This document summarizes research on modeling the effects of background selection on genetic variation using non-equilibrium demographic models. It discusses how background selection reduces genetic diversity and increases the proportion of rare variants by purging deleterious mutations. Forward simulations are used to model these effects over time and under different demographic scenarios, showing that background selection has a greater impact when populations are not at equilibrium. The approach is applied to human genetic data, finding that inferred demographic histories are altered depending on the level of background selection in genomic regions.

1. Background Selection With
Non-Equilibrium Demographic Models
Ryan D. Hernandez
SMBE 2015
ryan.hernandez@ucsf.edu
@rdhernand
Raul Torres
Talk 23.12:!
Thursday 10am!

2. Deleterious
mutations will
arise in the next
generation
Chromosomes in
a population with
standing variation
The Effect of Negative Selection

3. Deleterious
mutations will
arise in the next
generation
Chromosomes in
a population with
standing variation
Negative selection:
the action of natural
selection purging
deleterious mutations.
The Effect of Negative Selection

4. Deleterious
mutations will
arise in the next
generation
Chromosomes in
a population with
standing variation
Negative selection:
the action of natural
selection purging
deleterious mutations.
The Effect of Negative Selection

5. The Effect of Negative Selection
Consequences:!
• Some proportion of chromosomes are
eliminated each generation!
➡ Decreased effective population size (f0Ne)!
➡ Decreased neutral variation ( f0π )!
➡Excess of neutral rare variants
{
Background
selection
f0 = exp
U
s + R
⇥
. Charlesworth (MANY, 1993-)
Hudson & Kaplan. Genetics (1995)
Many others…

6. Wright-Fisher Island model
Many demographic bells and population structure whistles
Various distributions of selective effects
Mutation models (with or w/o CpG effects)
Coding versus non-coding
X versus autosome
Arbitrary recombination maps
Recently optimized…
Forward Simulations
Selection on Finite Sites under COmplex Demographic Events
(SFS_CODE)
Hernandez. Bioinformatics (2008)
http://sfscode.sourceforge.net

7. Performance
1e−050.0010.1110
RunTime(d)
1000 10000 1e+05 1e+06 1e+07
θ=ρ=0.001
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θ=ρ=0.005
N=10,000
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fwdpp_ind
slim
SFS_CODE
SFS_CODE (opt)
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0.010.1110
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~4.2 CPU years of computation Hernandez. Bioinformatics (2008)!
http://sfscode.sourceforge.net

8. Weak vs. Strong Background Selection
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0 50 100 150 200
0.650.700.750.800.850.900.951.00
γγ
ππππ0
Maximal effect: -25≤γ≤-5
π/π0: ratio of
observed to
expected
diversity at
neutral loci, a
measure of
the effect of
BGS
Deleterious lociNeutral
locus
Deleterious loci

9. Deleterious lociNeutral
locus
Deleterious loci
Beyond Equilibrium: BGS & π
0 2 4 6 8 10
0.00000.00100.00200.0030
π
γ = 0
γ = 2
γ = 5
γ = 10
γ = 20
γ = 50
γ = 100
81.0
γ = 2
γ = 5
0 2 4 6 8 10
0.00000.00100.00200.0030
π
81.0
0 2 4 6 8 10
0.00000.001
0 2 4 6 8 10
0.40.60.81.0
time (in 2Ne gens)
ππ0
NA = 10,000!
10-fold expansion

10. Beyond Equilibrium
Deleterious lociNeutral
locus
0 2 4 6 8 10
0.050.20.525101
time (in 2Ne gens)
RelPopSize:(NCNA)
Deleterious loci
NA = 10,000
Qualitatively similar patterns across a demographic models: BGS
substantially reduces the time to equilibrium

11. Beyond Equilibrium: BGS & SFS
ψ: Fraction of SNPs
that are singletons
NA = 10,000
10-fold expansion
0 2 4 6 8 10
0.20.30.40.50.60.7
ψ
γ = 0 γ = 2
γ = 5
γ = 10
γ = 20
γ = 50
γ = 100
02.5
0 2 4 6 8 10
0.20.30.40.50.60.7
ψ
2.5
0 2 4 6 8 10
0.20.30.4
0 2 4 6 8 10
1.01.52.02.5
time (in 2Ne gens)
ψψ0
Deleterious lociNeutral
locus
Deleterious loci

12. Demographic inference
• Complete Genomics Diversity Panel!
• ~50 individuals from each ofYRI, CEU, and CHS !
• High coverage Whole Genome Sequencing!
• Neutral sites in the human genome!
• Filtering based on PhyloP!
• High B-value (weak BGS)!
• Low B-value (strong BGS)!
• Four-fold degenerate sites
π/π0:Expected
diversityduetoBGS BGS in the human genome
McVicker et al. PLoS Genet (2009)
∂a∂i {

13. Human Demographic Inference
The most neutral regions of the genome: !
! High B-values and high recombination rates.
−500 −400 −300 −200 −100 0
050000100000150000200000
Effectivepopulationsize
Time (kya)
AF−EU−AS shared demography
EU−AS shared demography
AS demography
EU demography
AF demography

14. Human Demographic Inference
Regions of strong background selection (Low B)
significantly increase the inferred rate of growth
−500 −400 −300 −200 −100 0
0102030
Relativeeffpopsize(Nc/Na)
Time (kya)
AF−EU−AS shared demography
EU−AS shared demography
AS demography
EU demography
AF demography
High B
Low B

15. Human Demographic Inference
Four-fold degenerate synonymous sites are a
mixture of high and low BGS.
−500 −400 −300 −200 −100 0
0102030
Relativeeffpopsize(Nc/Na)
Time (kya)
AF−EU−AS shared demography
EU−AS shared demography
AS demography
EU demography
AF demography
Low B
4−fold
High B
−20 −15 −10 −5 0
0102030

16. Conclusions
• The effects of background selection are highly
dependent on demographics.!
• Every genome is composed of a mixture of high and
low background selection, so pooling sites should be
done with caution!!
• More modeling of non-equilibrium BGS is necessary.

17. Thanks!
Funding: NIH; QB3;
CHARM; CTSI; CFAR
ryan.hernandez@ucsf.edu
Nicolas
Strauli
Dominic
Tong
Raul
Torres
Lawrence
Uricchio
Zach
Szpiech
Kevin
Hartman
Dan
Vasco
Talk 23.12:
Thursday 10am! Poster: 555B