Lecture 14: Population Assignment and Individual Identity

October 8, 2015

Last Time

Sample calculation of FST

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/mech4710/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?

,)|(

)|()|,(

2

121 HGP

HGPLRGHHL

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/geneclass.html)

for m loci

m

kkPP

1

2lilk pP

for homozygote AiAi in population l at locus k

ljlilk ppP 2for heterozygote AiAj in population l at locus k

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

Based on likelihood analysis, fish was purchased rather than caught in lake

Lake Saimaa Market

--log10 of likelihood that the observed genotype could occur in Lake Saimaa

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))

Most are amplified in a single multiplex reaction and analyzed in a single capillary

Very high “exclusion power” (ability to differentiate individuals)

http://www.cstl.nist.gov/div831/strbase//mlt_abiid.htm

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?

,)|(

)|()|,(

2

121 HGP

HGPLRGHHL

What is H1 and what is H2?

Match Probability

Probability of observing a genotype at locus k by chance in population is a function of allele frequencies:

for m loci

m

kkPP

1

2ik pP

Homozygote

jik ppP 2Heterozygote

Assumes unlinked (independent loci) and Hardy-Weinberg equilibrium

Probability of Identity

Probability 2 randomly selected individuals have same profile at locus k:

i ji

jii

ikID pppP 24 )2(

Homozygotes Heterozygotes

for m loci

m

kkIDPP

1

Exclusion Probability (E): E=1-P

Which allele frequency to use? Human populations show

some level of substructuring

FST generally < 0.03

Challenge is to choose proper ethnic group and account for gene flow from other groups

http://books.nap.edu/openbook/0309053951/gifmid/95.gif

Illinois Caucasian

Georgia Caucasian

U.S. Black

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

jiSTiii ppFpppP 2])1([' 2

Homozygotes Heterozygotes

Why is it ‘conservative’ (from the standpoint of proving a match) to ignore substructure for

heterozygotes?

T

STST H

HHF

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

Heterozygotes

)21(4

1 2iiksibhoID ppP

2 alleles IBD1 allele IBD

0 alleles IBD

)21(4

1jijiksibheID ppppP

General Probability of Identity for Full Sibs:

Homozygotes 2 alleles IBD

0 alleles IBD

i iii

iiksibID pppP

2

224

2

11

4

1

Probability of identity for full sibs

i iii

iiksibID pppP

2

224

2

11

4

1

For a locus with 5 alleles, each at a frequency of 0.2:PID = 0.072PIDsib = 0.368

i ji

jii

ikID pppP 24 )2(

Probability of identity unrelated individuals

What is minimum probability of identity for full sibs?

i iii

iiksibID pppP

2

224

2

11

4

1

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