1. Recombination and genetic variation – models and inference
Simon Myers
Department of Statistics, Oxford

2. What does recombination do to genetic variation?
Informally, recombination shuffles up genetic diversity
We can see the effect of recombination in how ‘structured’ genetic variation is
Chromosomes
Sites
Xq13: 10kb
69 worldwide
Lipoprotein Lipase: 10kb
48 African Americans
Chromosome 22: 1Mb
57 Europeans

3. Human pairwise association revisited
Data for ENR131, Chromosome 2q, Chinese and Japanese population sample (The International HapMap Consortium, Nature 2005) LD
What is going on?
Recombination causes the association breakdown
Does the uneven pattern reflect
Chance?
Real strong differences in the underlying recombination rate in meiosis
We will explore two approaches to find out

4. Recombination and genealogical history
Forwards in time
Backwards in time
Grandpaternal sequence
Grandmaternal sequence x
TCAGGCATGGATCAGGGAGCT
TCACGCATGGAACAGGGAGCT
TCAGGCATGG
AACAGGGAGCT
Non-ancestral genetic material G A
G A

5. The ancestral recombination graph
The combined history of recombination, mutation and coalescence is described by the ancestral recombination graph
Coalescence
Mutation
Coalescence
Coalescence
Mutation
Coalescence
Recombination
Event

6. Deconstructing the ARG

7. Time
T(0)
T(0.5)
T(1)

8. Learning about recombination
Just like there is a true genealogy underlying a sample of sequences without recombination, there is a true ARG underlying samples of sequences with recombination
We can consider nonparametric and parametric ways of learning about recombination
There are several useful nonparametric ways of learning about recombination which we will consider first
These really only apply to species, such as humans, where we can be fairly sure that most SNPs are the result of a single ancestral mutation event
This is formally called the infinite sites model

9. Why use a non-parametric approach?
Non-parametric approaches require few assumptions about evolution
The infinite sites model, and that’s it!
We can attempt to learn features of the history of a sample based only on this assumption
Robust inference
Identify – “detect” the recombination events that shaped our sample
Clustering of multiple events in a region could signal a high underlying rate
Some drawbacks to this approach

10. The signal of recombination?
Ancestral chromosome recombines
Recurrent mutation
Recombination

11. Practical: detecting recombination from DNA sequence data
Look for all pairs of “incompatible” sites
Combine information across the pairs
Find minimum number of intervals in which recombination events must have occurred (Hudson and Kaplan 1985): Rm

12. Recombination and genetic variation – models and inference, part II
Simon Myers
Department of Statistics, Oxford

13. Example: 7q31
These results are based on a non-parametric minimum number of recombination intervals (events) Rh
Myers and Griffiths (2003) – improvement over Rm but identical assumptions
Results strongly suggest recombination “hotspots”

14. Example: humans vs. chimpanzees
Winckler et al. (2005)

15. Why use parametric approaches?
The infinite-sites model is not applicable to all species
There are many more recombination events in the history of the sample than the non-parametric methods can ever detect
Lack of mutations in the right places
Recombination events completely undetectable
HIV Subtype B (2kb segment)
HIV Subtype C (2kb segment)

16. Modelling recombination
Model-based approaches to learning about recombination allow us to ask more detailed questions than nonparametric approaches
What is the rate of recombination (as opposed to just the number of events)
Is the rate of recombination across a region constant?
Does gene A have a higher recombination rate than gene B?
What patterns of genetic diversity might I expect to see in other samples from the same (or different) population?
We need a model!

17. Adding recombination to the coalescent
Each generation, the probability of recombination between two loci is r, working in scaled time, this means that recombination occurs at rate r/2 per sequence where r = 4Ner
Recombination, mutation and coalescence occur independently:
Coalescence occurs as a Poisson process with rate n(n-1)/2
Recombination occurs as a Poisson process with rate nr/2
Mutations on edges added as a Poisson process with rate nq/2
The time until the next recombination or coalescence event is also a Poisson process with rate nr /2+ n(n-1)/2, and the probability that this next event is a recombination is

18. Recombination in non-ancestral material
Once a region has recombined, further recombination can occur in both ancestral lineages
However, recombination in non-ancestral DNA cannot in anyway influence patterns of diversity (under a neutral model)
We usually ignore such recombination events in the coalescent X X

19. Simulating histories with recombination

20. Properties of the ARG
Unlike the basic coalescent, there are few results about the effects of recombination on gene genealogies that we can derive analytically
For example, we cannot even calculate the expected number of recombination events in the history of a sequence
Though we can show it is less than infinity!
There are some useful results about how many recombination events we can see
The key is that only a small minority of recombination events that occur in the history of the sample can ever be directly detected by nonparametric methods
r=10, q=10
against log log sample size

21. Estimating the population recombination rate
The ideal inference procedure would calculate the likelihood of the data
Need to allow recombination rate to vary
….but full-likelihood inference is effectively impossible for anything but the simplest data sets (and models)
We need alternatives
Calculate the probability of some summary of the data (like ABC)
Approximate the coalescent model
Approximate the likelihood
The composite likelihood of Hudson (2001) approximates the likelihood of the full data by the product of the likelihoods for pairs of sites
Not the real likelihood!
Fast to calculate
Allows a variable recombination rate

22. Composite likelihood estimation of 4Ner: Hudson (2001)
DlnL
DlnL R R 15 7 1 2 4 3
Full likelihood
Composite-likelihood approximation
DlnL R

23. Fitting a variable recombination rate
Use a reversible-jump MCMC approach (Green 1995)
SNP positions
Cold
Split blocks
Hot
Merge blocks
Change block size
Change block rate

24. Acceptance rates
Hastings ratio
Composite likelihood ratio
Ratio of priors
Jacobian of partial derivatives relating changes in parameters to sampled random numbers
Include a prior on the number of change points that encourages smoothing

25. Broad scale validation: strong concordance between rates estimated from genetic variation and pedigrees
2Mb correlation between “Perlegen” and deCODE rates (Myers et al. 2005)

26. Fine-scale validation: strong concordance between fine-scale rate estimates from sperm and genetic variation
200kb region of human HLA
Rates estimated from sperm
Jeffreys et al (2001)
Rates estimated from genetic variation
McVean et al (2004)
In this region at least, human recombination clusters into 1-2kb wide hotspots
>90% of recombination in 6 hotspots
We have also developed a specific test for hotspots,
based on the same composite likelihood (likelihood ratio test)

27. Fine-scale rates across the human genome
Across chromosome12
Myers et al. (2005)
Throughout the genome, human recombination clusters into narrow hotspots
These explain LD breakdown sites

28. Data for ENR131, Chromosome 2q, Chinese and Japanese population sample (The International HapMap Consortium, Nature 2005)

29. Summary
Both non-parametric and model based approaches allow us to ask detailed questions about recombination from population genetic data
Recombination can be incorporated within the coalescent framework
The population recombination rate, r=4Ner, is the key quantity in determining the effect of recombination on genetic variation
Efficiently estimating recombination rates within a coalescent framework is difficult, but approximate methods have proved a powerful approach
Such methods have allowed us to successfully learn about recombination rates in humans and other species, and reveal “hotspots” across genomes