1. Population Genetics
As we all have an interest in genomic epidemiology we are likely all either in the process of sampling and ananlysising genetic data or will be in the near future and we are going to want to relate that information to phenotypes.
In statistics it’s important to understand the process that generated the data (population genetics goes further back in time).
Population genetics is the study of how genes evolve through time
There is a large and fascinating body of science on the topic
Can’t go through all of it so focus on that most relevant to genomic epidemiology

2. ...or “what processes led to the data we’re analysing?”
Population Genetics
...or “what processes led to the data we’re analysing?”
As we all have an interest in genomic epidemiology we are likely all either in the process of sampling and ananlysising genetic data or will be in the near future and we are going to want to relate that information to phenotypes.
In statistics it’s important to understand the process that generated the data (population genetics goes further back in time).
Population genetics is the study of how genes evolve through time
There is a large and fascinating body of science on the topic
Can’t go through all of it so focus on that most relevant to genomic epidemiology

3. Imagine we collect and sequence some samples...
ATAGAAAGACCAGACTCCATCGCTAGCAGCTACGCTAGAGTTA
N samples
ATTGAAAGACCATACTCCATCGCTAGCAGC-ACGCTAGAGTTA
ATAGAAAGACCAGACTCCATCGCAAGCAGC-ACCCTAGCGTTA
ATAGAAAGACCAGACTCCATCGCAAGCAGCTACGCTAGAGTTA . . .

4. ATAGATAGACCATACTGCATCGCAAGCAGCTACGCTAGCGTTA
Imagine we collect and sequence some samples...
Reference sequence
ATAGATAGACCATACTGCATCGCAAGCAGCTACGCTAGCGTTA
ATAGAAAGACCAGACTCCATCGCTAGCAGCTACGCTAGAGTTA
ATTGAAAGACCATACTCCATCGCTAGCAGC-ACGCTAGAGTTA
ATAGAAAGACCAGACTCCATCGCAAGCAGC-ACCCTAGCGTTA
ATAGAAAGACCAGACTCCATCGCAAGCAGCTACGCTAGAGTTA

5. ATAGATAGACCATACTGCATCGCAAGCAGCTACGCTAGCGTTA
Imagine we collect and sequence some samples...
ATAGATAGACCATACTGCATCGCAAGCAGCTACGCTAGCGTTA
.....A......G...C......T A....
..T C......T A....
As discussed yesterday there are many types of genetic variation. But to allow us to talk generally about the processes we are going to simplify the process assuming that at each polymorphism there are two alleles that segregate and that they are result from a single ancestral mutation event.
.....A......G...C C
.....A......G...C A....
Insertion / deletion polymorphism
SNPs

6. Outline Population genetic processes
Measuring correlations between alleles
Recombination
Differences between populations
Going to try and go through four areas
I’ll mostly be speaking with respect to human diversity, but the concepts are fundamental to surveys of genetic variation from all species.
Please do ask questions and interject.

7. ATAGATAGACCATACTGCATCGCAAGCAGCTACGCTAGCGTTA
Genetic variation
ATAGATAGACCATACTGCATCGCAAGCAGCTACGCTAGCGTTA
.....A......G...C......T A....
..T C......T A....
.....A......G...C C
.....A......G...C A....
...or, in cartoon form:
As discussed yesterday there are many types of genetic variation. But to allow us to talk generally about the processes we are going to simplify the process assuming that at each polymorphism there are two alleles that segregate and that they are result from a single ancestral mutation event.

8. Two chromosomes (= haplotypes) carried by each individual
Genetic variation
Two chromosomes (= haplotypes) carried by each individual
As discussed yesterday there are many types of genetic variation. But to allow us to talk generally about the processes we are going to simplify the process assuming that at each polymorphism there are two alleles that segregate and that they are result from a single ancestral mutation event.

9. 24 haplotypes (12 individuals) 100 SNPs on chromosome 20
Utah residents, ancestrally Northern and Western European
So as an example lets look at some real data from a small region of Human chromosome 20 the HapMap project.
There are clearly differences between in the patterns of diversity between these two groups, but what generated them?
Yoruba from Ibadan, Nigeria

10. Population genetic processes
Genetic drift
Mutation
Recombination
Natural selection
It is the combination of these fundamental processes that generate diversity within a population
TO understand these processes we need to think about how genes evolve through time.

11. Genetic Drift population current generation N N-1 N-2 ...
Lets start with thinking about what happens at a single locus

12. Genetic Drift current generation
Lets start with thinking about what happens at a single locus

13. Genetic Drift current generation
Dominic’s example of populating a whole city
There is an important role of chance in the process

14. Genetic drift Genetic drift creates correlations between alleles
current generation
N generations ago . .
Genetic drift creates correlations between alleles
As Dominic’s gene’s speed through the population by chance the haplotype that he passed on would remain intact and reduce genetic diversity.
Through this chance process ultimately the whole population would consist of a single haplotype.
Why doesn’t this happen?

