1. Slides of this talk: google “Alkes HSPH”
Impact of negative selection on
common variant disease architectures
Alkes L. Price Harvard School of Public Health
October 19, 2018
Slides of this talk: google “Alkes HSPH”

2. What is negative selection?
Negative selection is the negative pressure on allele frequencies of mutations that reduce fitness. 
Allele frequency
Allele frequency
Time Time
Kryukov et al Am J Hum Genet, Kiezun et al PLoS Genet

3. Negative selection: causal effect on trait is larger for rare and low-frequency variants
Let p be minor allele frequency (MAF).
Let β be per-allele causal effect on disease/trait.
Let h2 = β22p(1−p) be variance explained by a SNP.
Selection: α model
Var(β) ~ [p(1−p)]α
E(h2) ~ [p(1−p)]1+α
rare variants explain more h2
if α < 0 (negative selection)
than if α = 0 (no selection)
Speed et al Am J Hum Genet; also see Schoech et al. biorxiv 09/13/17
(analytical derivations support validity of α model for p above a threshold)

4. Negative selection: causal effect on trait is larger for rare and low-frequency variants
Let p be minor allele frequency (MAF).
Let β be per-allele causal effect on disease/trait.
Let h2 = β22p(1−p) be variance explained by a SNP.
Selection: α model
Var(β) ~ [p(1−p)]α
E(h2) ~ [p(1−p)]1+α
rare variants explain more h2
if α < 0 (negative selection)
α = −0.38
across 25 UK Biobank traits
(rare variants: larger causal effects but smaller per-SNP h2 vs. common variants)
Schoech et al. biorxiv 09/13/17; also see Zeng et al Nat Genet

5. Rare variants explain limited trait heritability,
despite larger causal effects + many rare variants
MAF = 5%
α = 0 (no selection)
Schoech et al. biorxiv 09/13/17; also see Zeng et al Nat Genet

6. Beyond the α model: does negative selection impact common variant disease architectures?
MAF = 5%
α = 0 (no selection)
Schoech et al. biorxiv 09/13/17; also see Zeng et al Nat Genet

7. Outline 1. LD-dependent architectures 2. Functional architectures
3. Polygenicity

8. Outline 1. LD-dependent architectures 2. Functional architectures
3. Polygenicity

9. What does “LD-dependent architecture” mean?

10. What does “LD-dependent architecture” mean?
• SNPs with higher LD have higher average χ2 association statistics
due to increased tagging of causal variants.
Pritchard & Przeworski 2001 Am J Hum Genet

11. What does “LD-dependent architecture” mean?
• SNPs with higher LD have higher average χ2 association statistics
due to increased tagging of causal variants.
“LD-dependent architecture”: dependence of causal effect sizes
on the level of LD of a SNP.
Speed et al Am J Hum Genet

12. What does “LD-dependent architecture” mean?
• Common SNPs have higher LD and higher causal variance than
rare SNPs => SNPs with higher LD have higher causal variance.
Schoech et al. biorxiv 09/13/17; also see Zeng et al Nat Genet

13. What does “LD-dependent architecture” mean?
• Common SNPs have higher LD and higher causal variance than
rare SNPs => SNPs with higher LD have higher causal variance.
“LD-dependent architecture”: dependence of causal effect sizes
on the level of LD of a SNP, after conditioning on MAF.

14. Inferring LD-dependent architectures from summary statistics using S-LDSC
Extend S-LDSC (Finucane et al Nat Genet) to continuous annot. q:
E(χ2) = 1 + NΣq τqLDscoreq
LDscoreq(SNP m) =
= normalized conditional effect of annot. q
(proportionate change in trait h2 per 1 s.d. increase in annot. q)
am,q = value of annot. q at SNP m
τq = conditional effect of annot. q
h2 = genome-wide trait heritability m m
Gazal et al Nat Genet

15. Inferring LD-dependent architectures using continuous LLD annotation
Level of LD ( LLD ): MAF-adjusted LD score
(MAF-stratified quantile normalization)
LDscoreLLD (SNP m) for continuous LLD annotation =
• Include “baseline model” annotations (Finucane et al Nat Genet)
• Also include binary annotations for 10 common SNP MAF bins
• Simulations confirm robust results (not shown)
Gazal et al Nat Genet

