The deleterious mutation load is insensitive to recent population history
Yuval B Simons et al.
Nature geneticcs 2014 Sep 1.
We further show that for many diseases, rare alleles are unlikely to contribute a large fraction of the heritable variation, and therefore the impact of recent growth is likely to be modest.
Keinan and Clark3 recently hypothesized that “Some degree of genetic risk for complex disease may be due to this recent rapid increase in the number of rare variants in the human population”.
However, for those diseases that have a direct impact on fitness, strongly deleterious rare mutations likely do play an important role, and recent growth will have increased their impact.
朝鮮人にあてはまる可能性が高い。13世紀のモンゴル軍侵攻により、当時の人口の約85％が失われたと推測しているが、その後に朝鮮半島では人口が急速に回復しているはずである
(i) a bottleneck;
(ii) exponential growth starting from a constant-sized population; and
(iii) a complex demographic model for African Americans (including rapid recent growth) and European Americans (including two bottlenecks followed by growth) inferred by Tennessen et al.5.
Our main results focus on selection against semi-dominant (i.e., additive) alleles in which the three genotypes have fitnesses 1, 1 − s/2 and 1 − s, respectively; and selection against recessive alleles with genotype fitnesses 1, 1, and 1 − s.
Figure 1 illustrates the impact of a bottleneck and population growth on the numbers of deleterious variants with strong selection (s=1%).
As expected, these demographic events have a major impact on the number and frequency spectra of deleterious variants:
the bottleneck causes a decrease in the total number of segregating sites in a population due largely to loss of rare variants, while the mean frequency of alleles that survive increases.
Meanwhile, exponential growth causes a rapid increase in the number of segregating sites due to a major influx of rare variants, but a consequent drop in the mean frequency at segregating sites.
Each data line shows the expected number of variants, or alleles per MB, assuming semi-dominant mutations (C and D) or recessive mutations (E and F) with s = 1% and mutation rate per site per generation=10−8.
The behavior of the recessive model is more complicated (Figures 1E and 1F).
In the bottleneck model, the mean number of deleterious variants per individual drops by 60% as a result of the bottleneck.This is due to the loss of rare alleles.
However, during the bottleneck, some deleterious alleles drift to higher frequencies11, 19, contributing disproportionately to the number of homozygotes.
In the semi-dominant case, the load is essentially unaffected by these demographic events (Figures 1C and 1D).
With growth, the increased number of segregating sites is exactly balanced by a decrease in mean frequency (and conversely for the bottleneck), so that the number of variants per individual stays constant.
This causes a transient increase in the number of deleterious homozygous sites per individual – i.e., the recessive load.
Meanwhile, population growth has a less pronounced effect on recessive variation, leaving the mean number of deleterious alleles per individual unchanged, but causing a slight decrease in load.
More generally, the manner in which demography affects load varies with the degree of dominance and the strength of selection (Figure 2 and Supplement Table 1 & Section 2).
The behavior of these models can be classified into three selection regimes (strong, weak and effectively neutral).
In the strong selection case, i.e., where selection is much stronger than drift (approximately s ≥ 10−3 for semi-dominant mutations), deleterious variants are extremely unlikely to fix, and virtually all of the genetic load is due to segregating variation.
In this range, we infer that human demography has had no impact on semi-dominant load (and more generally for mutations with at least some dominance component), and small effects on recessive load.
The weak selection case – where drift and selection have comparable effects – is more complex, as fixed alleles may contribute appreciably to load, and steady state load depends on population size20.
Finally, in the effectively neutral range – where selection has negligible effects on the population dynamics – segregating variation contributes negligibly and hence the load does not change with demography.
The plot shows mean frequencies in each population, plus and minus two standard errors, using exome sequence data from Fu et al.6. Here a site is considered an SNV if it is segregating in the combined AA-EA sample of 6515 individuals. The functional classifications of sites are from PolyPhen222 with bias-correcting modifications. The AA and EA mean frequencies are essentially identical within all five functional categories (p>0.05).
In summary, these observations are consistent with our model predictions that load should be very similar in these populations.
We note that David Reich, Shamil Sunyaev and colleagues have recently made similar observations regarding load in different populations (personal communication).
