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OTHER TOPICS
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SINGLE CONTRIBUTORS
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Profile and Match Probabilities
Profile Probability:
Pr(AA) = p2A + θpA(1 − pA) ≤ 2pA
Pr(AB) = 2pApB − 2θpApB ≤ 2pApB
Match Probability:
Pr(AA|AA) =[2θ + (1 − θ)pA][3θ + (1 − θ)pA]
(1 + θ)(1 + 2θ)
Pr(AB|AB) =2[θ + (1 − θ)pA][θ + (1 − θ)pB]
(1 + θ)(1 + 2θ)
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Relatives
Pr(AA|AA) = k2 + k1pA + k0p2A
Pr(AB|AB) = k2 +1
2(pA + pB)k1 + 2k0pApB
For unilineal relatives, k2 = 0, k1 + k0 = 1 and kinship θ = k1/4:
Pr(AA|AA) = p2A + 4θpA(1 − pA)
Pr(AB|AB) = 2pApB + 2θ(pA + pB − 4pApB)
For full-sibs, k1 = k0 = 1/4, k1 = 1/2:
Pr(AA|AA) =1
4(1 + pA)2
Pr(AB|AB) =1
4(1 + pA + pB + 2pApB)
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Relatives with Population Structure
Pr(AA|AA) = k2 + k12θ + (1 − θ)pA
1 + θ
+ k0[2θ + (1 − θ)pA][3θ + (1 − θ)pA]
(1 + θ)(1 + 2θ)
Pr(AB|AB) = k2 + k12θ + (1 − θ)(pA + pB)
2(1 + θ)
+ k02[θ + (1 − θ)pA][θ + (1 − θ)pB]
(1 + θ)(1 + 2θ)
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Paternity Index with Homozygous Mother
GM : Mother’s genotype; GC : Child’s genotype;AM : Maternal allele; AP : Paternal allele;GAF : Alleged father’s genotype; PI: Paternity index.
GM GC AM AP GAF PI
AA AA A A AA 1+3θ4θ+(1−θ)pA
AB 1+3θ2[3θ+(1−θ)pA]
AB A B BB 1+3θ2θ+(1−θ)pB
AB 1+3θ2[θ+(1−θ)pB
BC 1+3θ2[θ+(1−θ)pB]
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Paternity Index with Heterozygous Mother
GM : Mother’s genotype; GC : Child’s genotype;
AM : Maternal allele; AP : Paternal allele;
GAF : Alleged father’s genotype; PI: Paternity index.
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GM GC AM AP GAF PI
AB AA A A AA 1+3θ3θ+(1−θ)pA
AB 1+3θ2[2θ+(1−θ)pA]
AC A C CC 1+3θ2θ+(1−θ)pC
AC 1+3θ2[θ+(1−θ)pC ]
CD 1+3θ2[θ+(1−θ)pC ]
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GENETIC GENEALOGY
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Identity by Descent
Two alleles from the same ancestral allele are identical by de-
scent.
Individuals that share alleles identical by descent are related.
Individuals may share 0,1 or 2 pairs of alleles identical by descent:
e.g. they may have both, either or neither of their maternal and
paternal alleles identical by descent. The probabilities of these
three states are k0, k1, k2.
The kinship coefficient of two people is θ = k2/2 + k1/4.
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STR Kinship Coefficients
Relationship k2 k1 k0 θ = 12k2 + 1
4k1
Identical twins 1 0 0 12
Full sibs 14
12
14
14
Parent-child 0 1 0 14
Double first cousins 116
38
916
18
Half sibs∗ 0 12
12
18
First cousins 0 14
34
116
nth cousins 0(
14
)n1 −
(
14
)n (
14
)n+1
Unrelated 0 0 1 0∗ Also grandparent-grandchild and avuncular (e.g. uncle-niece).
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STR Kinship Coefficients
These kinship coefficients with forensic STR panels are not good
for distinguishing different types of relatives beyond half sibs.
Difficult even to separate half sibs from full sibs.
SNP panels, with up to a million SNPs allow distinguishing even
distant cousins. A different statistical measure is used, that takes
(lack of) recombination into account.
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Recombination
One Morgan is the length along a chromosome in which 1 recombinationevent is expected to occur. The human genome has a total map length of36M, meaning that each chromosome is expected to have 1-2 recombinationevents per generation. A centi-Morgan (cM) is one-hundreth of a Morgan.
Wegmann D et al. 2011. Nature Genetics 43:84
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First Cousins
G H
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HHHHHHHHHHHHj
�������������G C D H@
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a b c d
X Y
X, Y are first cousins, and are expected to share identical alleles
from one grandparent with probability 1/16.
But most parts of their genomes will not share identical alleles
and some blocks will have identity across the block.
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The Shared cM Project
https://thegeneticgenealogist.com/
https://thegeneticgenealogist.com/2017/08/26/august-2017-update-
to-the-shared-cm-project/
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The Shared cM Project
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The Shared cM Project
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The Shared cM Project
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Henn et al., 2012
“To infer identity by descent, we scanned each pair of genomes
for long runs of genotype pairs that lack opposite homozygotes.
We define inferred IBDhalf as the sum of the lengths of genomic
segments where two individuals share DNA identical by state for
at least one of the homologous chromosomes. This method is
computationally feasible in large sample sets .”
Henn BL, Hon L, Macpherson JM, Eriksson N, Saxonov S, Pe’er I, Moun-
tain JL. 2012. Cryptic distant relatives are common in both isolated and
cosmopolitan genetic samples. PLoS One 7:e34267.
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Henn et al., 2012
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Henn et al., 2012
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Henn et al., 2012
We inferred that two individuals share DNA IBD from unphased
data. We inferred boundaries of IBD by comparing two indi-
viduals’ genotypes at a locus and identifying SNPs where one
individuals genotype is homozygous for one allele and the other
individual’s genotype is homozygous for a second allele. By char-
acterizing stretches that lacked these opposite homozygotes, we
defined regions that contain at least half IBD between two in-
dividuals. That is, an IBDhalf segment was characterized by
a series of alleles that were identical by state for at least one
of the homologous chromosomes in a given pair of individuals.
We define IBDhalf as the sum of the lengths of genomic seg-
ments where two individuals are inferred to share DNA identical
by descent for at least one of the homologous chromosomes.
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Henn et al., 2012
We additionally enforced two criteria to increase our confidence
that a region represents DNA that is IBD: first, the region is
minimally 5 cM in length and second, it contains at least 400
genotyped SNPs that are homozygous in at least one of the two
individuals being compared, ensuring that there is both sufficient
genotype coverage and genetic distance defining the IBD region.
Finally, we accepted a comparison as IBD if the longest segment
in the comparison was at least 7 cM.”
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Henn et al., 2012
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Genealogy Search
Suppose a GEDMatch search for an evidence profile E reveals
two first cousins C1, C2.
E and C1 have two of their four grandparents in common. Think
of the four grandparents of C1 and trace their descendants D1:
these are the parents, uncles, aunts and cousins of C1.
E and C2 have two of their four grandparents in common. Think
of the four grandparents of C2 and trace their descendants D2:
these are the parents, uncles, aunts and cousins of C2.
The source of E belongs to both D1 and D2.
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CEU Example
A CEU individual in the 1000Genomes project appears to have
parents who were first cousins. Using 1,000 windows of 1000
SNPs, chromosome 22 shows:
0 200 400 600 800 1000
850
950
Chr 22 for a CEU Individual
Window
Matches
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