Transcript ppt
Lecture 14: Population Assignment and
Individual Identity
October 8, 2015
Last Time
u Sample calculation of FST
u Defining populations on genetic criteria:
introduction to Structure
Structure Program
One of the most widely-used programs in population
genetics (original paper cited >15,000 times since 2000)
Very flexible model can determine:
The most likely number of uniform groups
(populations, K)
The genomic composition of each individual
(admixture coefficients)
Possible population of origin
Structure is Hierarchical: Groups reveal more substructure when examined
separately
Rosenberg et al. 2002 Science 298: 2381-2385
Today
Principal Components Analysis
Genotype likelihoods
Population assignment
Forensic identification
Alternative clustering method: Principal
Components Analysis
Structure is very computationally intensive
Often no clear best-supported K-value
Alternative is to use traditional multivariate
statistics to find uniform groups
Principal Components Analysis is most commonly
used algorithm
EIGENSOFT (PCA, Patterson et al., 2006; PloS
Genetics 2:e190).
Eckert, Population Structure, 5-Aug-2008 49
Principal Components Analysis
Efficient way to summarize multivariate data like genotypes
Each axis passes through maximum variation in data, explains a
component of the variation
http://www.mech.uq.edu.au/courses/mech
4710/pca/s1.htm
Once you have populations defined, can you assign a
migrant individual to their population of origin?
Human Population Assignment with SNP
Assayed 500,000 SNP genotypes for 3,192 Europeans
Used Principal Components Analysis to ordinate samples in space
High correspondence betweeen sample ordination and geographic
origin of samples
Individuals assigned to
populations of origin with
high accuracy
Novembre et al. 2008 Nature 456:98
Population Assignment: Likelihood
Assume you find skin cells and blood under fingernails of
a murder victim
Victim had major debts with the Sicilian mafia as well as
the Chinese mafia
Can population assignment help to focus investigation?
P (G | H 1 )
L( H 1 , H 2 | G ) LR
,
P (G | H 2 )
What is H1 and what is H2?
Population Assignment: Likelihood
"Assignment Tests" based on allele
frequencies in source populations and
genetic composition of individuals
Likelihood-Based Approaches
Calculate likelihood that individual
genotype originated in particular
population
Assume Hardy-Weinberg and linkage
equilibria
Genotype frequencies corrected for
presence of sampled individual
Usually reported as log10 likelihood for
origin in given population relative to
other population
Implemented in ‘GENECLASS’ program
(http://www.montpellier.inra.fr/URLB/geneclass/g
eneclass.html)
Pk l p
2
i l
for homozygote AiAi in
population l at locus k
Pk l 2 pil p jl
for heterozygote AiAj in
population l at locus k
m
P Pk
k 1
for m loci
Power of Population Assignment using
Likelihood
Assignment success depends on:
Number of markers used
Polymorphism of markers
Number of possible source populations
Differentiation of populations
Accuracy of allele frequency estimations
Rules of Thumb (Cornuet et al. 1999) for 100% assignment success,
for 10 reference populations need:
30 to 50 reference individuals per population
10 microsatellite loci
HE > 0.6
FST > 0.1
Population Assignment Example: A Fish Story
Fishing competition on Lake
Saimaa in Southeast Finland
Contestant allegedly caught a 5.5
kg salmon, much larger than
usual for the lake
Compared fish from the lake to
fish from local markets
(originating from Norway and
Baltic sea)
7 microsatellites
Lake Saimaa
Based on likelihood analysis, fish
was purchased rather than
caught in lake
-log10 of likelihood that the observed
genotype could occur in Lake Saimaa
-
Market
Genetic Typing in Forensics
Highly polymorphic loci provide unique ‘fingerprint’
for each individual
Tie suspects to blood stains, semen, skin cells, hair
Revolutionized criminal justice in last 20 years
Also used in disasters and forensic anthropology
Principles of population genetics must be applied in
calculating and interpreting probability of identity
Markers in Genetic Typing
Standard set of 13 core loci for
forensics: CODIS (Combined DNA
Index System)
Sets of highly polymorphic
microsatellites (also called VNTR
(Variable Number of Tandem
Repeats), STR (Short Tandem
Repeat) or SSR (Simple Sequence
Repeat))
http://www.cstl.nist.gov/div831/strbase//mlt_abiid.htm
Most are amplified in a single multiplex reaction and analyzed in a
single capillary
Very high “exclusion power” (ability to differentiate individuals)
Individual Identity: Likelihood
Assume you find skin cells and blood under fingernails of
a murder victim
A hitman for the Sicilian mafia is seen exiting the
apartment
You gather DNA evidence from the skin cells and from
the suspect
They have identical genotypes
What is the likelihood that the evidence came from the
suspect?
P (G | H )
L( H 1 , H 2 | G ) LR
What is H1 and what is H2?
1
P (G | H 2 )
,
Match Probability
Probability of observing a genotype at locus k by
chance in population is a function of allele frequencies:
Pk p
Pk 2 pi p j
Homozygote
Heterozygote
2
i
m
P Pk
for m loci
k 1
Assumes unlinked (independent loci) and HardyWeinberg equilibrium
Probability of Identity
Probability 2 randomly selected individuals have same
profile at locus k:
PIDk pi4 (2 pi p j ) 2
i
Homozygotes
i
i j
Heterozygotes
m
P PIDk
for m loci
k 1
Exclusion Probability (E): E=1-P
Which allele frequency to use?
Human populations show
some level of
substructuring
Illinois Caucasian
FST generally < 0.03
Challenge is to choose
proper ethnic group and
account for gene flow
from other groups
Georgia Caucasian
U.S. Black
http://books.nap.edu/openbook/0309053951/gifmid/95.gif
Substructure in human populations
GST is quite high among the 5 major groups of human populations
for CODIS microsatellites
Relatively low within groups, but not 0!
NRC (1996) recommendations
Use population that provides highest probability of
observing the genotype (unless other information is
known)
Correct homozygous genotypes for substructure within
selected population (e.g., Native Americans, hispanics,
African Americans, caucasians, Asian Americans)
No correction for heterozygotes
P' [ pi2 pi (1 pi ) FST ] 2 pi p j
Homozygotes
Heterozygotes
Why is it ‘conservative’ (from the standpoint of
proving a match) to ignore substructure for
heterozygotes?
HT H S
FST
HT
H S = HT (1- FST )
What if the slimy mob defense attorney argues that
the most likely perpetrator is the mob hitman’s
brother, who has conveniently “disappeared”?
Does the general match probability apply to near
relatives?
Probability of identity for full sibs
Homozygotes
PIDhosibk
2 alleles IBD
1
2
(1 2 pi pi )
4
0 alleles IBD
2 alleles IBD
1 allele IBD
Heterozygotes
0 alleles IBD
1
PIDhesibk (1 pi p j 2 pi p j )
4
General Probability of Identity for Full Sibs:
PIDsibk
2
1
1
4
2
2
1 pi pi pi
4
i
2 i
i
Probability of identity for full sibs
PIDsibk
2
1
1
4
2
2
1 pi pi pi
4
i
2 i
i
Probability of identity unrelated individuals
PIDk pi4 (2 pi p j ) 2
i
i
i j
For a locus with 5 alleles, each at a frequency of 0.2:
PID = 0.072
PIDsib = 0.368
What is minimum probability of
identity for full sibs?
PIDsibk
2
1
1
4
2
2
1 pi pi pi
4
i
2 i
i
Example: World Trade Center Victims
Match victims using
DNA collected from
toothbrushes, hair
brushes, or relatives
Exact matches not
guaranteed
Why not?
Use likelihood to
match samples to
victims