All the plots assume an additive trait and, with the exception of (B), are based on simulations with semi-dominant selection under the Tennessen et al.5 demographic model. Results for the constant population size model are also provided for comparison. The upper plots show the cumulative fractions of genetic variance due to alleles at frequency < x, based on:
(A) simulated data with weak selection (s =.0002);
(B) assuming the observed frequency spectrum at “probably damaging” sites6, 22, where a constant population size of 14,474 and selection coefficient of 0.02% are used for comparison;
and
(C) simulated data with strong selection (s = .01).
Panel (D) depicts the fraction of variance due to rare alleles (i.e., < 0.1%) as a function of the selection coefficient;
(E) shows the per-site contribution to variance as a function of the selection coefficient under two extreme models, with effect sizes that are either independent of s (constant) or proportional to s;
(F) shows the expected fraction of the variance due to rare variants (i.e., < 0.1%) as a function of the correlation between the selection on, and effect size of variants. Further details on the model are provided in the Methods.
To study this, we computed the contributions of different allele frequencies to the heritable phenotypic variation among individuals in the population, namely x(1 − x)f (x)/2, where f (x) is the probability that a derived allele is at frequency x given the demographic model and selection coefficient.
Analysis of this model reveals several interesting points. For effectively neutral, or for weakly deleterious sites (Figure 4A), only a small fraction of the total variance comes from very rare alleles: although there are many rare alleles, each one contributes very little to population variance and individual load. The same is true for recessive variation across almost the entire range of selection coefficients (Supplement Section 4.2).
the Out-of-Africa bottleneck increases the contribution of intermediate frequency alleles to the genetic variance (Figure 4A–C): e.g., at probably damaging sites 62% of the variance in EAs is contributed by alleles with minor allele frequency above 10% compared to only 49% in AAs.
It is only for the case of strong, dominant selection that very rare variants (< 0.1%) become important (Figure 4C and 4D).
For example, for a selection coefficient of 1%, most of the variation is due to rare alleles that arose within the recent exponential growth phase. As a result, the contribution of extremely rare variants is much greater than it would have been in the absence of growth: e.g., in AAs and EAs, 80%, and 65% of the variance is due to alleles below frequency 0.1%, compared to just 25% in the constant population model.
Yuval B Simons et al.
Nature geneticcs 2014 Sep 1.
この論文で言うところのボトルネックは、出アフリカ後に生じた今日のアフリカ人以外の全人類に生じたボトルネックである。特定の集団に生じたボトルネック効果ではない。（通常、ボトルネックは、人口減少比率ではなく、人口絶対数である。）
図の3では、
①頻度1.5％をもってdeleteriousでなく、benigh とし、
②頻度1.0％をもって、多分deleterious としている。
③頻度0.5％をもって、同様に多分deleterious としている。
韓国人の知性に決定的な影響を及ぼしている可能性が高い遺伝子の一つにCSMD1遺伝子がある。
NCBIでCSMD1遺伝子のSNPを調べると160万以上出てくるが、やはり、韓国人には頻度0.5％以下の韓国人固有の変異が多いことが、サンプル的に調べて見ると確認しえた。(600SNPについて、11の韓国人固有の変異が、0.5%以下の頻度で生じている。)
恐らくは、韓国人DNA全体について同様であろうが、いつも感じることだが、モンスターに怖くなる。韓国人DNAは、頻度5％以下の変異が多いことは既に明らかにされているが、頻度0.5％以下の韓国人固有の遺伝子変異（＝韓国人固有の有害変異）が多い可能性が高い。
図の3では、
①頻度1.5％をもってdeleteriousでなく、benigh とし、
②頻度1.0％をもって、多分deleterious としている。
③頻度0.5％をもって、同様に多分deleterious としている。
韓国人の知性に決定的な影響を及ぼしている可能性が高い遺伝子の一つにCSMD1遺伝子がある。
NCBIでCSMD1遺伝子のSNPを調べると160万以上出てくるが、やはり、韓国人には頻度0.5％以下の韓国人固有の変異が多いことが、サンプル的に調べて見ると確認しえた。(600SNPについて、11の韓国人固有の変異が、0.5%以下の頻度で生じている。)
恐らくは、韓国人DNA全体について同様であろうが、いつも感じることだが、モンスターに怖くなる。韓国人DNAは、頻度5％以下の変異が多いことは既に明らかにされているが、頻度0.5％以下の韓国人固有の遺伝子変異（＝韓国人固有の有害変異）が多い可能性が高い。
- rs293876 [Homo sapiens]
- Variant type:
- SNV
- Alleles:
- G>A,C,T [Show Flanks]
- Chromosome:
- 8:4727163 (GRCh38)
8:4584685 (GRCh37) - Canonical SPDI:
- NC_000008.11:4727162:G:A,NC_000008.11:4727162:G:C,NC_000008.11:4727162:G:T
- Gene:
- CSMD1 (Varview)
- Functional Consequence:
- genic_upstream_transcript_variant,intron_variant
- Validated:
- by frequency,by alfa,by cluster
- MAF:
Abstract
This prediction is supported by two exome sequence datasets showing that individuals of west African and European ancestry carry very similar burdens of damaging mutations.We further show that for many diseases, rare alleles are unlikely to contribute a large fraction of the heritable variation, and therefore the impact of recent growth is likely to be modest.