16. SNPs with lower MAF-adjusted level of LD (LLD) have larger causal effect sizes
Same sign of effect across all 56 traits (average N=101K)

17. Many annotations correlated to LD could contribute to LD-dependent architectures
LD-related annotations
Predicted allele age (ARGweaver; Rasmussen et al PLoS Genet)
LLD in Africans (LLD-AFR)
Recombination rate (±10kb window; Hussin et al Nat Genet)
GC-content (±1Mb window; Loh et al. 2015b Nat Genet)
Replication timing (Koren et al Am J Hum Genet)
Background selection (1 − B statistic; McVicker et al PLoS Genet)
Nucleotide diversity (SNPs per kb; ±10kb window)
CpG content (±50kb window)
Functional annotations (Finucane et al Nat Genet)
Coding, regulatory, conserved, etc.

18. Many annotations correlated to LD could contribute to LD-dependent architectures|
LD-related
annotations
Functional annotations from “baseline model”
(Finucane et al Nat Genet)

19. Many annotations correlated to LD could contribute to LD-dependent architectures|
LD-related
annotations
Functional annotations from “baseline model”
(Finucane et al Nat Genet)

20. Many annotations correlated to LD could contribute to LD-dependent architectures|
LD-related
annotations
Functional annotations from “baseline model”
(Finucane et al Nat Genet)

21. Many LD-related annotations impact causal effect sizes
+ MAF
Annotation
+ baseline model
+ MAF
Meta-analysis of 31 independent traits

22. Many LD-related annotations impact causal effect sizes
+ MAF
Annotation
+ baseline model
+ MAF
Recombination rate has discordant sign of effect (Hill & Robertson 1966 Genet Res)
Heritability is enriched in SNPs with low LLD in low recombination rate regions
r = −0.63
Meta-analysis of 31 independent traits

23. Many LD-related annotations impact causal effect sizes after conditioning on baseline model
+ MAF
Annotation
+ baseline model
+ MAF
Meta-analysis of 31 independent traits

24. Many LD-related annotations impact causal effect sizes after conditioning on baseline model
+ MAF
Annotation
+ baseline model
+ MAF
LLD effect is 0.37x smaller when including annotations from baseline model
Some, but not all, of LD-dependent architecture due to DHS, enhancers, etc.
0.37x
Meta-analysis of 31 independent traits

25. Many LD-related annotations impact causal effect sizes after conditioning on baseline model
+ MAF
Annotation
+ baseline model
+ MAF
LLD effect is 0.51x smaller after adding baseline model
Predicted allele age has largest effect.
Meta-analysis of 31 independent traits

26. Many LD-related annotations impact causal effect sizes in joint fit with baseline model  baseline-LD model
Annotation
+ MAF
Annotation
+ baseline model
+ MAF
Joint-fit annotations
+ baseline model
+ MAF
Meta-analysis of 31 independent traits

27. Many LD-related annotations impact causal effect sizes in joint fit with baseline model  baseline-LD model
Annotation
+ MAF
Annotation
+ baseline model
+ MAF
Joint-fit annotations
+ baseline model
+ MAF
LLD effect is 0.51x smaller af
6 significant annotations in joint fit
Meta-analysis of 31 independent traits

28. Many LD-related annotations impact causal effect sizes in joint fit with baseline model  baseline-LD model
Annotation
+ MAF
Annotation
+ baseline model
+ MAF
Joint-fit annotations
+ baseline model
+ MAF
LLD effect is 0.51x smaller af
predicted allele age has largest effect
Meta-analysis of 31 independent traits

29. Forward simulations show that negative selection explains LD-dependent architectures
Annotation
+ MAF
Annotation
+ baseline model
+ MAF
Joint-fit annotations
+ baseline model
+ MAF
Forward
Simulations:
impact on s
• Forward simulations using
SLiM (Messer 2013 Genetics) under
African-European demographic
model (Gravel et al PNAS)
• Jointly regress selection coeff s
on 4 LD-related annotations and
minor allele frequency X X
31 traits Simulations

30. Proportion of heritability
Quintiles illustrate large effects of LD-related annotations from baseline-LD model
40%
30%
Proportion of heritability
20%
10% 0%
Youngest 20% explain 3.8x more heritability than oldest 20%
vs. 1.8x
for MAF

