Evolutionary Genetics: Part 7 Recombination –Linkage ...
Transcript of Evolutionary Genetics: Part 7 Recombination –Linkage ...
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Evolutionary Genetics: Part 7
Recombination – Linkage Disequilibrium
S. peruvianum
S. chilense
Winter Semester 2012-2013
Prof Aurélien TellierFG Populationsgenetik
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Color code
Color code:
Red = Important result or definition
Purple: exercise to do
Green: some bits of maths
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Population genetics: 4 evolutionary forces
random genomic processes
(mutation, duplication, recombination, gene conversion)
natural
selection
random demographic
process (drift)
random spatial
process (migration)
molecular diversity
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Recombination
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Recombination and crossing over
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Physical map
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Genetic map
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Independent segregation (Mendel’s law)
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Non-independent segregation
This is genetic linkage
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Non-independent segregation
� Recombination rate
� In general:
� The recombination rate of two loci on different chromosomes = 0.5
� The recombination rate between loci on same chromosome 0<ρ<0.5
� The recombination rate of two loci on the same chromosome increases
monotonically with distance
� BUT there are recombination hotspots (or cold spots) in the genome
number of recombined gametes
total number of gametesρ =
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Non-independent segregation
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Recombination and crossing-over
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Genetic map length - Morgan
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Model without recombination
A
B
Your
chromosomes
A
B
A
B
Inherited from
your mother
From your grandfather or
your grandmother
Inherited from
your father
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Model with recombination
A
B
Your
chromosomes
A
B
A
b
a
B
Inherited from
your mother
From your
grandfather
From your
grandmother
Inherited from
your father
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Model with recombination
� So two loci on the same chromosome can come
� From a single parent if there is no recombination
� From two parents if there is recombination
� With recombination, the chromosome of your parents are mosaics of
pieces of chromosomes from their parents
� We define ρ as the probability that a recombination event happens
P[two loci have the same parent] = 1-ρ
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Model with recombination
� we define ρ as the probability that a recombination event happens
� P[two loci have the same parent] = 1-ρ
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Coalescence with recombination
� Take one linage
� Tracing it back in time, recombination events can happen
� Recombination happens with probability ρ at every generation
P[recombination event t generation ago]=ρ(1-ρ)t-1
� This is again a geometric (exponential) distribution
� Backward in time:
� There can be
� coalescence of two lineages
� or recombination event
� recombination creates two lineages backward in time: one with locus A
and the other with locus B
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Coalescence with recombination
� The number of lineages is increased by recombination, so it can take a while to
find the MRCA
� However, if the number of lineages increases (k), this will increase also the rate
of coalescence, so an MRCA will be found
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Coalescence with recombination
� Along the genome, a serie of sites have a coalescent tree
� In fact, recombination slowly breaks link between sites
� The higher the recombination, the more independent are the loci
� Virtually, every locus has its own MRCA
� If recombination rates vary along the genome, this means that loci have
different recombination in their tree
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Coalescence without recombination
� Along the genome, ONLY ONE tree for all loci
� The higher the recombination, the more independent are the loci
� Recombination is important, otherwise, each chromosome would be only one
data point (= one tree)
� This is the case for: Y-chromosome in humans, Mitochondrial DNA,
Chloroplast DNA where there is no recombination (= one tree for all loci)
� Why is this a problem if no recombination?
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Coalescence without recombination
� Why is this a problem if no recombination?
� This is the case for: Y-chromosome in humans, Mitochondrial DNA,
Chloroplast DNA where there is no recombination (= one tree for all loci)
� Understanding the evolution in the genome requires to have independent
information about ONE evolutionary process (= different trees which come from
the same evolutionary scenario)
� Information comes from the variance between loci
� If all loci are linked, what is neutral evolution? If some genes are under
selection?
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Coalescence with recombination
� How far along the genome do you have to go to find a recombination event?
� define r as the per site (bp) recombination rate
� if two sites are distant of d, the recombination rate ρ = rd
� the coalescence rate is 1/2N, we want at least 50% chance to have a
recombination event
P[recombination before coalescence] =
� this can be simplified as 4Nrd > 1 or d >1/4Nr
� For humans, Ne=104 and r= 10-8, we get d > 2500bp
� In Drosophila where Ne=106, the distance is 100 times shorter
2 11 0.5
2 1/ 2 4 1
rd
rd N Nrd= − ≥
+ +
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Recombination and data
Linkage disequilibrium
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Recombination in data: 4 gamete rule
� There is one rule to recognize if recombination happened
� the four gamete rule
� Did recombination happen on the right or on the left of the 2nd site?
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Recombination in data: LD
� Linkage Disequilibrium (LD) is measured as D
� Two loci A and B with alleles A1 and A2, B1 and B2
� Frequencies are: A1B1 = p11 ; A1B2 = p12 ; A2B1 = p21 ; A2B2 =p22
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Recombination in data: LD
� The A1B1 and A2B2 gametes are called coupling gametes
� The A1B2 and A1B2 gametes are called the repulsion gametes
� LD is a measure of the excess of coupling over repulsion gametes
� If D>0, there are more coupling gametes than expected at equilibrium
� If D<0, there are more repulsion gametes than expected
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Recombination in data: LD
� Linkage Disequilibrium (LD)
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Recombination in data: LD
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Recombination in data: LD
� Linkage Disequilibrium (LD) is measured as D and r2
� The change in D in a single generation is: ∆D = –ρD
� After t generations:
� Dt = (1 –ρ)t D0
� This is again and again a geometric function of time
�
�This means that the ultimate state of the population is D=0
� BUT there is memory of LD in time
� LD decreases away from a given site in the genome also following a
geometric function
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Recombination in data: haplotypes
� Linkage Disequilibrium (LD) can be seen in the presence of haplotypes
� Example: (Plos Genetics 2006)
� Do you expect long or short haplotypes under recombination?
� If genes can show different recombination rates, what does this
mean for haplotypes?
� Length and frequency of haplotypes are important signatures to
detect deviation from neutral evolution!!!
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Recombination in data
� Using DnaSP
� Using the TNFSF5 and the droso files
� Look at the haplotypes ( Generate => Haplotype Data File)
� Why are haplotypes important to study recombination? What about the
infos on distance between sites?
� Can you look at recombination? Measure of LD, r2 and also the number
of four-gamete rule
� Use Analysis => Recombination
� Decay of LD from sites?