Keinan and Clark3 recently hypothesized that “Some degree of genetic risk for complex disease may be due to this recent rapid increase in the number of rare variants in the human population”.
However, for those diseases that have a direct impact on fitness, strongly deleterious rare mutations likely do play an important role, and recent growth will have increased their impact.
朝鮮人にあてはまる可能性が高い。13世紀のモンゴル軍侵攻により、当時の人口の約85％が失われたと推測しているが、その後に朝鮮半島では人口が急速に回復しているはずである
Results
We studied three types of demographic models thought to be relevant for human populations:(i) a bottleneck;
(ii) exponential growth starting from a constant-sized population; and
(iii) a complex demographic model for African Americans (including rapid recent growth) and European Americans (including two bottlenecks followed by growth) inferred by Tennessen et al.5.
Our main results focus on selection against semi-dominant (i.e., additive) alleles in which the three genotypes have fitnesses 1, 1 − s/2 and 1 − s, respectively; and selection against recessive alleles with genotype fitnesses 1, 1, and 1 − s.
The impact of demographic changes on individual load
Individual load is directly related to the number of deleterious alleles carried by an individual, or for recessive mutations to the number of homozygous sites per individual (see the Methods and Supplement for further details).Figure 1 illustrates the impact of a bottleneck and population growth on the numbers of deleterious variants with strong selection (s=1%).
As expected, these demographic events have a major impact on the number and frequency spectra of deleterious variants:
the bottleneck causes a decrease in the total number of segregating sites in a population due largely to loss of rare variants, while the mean frequency of alleles that survive increases.
Meanwhile, exponential growth causes a rapid increase in the number of segregating sites due to a major influx of rare variants, but a consequent drop in the mean frequency at segregating sites.
Figure 1. Time course of load and other key aspects of variation through a bottleneck (A) and exponential growth (B).
Each data line shows the expected number of variants, or alleles per MB, assuming semi-dominant mutations (C and D) or recessive mutations (E and F) with s = 1% and mutation rate per site per generation=10−8.
The behavior of the recessive model is more complicated (Figures 1E and 1F).
In the bottleneck model, the mean number of deleterious variants per individual drops by 60% as a result of the bottleneck.This is due to the loss of rare alleles.
However, during the bottleneck, some deleterious alleles drift to higher frequencies11, 19, contributing disproportionately to the number of homozygotes.
In the semi-dominant case, the load is essentially unaffected by these demographic events (Figures 1C and 1D).
With growth, the increased number of segregating sites is exactly balanced by a decrease in mean frequency (and conversely for the bottleneck), so that the number of variants per individual stays constant.
This causes a transient increase in the number of deleterious homozygous sites per individual – i.e., the recessive load.
Meanwhile, population growth has a less pronounced effect on recessive variation, leaving the mean number of deleterious alleles per individual unchanged, but causing a slight decrease in load.
More generally, the manner in which demography affects load varies with the degree of dominance and the strength of selection (Figure 2 and Supplement Table 1 & Section 2).
The behavior of these models can be classified into three selection regimes (strong, weak and effectively neutral).
In the strong selection case, i.e., where selection is much stronger than drift (approximately s ≥ 10−3 for semi-dominant mutations), deleterious variants are extremely unlikely to fix, and virtually all of the genetic load is due to segregating variation.
In this range, we infer that human demography has had no impact on semi-dominant load (and more generally for mutations with at least some dominance component), and small effects on recessive load.