31. Proportion of heritability
Quintiles illustrate large effects of TMRCA annotation inferred using ASMC
• ASMCavg annotation:
Average TMRCA inferred by
Ascertained Sequentially Markovian Coalescent (ASMC) in GoNL WGS data
• Jointly statistically significant with other LD-related annotations
(τ* = ‒0.25±0.01)
Proportion of heritability
Low-TMRCA 20% explain 3.8x more heritability than high-TMRCA 20%
Palamara et al Nat Genet

32. LD-dependent architectures can lead to bias in
estimates of heritability and functional enrichment
Modeling LD-dependent architectures is critically important.
Speed et al Am J Hum Genet, Gusev et al PLoS Genet,
Yang et al Nat Genet, Speed et al Nat Genet, Gazal et al Nat Genet

33. How well does the baseline-LD model fit the data?

34. How well does the baseline-LD model fit the data?
Idea (Speed et al Nat Genet):
use out-of-sample likelihoods for formal model comparisons
Speed et al Nat Genet:
LDAK model > infinitesimal model (“GCTA model”)
in analysis of 1000G SNPs

35. 2.8M 1000G SNPs: LDAK model > GCTA model
y-axis = change in log likelihood vs. LDAK model (16 UK Biobank traits)
“GCTA” = infinitesimal model
2.8M SNPs
from 1000G
4.6M SNPs
from HRC
ASHG 2018 poster 3432/W Price + Gazal et al. biorxiv 10/16/18

36. 4.6M HRC SNPs: GCTA model (>) LDAK model
y-axis = change in log likelihood vs. LDAK model (16 UK Biobank traits)
“GCTA” = infinitesimal model
2.8M SNPs
from 1000G
4.6M SNPs
from HRC
ASHG 2018 poster 3432/W Price + Gazal et al. biorxiv 10/16/18

37. baseline-LD > LDAK and GCTA in both SNP sets
y-axis = change in log likelihood vs. LDAK model (16 UK Biobank traits)
“GCTA” = infinitesimal model (also see Yang et al Nat Genet; LDMS model)
“Gazal-LD” = LD + MAF annotations only from baseline-LD model
“baseline-LD+LDAK” = model with baseline-LD + LDAK annotations
2.8M SNPs
from 1000G
4.6M SNPs
from HRC
ASHG 2018 poster 3432/W Price + Gazal et al. biorxiv 10/16/18

38. Outline 1. LD-dependent architectures 2. Functional architectures
3. Polygenicity
image from Shlyueva et al Nat Rev Genet

39. Common variant functional architectures: coding + regulatory (tissue-specific)
Coding variants explain ~10% Regulatory variant enrichments
of common variant h are often tissue/cell-type-specific
Finucane et al Nat Genet; also see Finucane et al Nat Genet

40. Low-frequency variant functional architectures: ??? + ???
Coding variants explain ??? Regulatory variants explain ???
of low-frequency variant h of low-frequency variant h2
???
???
???
???
Coding variants likely important for low-frequency variant architectures:
UK10K 2015 Nature, Astle et al Cell, Marouli et al Nature

41. Inferring low-frequency variant functional architectures by extending S-LDSC
Multi-linear Regression:
χ2 statistic = 1 + Σq(Nτq)LDscoreq
• Separate annotations for common and low-frequency SNPs
• Also include binary annotations for 5 low-frequency MAF bins
• UK Biobank target samples + UK10K LD reference samples
• Simulations confirm robust results (not shown) m m,
ASHG 2018 poster 2699/F Gazal + Gazal et al Nat Genet

42. Inferring low-frequency variant functional architectures by extending S-LDSC
Common variant enrichment (CVE) of an annotation
= prop. of hc2 / prop. of common SNPs
Low-frequency variant enrichment (LFVE) of an annotation
= prop. of hlf2 / prop. of low-frequency SNPs
• Separate annotations for common and low-frequency SNPs
• Also include binary annotations for 10 low-frequency MAF bins
• UK Biobank target samples + UK10K LD reference samples
• Simulations confirm robust results (not shown)
ASHG 2018 poster 2699/F Gazal + Gazal et al Nat Genet

