Fig 1.
(A) Two populations (A and B) evolve independently, fixing substitutions in their genome, represented by filled bars, until introgression at some point moves alleles from A into B. (B) Three types of alleles may introgress as a result: new alleles which are derived in A and ancestral in B (blue fill), ancestral alleles which are ancestral in A and derived in B (dashed outline) and replacement alleles in which both A and B have fixed alternate variants (dashed outline, blue fill). Each of these types of alleles will on average have different fitness effects, and either introduce new epistatic interactions (solid arrows), or remove existing ones (dashed arrows) (C) An introgressing haplotype of length x carrying all 3 types of alleles will both introduce novel epistatic interactions (solid arrows) and remove existing ones (dashed) in individuals carrying the haplotype compared to others in the population.
Fig 2.
(A) When divergence (b) is low, even fairly small introgressing haplotypes carry sufficient positive interactions between introgressed derived alleles to cancel out potential deleterious effects. As divergence increases, however, the fitness of smaller haplotypes rapidly declines, and it takes increasingly larger haplotypes to cancel out potential DMIs. If each allele has only direct negative selection on it in the receiving population (solid black line), a simple linear relationship in fitness is expected. Note that we assume direct selection on each allele is on average negative, and so the positive selection is entirely driven by epistasis. (B) When the introgressing haplotype is only carrying novel alleles (f = 0), increasing the number of alleles introgressing introduces increasing amounts of positive epistasis. However, as it replaces more and more of existing substitutions in the receiving population, it becomes more and more strongly selected against. In both panels, it is assumed all alleles are carrying either new or ancestral variants, with no replacement alleles (xreplacement = 0). Solid lines show exact numeric solutions, while dashed lines show approximations from Eq (5). The code underlying this figure can be located in S1 File.
Fig 3.
The effect of replacement alleles mimics introgressing ancestral variation.
Examining how the selection coefficient on an introgressing haplotype changes as the fraction of substitutions it carries varies between new, ancestral, and replacement alleles. Parameters listed in top left and calculations based on exact numerical evaluation of fitness (see S3 Fig for approximation using Eq (5)). Early in divergence (top row), carrying more ancestral variants has a more strongly deleterious effect than carrying replacement alleles. However, as divergence increases (lower plots), haplotypes that carry replacement alleles begin looking largely like haplotypes that carry entirely ancestral variants. In all cases, haplotypes carrying only novel alleles are the least deleterious. The code underlying this figure can be located in S1 File.
Fig 4.
(A) Previous work has identified an introgression event between Western African D. melanogaster (West) into North American populations (OOA2). South African populations (South1) are ancestral to both and used as an outgroup. Using previously published data, we calculated branch scores (normalized Population Branch Statistics), for 25,874 windows across the genome with some evidence for introgression. fD statistics were calculated using the population relationship shown in A, with OOA1 as a sister population with OOA2. (B) The genome-wide density of relative branch scores is clustered at values indicating high differentiation between OOA2 and both of the other populations (red values—high density, blue—low). However, the higher introgression windows (fD > 0.5) are depleted for long OOA2 branches and show many more windows with longer West and South1 branches. (C) Density plot of recombination rate versus fD, each bin is colored by the number of windows within the bin. A negative relationship between local recombination rate and introgression exists for all windows with fD >0 and (D) a similar negative relationship exists for OOA2 branch score and introgression, indicating diverged windows are more resilient to introgression. No significant relationship between West branch length and fD was identified. Slopes and p-values are from individual linear models for each plot. The code and data underlying this figure can be located in S1 File.