15. Recombination Paternal (father) Maternal (mother) Recombination
A picture of the mechanism of recombination
Recombination
No recombination

16. Recombination breaks down the correlation between alleles. .
Recombination breaks down the correlation between alleles

17. Thinking backwards in time
As chromosome are passed from one generation to the next patterns of diversity evolve
When we take data from the present we need to think about the past.
What are the ancestral processes that generated the data?
It is perhaps more natural to think backwards in time

18. Ancestral history
Present day

19. Ancestry of the population
Present day

20. Ancestry of sample
Present day

21. Ancestry of sample
The probability that two chromosomes share a common ancestor in the previous generation is 1/2N

22. Ancestral processes 2μ 2r 1/2N
Mutation
Recombination
Coalesce
2μ r 1/2N
If two chromosome coalesce before they incur a mutation or recombination event then they will be identical

23. Genetic diversity
The probability that two individuals share a common ancestor in the previous generation is 1/2N
The expected time to two individuals coalesce is 2N
The probability two chromosomes are identical (by descent) is:
Important thing here is that the probability depends on the (effective) population size 2N.
Higher population size => longer coalescence times => lower probability of identity by descent (for a region of a given size.)

24. Large and small ancestral populations
In large populations we have to go further back in time to time to find the common ancestor
Consequently there is more opportunity for
Mutation, increasing genetic diversity
Recombination, decreasing correlation between alleles

25. Human population history
The recent migration of European from Africa has lead to small effective population sizes

26. 24 haplotypes (12 individuals) 100 SNPs on chromosome 20
Utah residents, ancestrally Northern and Western Europe
We’ve explained a good deal in this picture.
(Probably a good time to pause.)
Yoruba from Ibadan, Nigeria

27. Natural Selection
When a beneficial mutation arises it spreads quickly through the population generating strong correlations between alleles

28. Natural Selection
Big differences in the patterns of diversity between populations can be generated by natural selection

29. Differences between populations
Big differences in the patterns of diversity between populations can be generated by natural selection

30. Population genetics
Genetic drift generates correlations between alleles
Recombination breaks them down
The ancestral population size and history determines the amount of diversity and how it is structured
Natural selection can generate strong differences between populations

31. Measuring correlations
In genetics correlation between alleles is called linkage disequilibrium (LD)
There are several measures of LD
Understanding LD in natural populations is important for genomic epidemiology

32. Linkage equilibrium A B AB Ab a b ab aB
Independence between the two loci.
The expected frequency of the AB haplotype is just the product of the marginal allele frequencies.
Haplotype frequencies are determined by SNP allele frequencies (they are in equilibrium)

33. Linkage disequilibriumAB Ab aB ab
Haplotype frequencies differ from those expected if the SNPs are independent (they are in disequilibrium)

34. Measuring LD D ≈ 0 when near linkage equilibrium
D ≠ 0 when there is linkage disequilibrium
Two measures

35. Haplotypes and LD 1 2 3 4
r2 is less than one unless SNP A is a perfect surrogate of SNP B in the sample
D’ statistic less than one if and only if all four haplotypes are present in sample
So D’ is 1 unless visible recombination has occurred

36. Recombination and physical distance
Correlations decay with distance (due to recombination)

37. Looking at patterns of LD
High r2
Low r2
Assume similar physical spacing
LD patterns are complicated

38. Recombination clusters along chromosomes
Studies have shown that recombination is not uniform along chromosomes

39. Recombination hotspots
Recombination hotspots occur through out the genome

40. Hotspots and haplotypes
Hotspots can break down
correlations over short distances

41. Hotspots and haplotypes
Recombination hotspots lead to regions of strong correlation separated by regions of low LD

42. LD and Recombination There are lots of ways to measure LD
Recombination is not uniform along chromosomes
Much of the recombination happens in hotspots and these demark breakdown in correlations
Correlations do persist across hot spots

43. Differences between populations
The overall pattern of LD is conserved
The different ancestral histories lead to different levels of LD

44. Differences between populations
The overall pattern of LD is conserved
The different ancestral histories lead to different levels of LD

45. Population structure in Africa
There is evidence for widespread population structure across Africa

46. Population structure in Africa
Add population differences between groups from the same region

47. Maasai in Kinyawa, Kenya
24 haplotypes (12 individuals) 100 SNPs on chromosome 20
Luhya in Webuye, Kenya
Maasai in Kinyawa, Kenya

48. Differences in patterns of LD
An experiment:
Take genome-wide SNP data collected from a European population (A)
Take each SNP and find the SNPs which is most correlated with it (and remember how correlated it is)
Go to another European population (B) and compare the correlation between the two SNPs in the new population
(Measure correlation as r2)

49. Differences in patterns of LD
Across Europe
Within Kenya
We will look at this in the practical

50. Summary
Different ancestral histories have led to different patterns of diversity
Natural selection can generate strong differences in haplotype patterns
Population structure across Africa, and between groups in Africa, will lead to differences in the structure of LD

53. Genetic drift
Allele frequencies change by chance over time

54. Genetic diversity
180 haplotypes (90 individuals) from Luhya in Webuye, Kenya typed at 6856 SNPs in 10 Mb region on chromosome 20