43. LFVE is correlated to CVE LFVE > CVE when CVE is large
33 main annotations:
r(LFVE,CVE) = 0.79
Meta-analysis across
40 UK Biobank traits
(average N = 363K) assoc. method: BOLT-LMM
(Loh et al Nat Genet)
Low-frequency variant enrichment (LFVE)
Common variant enrichment (CVE)

44. LFVE is correlated to CVE LFVE > CVE when CVE is large
33 main annotations:
r(LFVE,CVE) = 0.79
Non-synonymous variants:
17.3% of hlf2 vs. 2.1% of hc2
(Even larger LFVE for n.s. variants
• predicted as damaging: PolyPhen-2
• in genes under strong selection: shet)
Low-frequency variant enrichment (LFVE)
Common variant enrichment (CVE)

45. LFVE ≈ CVE for most regulatory annotations but LFVE > CVE for brain annotations
637 cell-type-specific (CTS)
annotation-trait pairs with significant CVE
(Finucane et al Nat Genet)
Low-frequency variant enrichment (LFVE)
55 brain annotation-trait pairs
with LFVE/CVE>2x
Common variant enrichment (CVE)

46. LFVE ≈ CVE for most regulatory annotations but LFVE > CVE for brain annotations
H3K4me3 in brain DPFC-Neuroticism:
56.9% of hlf2 vs. 11.7% of hc2 (P = )
Low-frequency variant enrichment (LFVE)
Common variant enrichment (CVE)

47. LFVE/CVE ratio depends primarily on strength of selection
sdn = avg selection coefficient of
deleterious de novo variants
π = prob. that de novo variant is
causal for trait
Forward simulations
(SLiM2 + τEyre-Walker)
LFVE/CVE ratio
Non-synonymous variants:
LFVE/CVE=5x, sdn=‒0.003
55 brain annotation-trait pairs:
LFVE/CVE>2x, sdn<‒0.0006
(potentially useful for WGS)
Proportion of causal variants (π)

48. Outline 1. LD-dependent architectures 2. Functional architectures
3. Polygenicity
image from Evangelou et al Nat Genet

49. Complex traits are extremely polygenic
Systolic blood pressure: GWAS of 1 million people identifies
901 genome-wide significant loci explaining
5.7% of trait variance (vs. total SNP-heritability = 21%)
Evangelou et al Nat Genet; also see
Purcell et al Nature, Yang et al Nat Genet, Stahl et al Nat Genet,
PGC-SCZ 2014 Nature, Loh et al. 2015b Nat Genet, Zhang et al Nat Genet

50. Omnigenic model: polygenicity arises from extraordinary biological complexity
Boyle et al Cell
also see Wray et al Cell, Liu et al. biorxiv 09/24/18

51. Flattening hypothesis: polygenicity arises because negative selection flattens common variant effect sizes
(always small)
ASHG 2018 poster 3528/W O’Connor + O’Connor et al. biorxiv 09/18/18

52. New definition of polygenicity: effective number of associated SNPs (Ma)
No LD between causal SNPs:
(M = #SNPs, β = normalized effect size)

53. New definition of polygenicity: effective number of associated SNPs (Ma)
No LD between causal SNPs:
(M = #SNPs, β = normalized effect size)
If SNP effects follow normal distribution:
Ma = number of SNPs
If SNP effects follow point-normal distribution:
Ma = number of causal SNPs

54. New definition of polygenicity: effective number of associated SNPs (Ma)
No LD between causal SNPs:
(M = #SNPs, β = normalized effect size)
If SNP effects follow normal distribution:
Ma = number of SNPs
If SNP effects follow point-normal distribution:
Ma = number of causal SNPs
Estimates of the number of causal SNPs under a point-normal model are sample size dependent (Zhang et al Nat Genet, O’Connor et al. biorxiv 09/18/18)

55. New method to estimate Ma: Stratified LD 4th moments regression (S-LD4M)
S-LDSC (Finucane et al Nat Genet):
• Regress χ2 statistics on stratified LD scores (∑ r2)
• Include baseline-LD model annotations (Gazal et al Nat Genet)
S-LD4M (O’Connor et al. biorxiv 09/18/18):
• Regress squared χ2 statistics on stratified LD 4th moments (∑ r4)

56. New method to estimate Ma: Stratified LD 4th moments regression (S-LD4M)
S-LD4M (O’Connor et al. biorxiv 09/18/18):
• Regress squared χ2 statistics on stratified LD 4th moments (∑ r4)
• Include baseline-LD model annotations (Gazal et al Nat Genet)
Applicable to genome-wide SNP or categories of SNPs
(e.g. low-frequency SNPs, coding SNPs, etc.)

