Deleterious variation mimics signatures of genomic incompatibility and adaptive introgression

While it is appreciated that population size changes can impact patterns of deleterious variation in natural populations, less attention has been paid to how population admixture affects the dynamics of deleterious variation. Here we use population genetic simulations to examine how admixture impacts deleterious variation under a variety of demographic scenarios, dominance coefficients, and recombination rates. Our results show that gene flow between populations can temporarily reduce the genetic load of smaller populations, especially if deleterious mutations are recessive. Additionally, when fitness effects of new mutations are recessive, between-population differences in the sites at which deleterious variants exist creates heterosis in hybrid individuals. This can lead to an increase in introgressed ancestry, particularly when recombination rates are low. Under certain scenarios, introgressed ancestry can increase from an initial frequency of 5% to 30-75% and fix at many loci, even in the absence of beneficial mutations. Further, deleterious variation and admixture can generate correlations between the frequency of introgressed ancestry and recombination rate or exon density, even in the absence of other types of selection. The direction of these correlations is determined by the specific demography and whether mutations are additive or recessive. Therefore, it is essential that null models include both demography and deleterious variation before invoking reproductive incompatibilities or adaptive introgression to explain unusual patterns of genetic variation.


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There is tremendous interest in quantifying the effects that demographic history has had 55 on the patterns and dynamics of deleterious variation and genetic load (

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In particular, gene flow may be important for shaping patterns of deleterious variation. 4 effective migration rates between populations  and may play a 103 significant role in determining the fitness of highly structured populations .

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Heterosis may also increase introgression and the probability that introgressed ancestry will 105 persist in an admixed population, even if the introgressed ancestry contains more deleterious 106 variation (Harris and Nielsen 2016). The extent to which heterosis contributes to increases in the 107 frequency of introgressed ancestry and confounds inference of adaptive introgression is also not 108 well understood.

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The objective of this study is to develop a clearer picture of the effect of deleterious occurs at an initial proportion of 5%, in one direction and for one generation, at some time after 128 the split (Figure 1, Table 1). Throughout, we will refer to the subpopulation from which gene 129 flow occurs as the source subpopulation, and the subpopulation which receives gene flow as the 130 recipient subpopulation. Furthermore, we will refer to ancestry in the recipient subpopulation that 131 originated in the source subpopulation as introgression-derived ancestry. We tracked the 132 frequency of introgression-derived ancestry in simulations by placing marker mutations in one 133 subpopulation, and use p I to denote the estimated total proportion of ancestry in the recipient 134 subpopulation that is introgression-derived. The sizes of the subpopulations were varied as 135 described in the forthcoming sections and in Figure 1 and Table 1.

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Unless specified otherwise, we simulated approximately 5 Mb of sequence, with 137 randomly generated genic structure (see Methods). The mutation rate (µ) was set at a constant rate 138 of 1.5x10 -8 per bp per generation. All simulated mutations were either neutral or deleterious, and 139 only nonsynonymous mutations had nonzero selection coefficients. Deleterious mutations had 140 selection coefficients (s) were all drawn from the same distribution of fitness effects (Kim et al. 141 2017). In other words, the selection coefficients did not depend on the population in which 142 mutations occurred. No positively selected mutations were simulated in any of our models. We 143 simulated additive (h=0.5) and recessive (h=0.0) mutations separately. Additive fitness effects 144 were computed by multiplicatively calculating fitness at each locus. Recessive fitness effects 145 were computed additively, but only at homozygous loci. All fitness effects were computed 146 multiplicatively across loci. To assess the effect of recombination rate, we also varied the per-147 base pair per chromosome recombination rate, r, between sets of simulations (r∈{10 -6 ,10 -7 ,10 -148 8 ,10 -9 }). See Methods for additional details on the simulations and calculation of fitness.

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In each simulation, we recorded the fitness of each subpopulation, the proportion of 150 ancestry that is introgression-derived, and other measures of genetic load (Figures S1-S3) at 151 different time points. Differences in subpopulation fitness are presented as (w R /w S ), which 152 represents the relative differences in load between the recipient and source subpopulation.

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Subpopulation fitnesses are presented separately in Figure S1.

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After admixture, homozygosity in the recipient population is immediately decreased (Figure S3),

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with a corresponding increase in the fitness of the recipient population (Figures 2 and S1).

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Importantly, the number of derived deleterious variants per haplotype in the recipient 178 subpopulation is unaffected by gene flow (Figure S2). After the initial increase in fitness due to 179 admixture, the decline in fitness following admixture is slow, such that fitness will be greater than 180 the pre-admixture value for many generations following admixture (Model 0, h=0, Figure S1).

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Notably, the fitness increase conferred by heterosis is the most pronounced (≈2.5% increase) and 182 lasts the longest (>10,000 generations after admixture) in simulations with low amounts of 183 recombination (r=10 -9 ). This occurs for two reasons. First, fitness declines more quickly when 184 recombination rates are low (Muller 1964), resulting in stronger selection against non-admixed 185 individuals. Second, introgression-derived haplotypes remain intact, maximizing the heterotic 186 advantage of admixed individuals.

