosophila melanogaster, with some support for both. Finally, the model provides a potential alternative explanation to asymmetry in the direction of introgression, with expectations of higher introgression from rapidly diverged populations into slowly evolving ones.