57. New method to estimate Ma: Stratified LD 4th moments regression (S-LD4M)
S-LD4M (O’Connor et al. biorxiv 09/18/18):
• Regress squared χ2 statistics on stratified LD 4th moments (∑ r4)
• Include baseline-LD model annotations (Gazal et al Nat Genet)
Applicable to genome-wide SNP or categories of SNPs
(e.g. low-frequency SNPs, coding SNPs, etc.)
Robust results in simulations

58. Approaches to understanding polygenicity
Love is Understanding.
-- Madonna
Data is Understanding.
-- Alkes

59. Brain-related traits are particularly polygenic (Number of children is even more polygenic)
Results sub-selected from 33 diseases and complex traits (average N = 361K)

60. Common variants are more polygenic than low-frequency variants
Polygenicity (Ma) of common vs. low-frequency SNPs
Common variants: ~4x more polygenic than low-frequency variants
(evolutionary modeling: ≥30x more polygenic than de novo variants)

61. Functional categories are more polygenic
(in proportion to heritability enrichment)
Main functional categories from baseline-LD model
Results aggregated across common + low-frequency variants
heritability enrichment reflects differences in the number of associations rather than their magnitude (which is constrained by selection)

62. Flattening hypothesis: polygenicity arises because negative selection flattens common variant effect sizes
(always small)
ASHG 2018 poster 3528/W O’Connor + O’Connor et al. biorxiv 09/18/18

63. Flattening hypothesis: implications for GWAS
• GWAS effect sizes are largely determined by negative selection,
not just the biological importance of the implicated gene.

64. Flattening hypothesis: implications for GWAS
• GWAS effect sizes are largely determined by negative selection,
not just the biological importance of the implicated gene.
• Weak perturbations to strongly constrained genes will yield more
insights than strong perturbations to weakly constrained genes.

65. Flattening hypothesis: implications for GWAS
• GWAS effect sizes are largely determined by negative selection,
not just the biological importance of the implicated gene.
• Weak perturbations to strongly constrained genes will yield more
insights than strong perturbations to weakly constrained genes.
37 fine-mapped IBD loci (Huang et al Nature):
0/8 candidate genes with fine-mapped coding variants vs.
12/29 candidate genes near fine-mapped non-coding variants
were loss-of-function intolerant (pLI ≥ 0.9; Lek et al Nature)
(P = for difference)

66. Flattening hypothesis: implications for GWAS
• GWAS effect sizes are largely determined by negative selection,
not just the biological importance of the implicated gene.
• Weak perturbations to strongly constrained genes will yield more
insights than strong perturbations to weakly constrained genes.
• Rare variant association studies (in very large sample sizes)
will usefully complement GWAS, as rare variant architectures
are less impacted by flattening due to negative selection.

67. Outline 1. LD-dependent architectures 2. Functional architectures
3. Polygenicity

68. Conclusions
• Low-LD variants have larger causal effect sizes (at a given MAF),
consistent with negative selection (Gazal et al Nat Genet);
the baseline-LD model attains higher likelihoods than other models
in formal model comparisons (Gazal et al. biorxiv 10/16/18).
Modeling LD-dependent architectures is critically important.
• Non-synonymous + conserved + some brain-related annotations
have LFVE >> CVE, consistent with strong negative selection
(Gazal et al Nat Genet).
• Common variants are more polygenic than low-frequency variants
+ common variants are far more polygenic than de novo variants,
due to negative selection (O’Connor et al. biorxiv 09/18/18).

69. Acknowledgements Harvard T.H. Chan School of Public Health:
• Steven Gazal
• Luke O’Connor
Broad Institute:
• Hilary Finucane
BWH/Harvard Medical School:
• Shamil Sunyaev
• Po-Ru Loh
• All authors of Gazal et al Nat Genet,
Gazal et al. biorxiv 10/16/18,
Gazal et al Nat Genet,
O’Connor et al. biorxiv 09/18/18
Additional thanks to UK Biobank and 23andMe