1. Genetic Linkage

3. Two pops may have the same
allele frequencies but different
chromosome frequencies.

4. Conditions for Linkage Equilibrium
(Two locus case)
Frequency of B is the same on chromosome A and a
Frequency of haplotypes AB, ab, Ab, aB can be calculated
from allele frequencies A=p, a=q, B=t, and b=s.
f(AB) = pt f(ab) = qs f(Ab) = ps f(aB) = pt
3) Coefficient of linkage disequilibrium (D) = 0
f(AB) x f(ab) - f(Ab) x f(aB) = D
ps x qt - pt x qs = 0
(ranges from to +0.25)

5. Hardy Weinberg Principle for Two Loci
Chromosome frequencies remain unchanged across generations
if loci are in linkage equilibria.
If loci are in linkage disequilibria, the chromosome frequencies
will move closer to linkage equilibrium each generation.
What Creates Linkage Disequilibrium in a Population?
selection, drift, and population admixture

6. Effects of Selection on Chromosome Frequencies
ab/ab = body size of value 10
each additional A or B adds 1 value
predators eat all individuals of size 12 or less
65.28%
survive

7. Locus A and B are in disequilibrium among the survivors
Freq a = ( ) / .6528)/2
= 0.24
Freq b = ( ) / .6528)/2
= 0.09
Freq ab = .24 x .09 = .02
however!
65.28%
survive
Locus A and B are in disequilibrium
among the survivors

8. Genetic Drift, followed by selection can cause linkage disequilibrium

9. Combination of Two Different Gene Pools
Admixture

10. Recombination Breaks Down Linkage Disequilibria
The rate of decline in LD increases with r

11. LD declines over time
(rate depending on r)
r = D
sqrt(pqst)

13. All allele combinations All allele combinations
Concept of Linkage
Law of Independent Assortment ab
= 0.25 A B b
Meiosis
All allele combinations
in gametes
equally probable aB
= 0.25 a Ab
= 0.25 AB
= 0.25
Probability of recombination = 0.5 ab
= 0.25 A a B b
All allele combinations
in gametes
equally probable
Meiosis aB
= 0.25 Ab
= 0.25 AB
= 0.25

14. All allele combinations All allele combinations
Linked Loci
Probability of recombination = 0.3 ab
= 0.35 A a
Meiosis aB
= 0.15 B b
All allele combinations
in gametes NOT
equally probable Ab
= 0.15 AB
= 0.35
Probability of recombination = 0.1 ab
= 0.45 A a B b
Meiosis
All allele combinations
in gametes NOT
equally probable aB
= 0.05 Ab
= 0.05 AB
= 0.45

15. Why important? Concept: The closer two loci are on a chromosome,
the lower the probability of recombination.
Why important?
(1) Affects rate that LD is broken down.
(2) Allows one to determine the linear order of genes on a chromosome (make a genome map).
(3) Maps allow for the localization of genes, mutant phenotypes, and QTL in the genome.

16. Selection at a single locus affects other loci under LD
Selection has
an effect on
frequency of B
alleles

17. new mutations are linked to deleterious sites or arise
LD may retard rate of
evolution
If:
new mutations are linked
to deleterious sites or arise
in the ‘wrong’ chromosomal
backgrounds
(255 genes examined)
A comparison of substitution
rates between D. simulans
and D. melanogaster for
synonomous and
non-synonomous sites

18. LD among 1504 marker
Loci on Human
Chromosome 22.
(Dawson et al. 2002)

19. Where did CCR5 D32 come from?
There is strong linkage
disequilibrium between
CCR5 and two neutral
marker loci.

20. Pg = (1 - c - m)g Prob recombination Prob mutation
Probability that D has remained unchanged across generations:
Pg = (1 - c - m)g
Prob recombination
Prob mutation
Estimated p = 0.848, m = 0.001, c = 0.005
g = 27.5
~ 27.5 x 25 = 688 yrs

21. How does LD help identify genes that may be under
positive natural selection?
For neutral alleles: Genetic drift is the primary evolutionary
mechanism. So:
If LD is detectable, indicates that an allele is young.
Expect magnitude of LD is proportional to the age of an allele.
If LD is not detectable, indicates that an allele is old.
Expect old and frequent alleles, or old and rare alleles,
But do not expect young, high frequency alleles.
Indicates alleles at the locus may be under selection.

22. G6PD polymorphism
and deficiency
Countries with malaria
have highest frequency
of a reduced-activity
allele.

23. LD is higher for the G6PD-202A allele; suggests positive selection
Probability
that 2 randomly
chosen “a” chromosomes
have the same snps
across a physical
distance