1. Linkage: Statistically, genes act like beads on a string
Thomas Hunt Morgan

2. Linkage
We humans are diploid (i.e., we have two copies of a gene), inheriting one chromosome from mother, the other from father. In transmitting a chromosome to an offspring, however, the physical process of recombination (crossing over) results in a chromosome that contains part of the maternal chromosome and part of the paternal chromosome. Recombination also makes possible a number of different analytical strategies in genetics: linkage, ancestry tracing, and some forms of association.

3. Recombination (Crossing Over)
In meiosis, homologous chromosomes join together at a section and exchange genetic material.
Homologous chromosomes: chromosomes with the same genes on them. E.g., your paternal chromosome number 1 and your maternal chromosome number 1.

4. Example: A b C d a B c D A b C d a B c D A b c D C d a B

5. Original Chromosomes:T C G CC TT AA
Pair Up
Dad
Mom
Original Chromosomes:
Exchange Material
New Chromosomes:
Allele 1
Allele 2

6. Key Point about Recombination:
Recombination is a function of physical distance.
If two alleles are separated by 8 nucleotides, then there are “8 chances” of a recombination event between the two..
If two alleles are separated by 257 nucleotides, then then are “257 chances” of a recombination event between the two.
Therefore, alleles on the same DNA strand that are far away are more likely to be broken up by recombination than alleles that are close together.

7. A T C G
3 chances
10 chances
17 chances

8. In other words:
Alleles close together on the same DNA strand (i.e., the same chromosome) tend to be transmitted as a unit. Alleles far away on the same DNA strand tend to be broken up.

9. Relationship dilemma:
Close together, stay together;
Far apart, break apart

10. Series of alleles along a short section of the same strand of DNA
Haplotype
Series of alleles along a short section of the same strand of DNA
ATCTGCCTCGCCATAAAGTCATTCGCTCAT
ATCTGCCTCGCCATAAAGTCATTCGCTGAT
ATCAGCCTCGCCATAAAGTCATTCGCTCAT
ATCAGCCTCGCCATAAAGTCATTCGCTGAT
DNA Strand:
Haplotype: TC TG AC AG
T allele
A allele
position 4:
C allele
G allele
position 28:

11. NOTE: Smith and Jones have the same genotypes but different haplotypes.

12. Linkage Equilibrium & Disequilibrium
If I know the first allele in a haplotype, can I predict the second allele?
Yes No
Linkage Disequilibrium
Linkage Equilibrium

13. Linkage Equilibrium & Disequilibrium
In other words:
Equilibrium: Frequency of a haplotype is due to chance.
Disequilibrium: Frequency of a haplotype differs from chance frequency.

14. Haplotype
(Graduate)
Chance: If the frequency of allele T is .2 and the frequency of allele C is .4, then the frequency of haplotype TC is .2*.4 = .08.
Nonchance: If the frequency of allele T is .2 and the frequency of allele C is .4, then the frequency of haplotype TC is significantly different from .08.

15. Disequilibrium:
Is the norm rather than the exception for short sections of DNA (100,000 nucleotides).
Generates “haplotype blocks” (see next slide).
Haplotype Mapping Project (HapMap): provide a map of the haplotype blocks for the human genome.
Allows genome-wide association studies.

16. Haplotype Blocks: Section of DNA (vertical bar = polymorphism):
Haplotype Block: Series of adjacent alleles in strong disequilibrium.
Logic: Instead of genotyping all 37 polymorphisms, genotype one in each block.
If there is a “hit,” then go back and genotype the other polymorphisms in that block.

17. Haplotype block structure of the cytochrome P450 CYP2C gene cluster on chromosome 10.
From Walton et al. (2005), Nature Genetics 37,

18. Haplogroup: Group of similar haplotyes
Hierarchical: haplogroups can contain haplogroups

19. Example of a Y-chromosome haplogroup using STR (short tandem repeat) polymorphisms
Locus         a b           a b             a b c d
Number of repeats 12 23 13 10 16 17 14 31 18 8 9 11 27 19 28 15
From: May, 2017

20. From: https://en. wikipedia
From: May, 2017

21. Major mtDNA haplogroups and probably migration routes
From: Nature Reviews Genetics 16, 530–542 (2015)

22. The following slides are for graduate students

24. Gametes under linkage:

25. Genotypes under linkage:

26. Genotypes under linkage:

27. Haplotype
(Graduate)
Position 4:
Position 28: T A TC TG AC AG C G

28. Equilibrium T A C G .2 .8 .6 .4 .08 .32 .12 .48 (Graduate)
Position 4:
Position 28: T A C G .2 .8 .6 .4
.08
.32
.12
.48

29. Disequilibrium T A C G .2 .8 .6 .4 .16 .14 .04 .56 (Graduate)
Position 4:
Position 28: T A C G .2 .8 .6 .4
.16
.14
.04
.56

30. Statistics for Equilibrium
(Graduate)
Position 4:
Position 28: T A C G p1 q1 q2 p2
X11
X21
X12
X22

31. Statistics for Equilibrium
(Graduate)
d = X11X22 - X12X21= cov(L1, L2)
D = X11- p1p2 = X22 - q1q2
If D > 0, D = D/Dmax where Dmax = min(p1q2, p2q1)
If D > 0, D = D/Dmax where Dmax = min(p1p2, q1q2)
R2 = d2 / (p1p2q1q2)
D and R2 are the most often used stats.

32. Formation of Disequilibrium
(Graduate)
Mutation occurs and creates a new spelling variation (polymorphism).
This creates linkage disequilibrium with those polymorphisms along the same DNA strand with the mutation.
Over generations, recombination will break up the disequilibrium with polymorphisms that are far away from the mutation.
Polymorphisms close to the original mutation, however, will remain in disequilibrium for a longer time.
Hence, polymorphisms close to the mutation will be in disequilibrium longer than polymorphisms farther away from the mutation.