Lecture 19: Causes and Consequences of
Linkage Disequilibrium
March 21, 2014

u
Wednesday, March 26 at 6:30 in lab u
Genetic Drift, Population Structure,
Population Assignment, Individual
Identity, Paternity Analysis, and Linkage
Disequilibrium u
Sample exam posted on website u
Review on Monday, March 24

Multiple loci and independent segregation
Estimating linkage disequilibrium
Effects of drift on LD

Effects of inbreeding, population structure, mutation, and selection on LD
LD calculation: effects of admixture
Selective sweeps and LD

How should inbreeding affect linkage disequilibrium?

Joint effects of selfing and recombination on LD
High levels of inbreeding cause associations even between unlinked loci (c=0.5)
LD can be predicted as a function of selfing rate and recombination rate
D t

1

1
2


1
 
2

S



1
 
2

S


2

2 S



D t
Where S is selfing rate and
λ = 1-2c
(scales recombination effect from 0 to 1, just like selfing)
For c=0.5:

Population admixture and LD
If differentiated populations mix, nonrandom allelic associations result
Hybridization of different species fixed for different alleles at two loci:
A
1
B
1
A
2
B
2
What is D’ in this case?
If D is positive, D max or p
2 q
1 is lesser of p
1 q
2
If D is negative, D max is lesser of p
1 q
1 or p
2 q
2

Historical population admixture and LD
A1
B1
A1
B1
C1
D1
C1
D1
E1 E1
A2
B2
A2
B2
C2
D2
C2
D2
E2 E2
Two populations with fixed allelic differences (e.g., different species)
Recombinant gametes are undetectable: LD is low A1
B1
C1
D1
E1
A2
B2
C2
D2
E2
Hybrids between these will be completely heterozygous with strong allelic associations
A2
B2
C1
D1
E1
A2
B2
C2
D1
E1
A1
B1
C1
D1
E2
A1
B1
C1
D2
E2
Recombinant gametes will have high
LD between adjacent markers: few recombinations to break up allelic associations

Mutation and LD: High mutation rates
Allelic associations are masked by high mutation rates, so LD is decreased
Gamete Pool with Low Mutation Gamete Pool with High Mutation

LD and neutral markers
Low LD is the EXPECTED condition unless other factors are acting
If LD is low, neutral markers represent very small segment of the genome in most cases
 In most parts of the genome, LD declines to background levels within 1 kb in most cases (though this varies by organism and population)
Care must be taken in drawing conclusions about selection based on population structure derived from neutral markers

Selection and Linkage Disequilibrium (LD)
Selection can create LD between unlinked loci
Epistasis: two or more loci interact with each other nonadditively
 Phenotype depends on alleles at multiple loci
Change in D over time due to epistatic interactions between loci with directional selection
Why does D decline after generation 15 in this scenario?
D
 max min( p
1 q
2
, p
2 q
1
) for D > 0

Epistasis and LD
Begin with highly diverse haplotype pool
Directional selection leads to increase of certain haplotype combinations
Generates nonrandom association between alleles at different loci (LD)

Recombination vs Polymorphism in Poplar
LG VII
0.006
0.005
0.004
0.003
0.002
0.001
4 Nec

Nucleotide diversity (π) is positively correlated with population recombination rate (4N e
c)
(R 2 =0.38)
0.000
0 2 4 6 8
Position (Mb)
10 12 14

Recombination vs Polymorphism
Recombination rate varies substantially across
Drosophila genome
Nucleotide diversity is positively correlated with recombination rate
Hartl and Clark 2007

Why is polymorphism reduced in areas of low recombination?
(or why is polymorphism enhanced in areas of high recombination)

Selection and LD
Selection affects target loci as well as loci in LD
Hitchhiking: neutral alleles increase in frequency because of selective advantage of allele at another locus in LD
Selective Sweep: selectively advantageous allele increases in frequency and changes frequency of variants in LD
Background Selection: selection against detrimental mutants also removes alleles at neutral loci in LD
Hill-Robertson Effect: directional selection at one locus affects outcome of selection at another locus in LD

Selective Sweep in Plasmodium
Pyrimethamine used to treat malaria parasite (Plasmodium falciparum)
Parasite developed resistance at locus dhfr, which rapidly became fixed in population (6 years on Thai border)
Microsatellite variation wiped out in vicinity of dhfr http://medinfo.ufl.edu/

Selective Sweep
Positive selection leads to increase of a particular allele, and all linked loci
Results in enhanced LD in region of selected polymorphism
Accentuated in rapidly expanding population

Derived Alleles and Selective Sweeps
Recent, incomplete selective sweeps are expected to leave a molecular signature of
• High frequency of derived alleles
• Strong geographic differentiation
• Elevated LD chimp
AA AA
Africans
A C
AC
Europeans

LD Provides evidence of recent selection
Regions under recent selection experience selective sweep, show high LD locally
Patterns of LD in human genome provide signature of selection
A statistic based on length of haplotypes and frequency of
“derived alleles” reveals regions under selection (“iHS” statistic)
Selective sweep for lactase enzyme in Europeans after domestication of dairy cows
Voight et al. 2006 Plos Biology 4: 446-458

Some factors that affect LD
Factor Effect
Recombination rate
Genetic Drift
Inbreeding
Population Structure
Mutation rate
Epistasis
Selection
Higher recombination lowers LD
Increases LD
Increases LD
Increases LD
High mutation rate decreases overall LD
Increases LD
Locally increased LD