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The effect of selection on deleterious variation also influences the fraction of ancestry 188 that is introgressed in the recipient population. Considering that immediately following 189 admixture, 5% of the ancestry in the recipient population is introgression-derived (p I =5%), it 190 follows that in the absence of allele frequency changes due to selection the expected proportion of   Figure 3). The increase in p I is inversely related to the recombination rate. Specifically, the 198 increase in p I is greatest (average p I~3 5% at 10,000 generations after the split, Figure 3) for the 199 lowest recombination rate r=10 -9 , (Figures 2 and S1). This effect is still observed even when the 200 simulated recombination rate is greater than 10 -9 , but the magnitude of the effect is far less 201 pronounced, with increases to p I ≈ 6-9%. These results also corroborate studies which showed that 202 heterosis can increase effective migration rates  or enhance the   Figures 2 and S1). Therefore, gene flow has no effect on the additive load or the 217 number of deleterious variants per haplotype ( Figure S2) in the recipient population, and there is 218 no selection on introgressed ancestry in this model.

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We found broadly similar patterns when deleterious mutations were recessive, with some 220 important differences. Our simulations show that the bottleneck causes an additional ~2% decline 221 in the recipient population's mean fitness prior to admixture (Model 1, Figure S1) due to a small 222 increase in homozygosity ( Figure S3). However, the average number of deleterious variants per 223 haplotype is unaffected by any selection against the increased proportion of homozygotes (Model 224 1, Figure S2). Fitness increases quickly after admixture, but consistently remains slightly less 225 than the model without a bottleneck, suggesting that any change in load due to an increased 226 number of homozygous sites is mostly cancelled out by the increased heterozygosity that results 227 from admixture ( Figure S3). The magnitude of the fitness increase from admixture is again 228 inversely related to the recombination rate, in a manner similar to that in the model without a

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The frequency of introgression-derived ancestry was largely unaffected by the short 231 bottleneck. When fitness effects were additive, the average frequency of introgressed ancestry 232 remained at the initial admixture proportion of p I = 5%, 10,000 generations after the admixture 233 event (Model 1, Figure 3). When fitness effects were recessive, introgression-derived ancestry 234 increased in frequency by carrying protective alleles, similar to the simulations with identical 235 subpopulation size. The same inverse relationship to the recombination rate was also observed. In 236 the case of recessive mutations, the long-term frequency of introgression-derived ancestry (e.g. p I 237 8 ≈ 33% for r=10 -9 , Model 1 in Figure 3) was similar but slightly lower than the model without a 238 bottleneck (e.g. p I ≈ 35% for r=10 -9 , Model 0 in Figure 3).

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Long-term population contractions greatly influence the dynamics of introgression 241 At equilibrium, smaller populations will have a greater reductions of fitness due to 242 deleterious variation than larger populations (Kimura et al. 1963). Therefore, a long-term 243 reduction in population size should have different implications for fitness and the fate of 244 introgression-derived ancestry than the short bottleneck described above.

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To investigate the effect of long-term differences in population size and subsequent gene 246 flow on patterns of deleterious alleles, we simulated a split model with the addition of a long-term 247 reduction in population size. Immediately following the split, the size of one subpopulation was 248 reduced 10-fold to 1,000 diploids (Models 2 and 3, Figure 1). After 20,000 additional 249 generations, gene flow occurred in a single generation at an admixture proportion of 5%. In

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Model 2, the direction of admixture is from the small into the large population, and in Model 3 251 the direction of admixture is from the large into the small population.

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As a consequence of long-term differences in population size, the additive fitness of the 253 small subpopulation is 7-10% less than that of the large subpopulation (Models 2 and 3 in

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Again, we observe that the magnitude of this effect is inversely related to the recombination rate.

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Specifically, the proportion of introgression-derived ancestry decreased or increased at the 295 greatest magnitude in simulations with low recombination, and the least in simulations with a 296 high recombination rate (Models 2 and 3 in Figure 3).

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When fitness effects were recessive, the frequency of introgression-derived ancestry in 298 the recipient subpopulation were determined by heterosis and differences in genetic load between 299 subpopulations. Gene flow from the large to the small subpopulation (Model 3) resulted in slight 300 (p I =7%, r=10 -6 ) to drastic increases (p I =51%, r=10 -9 ) in the average proportion of introgression-

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It is also notable that the frequency of introgression-derived ancestry (p I ) in each window 416 appears to be driven by exon density, or the local concentration of sites at which deleterious 417 mutations can occur. For recessive mutations, p I is greatly increased on the left-hand side of the 418 simulated chromosome, which tends to be more gene-rich than the right-hand side of the 419 chromosome (Figures 5 and S5). For additive mutations, the pattern is not as straightforward.

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These effects can be long lasting, persisting for thousands of generations in some of our 462 simulations (Figures 2, 3, S1). If gene flow or hybridization is a significant feature of a study 463 population, studies concerning load should consider the fitness consequences of admixture as 464 well as population size changes.

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That dynamics of introgression-derived ancestry can thus be driven by deleterious 466 variation also is particularly relevant for the study of gene flow between populations or species.

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Patterns of introgression between hybridizing species are often asymmetric, vary across the

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Importantly, we chose to discard from our simulations, and therefore from calculations of 585 fitness, mutations that were fixed in the ancestral or both subpopulations. Although fixed 586 deleterious variants contribute to the overall genetic load of finite populations, they will have no 587 effect on the relative differences between admixing subpopulations and no effect on the dynamics 588 of introgression-derived ancestry. Therefore, each fitness calculation does not reflect the true 589 fitness, but rather the fitness components that are relevant during gene flow.