Figure 2. Changes in load due to changes in population size during the histories of European and African Americans for (A) semi-dominant and (B) recessive sites.
The weak selection case – where drift and selection have comparable effects – is more complex, as fixed alleles may contribute appreciably to load, and steady state load depends on population size20.
Finally, in the effectively neutral range – where selection has negligible effects on the population dynamics – segregating variation contributes negligibly and hence the load does not change with demography.
Analysis of exome data
To test these predictions, we analyzed two recent data sets of exome sequences from individuals of west African and European descent.
Figure 3. Observed mean allele frequencies in African and European Americans at various classes of SNVs.
The plot shows mean frequencies in each population, plus and minus two standard errors, using exome sequence data from Fu et al.6. Here a site is considered an SNV if it is segregating in the combined AA-EA sample of 6515 individuals. The functional classifications of sites are from PolyPhen222 with bias-correcting modifications. The AA and EA mean frequencies are essentially identical within all five functional categories (p>0.05).
In summary, these observations are consistent with our model predictions that load should be very similar in these populations.
We note that David Reich, Shamil Sunyaev and colleagues have recently made similar observations regarding load in different populations (personal communication).
The impact of demography on the genetic architecture of disease susceptibility
Although population size changes have had little impact on the average load carried by individuals, growth has greatly increased the number of rare variants in populations.
So do rare variants play a greater (and substantial) role in the genetics of disease as a result of recent growth (Figure 4)?
Figure 4. Predicted effect of demography on the genetic architecture of disease risk.
All the plots assume an additive trait and, with the exception of (B), are based on simulations with semi-dominant selection under the Tennessen et al.5 demographic model. Results for the constant population size model are also provided for comparison. The upper plots show the cumulative fractions of genetic variance due to alleles at frequency < x, based on:
(A) simulated data with weak selection (s =.0002);
(B) assuming the observed frequency spectrum at “probably damaging” sites6, 22, where a constant population size of 14,474 and selection coefficient of 0.02% are used for comparison;
and
(C) simulated data with strong selection (s = .01).
Panel (D) depicts the fraction of variance due to rare alleles (i.e., < 0.1%) as a function of the selection coefficient;
(E) shows the per-site contribution to variance as a function of the selection coefficient under two extreme models, with effect sizes that are either independent of s (constant) or proportional to s;
(F) shows the expected fraction of the variance due to rare variants (i.e., < 0.1%) as a function of the correlation between the selection on, and effect size of variants. Further details on the model are provided in the Methods.
To study this, we computed the contributions of different allele frequencies to the heritable phenotypic variation among individuals in the population, namely x(1 − x)f (x)/2, where f (x) is the probability that a derived allele is at frequency x given the demographic model and selection coefficient.
Analysis of this model reveals several interesting points. For effectively neutral, or for weakly deleterious sites (Figure 4A), only a small fraction of the total variance comes from very rare alleles: although there are many rare alleles, each one contributes very little to population variance and individual load. The same is true for recessive variation across almost the entire range of selection coefficients (Supplement Section 4.2).
the Out-of-Africa bottleneck increases the contribution of intermediate frequency alleles to the genetic variance (Figure 4A–C): e.g., at probably damaging sites 62% of the variance in EAs is contributed by alleles with minor allele frequency above 10% compared to only 49% in AAs.
It is only for the case of strong, dominant selection that very rare variants (< 0.1%) become important (Figure 4C and 4D).
For example, for a selection coefficient of 1%, most of the variation is due to rare alleles that arose within the recent exponential growth phase. As a result, the contribution of extremely rare variants is much greater than it would have been in the absence of growth: e.g., in AAs and EAs, 80%, and 65% of the variance is due to alleles below frequency 0.1%, compared to just 25% in the constant population model.
Conclusion
While recent demographic events have had well-documented effects on the frequency spectrum of SNVs in modern populations, we find that these events have had negligible impact on the average burden of mutations carried by individuals.
Moreover, we conclude that although there are large absolute numbers of rare variants, they do not necessarily contribute a large fraction of the genetic variance underlying complex traits.
To summarize, it is only for diseases that are primarily due to strongly deleterious mutations that we can expect much of the variance to be due to rare alleles: these will likely tend to be diseases that are tightly coupled to fitness.
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