Lecture 16: Individual Identity and Paternity Analysis

March 7, 2014

Last Time

Interpretation of F-statistics

More on the Structure program

Principal Components Analysis

Population assignment

Individual identity (in lab)

Today

Population assignment examples

More on forensic evidence and individual identity

Introduction to paternity analysis

Population Assignment: Likelihood "Assignment Tests" based on allele

frequencies in source populations and genetic composition of individuals

for m loci

2lilk pP

for homozygote AiAi in population l at locus k

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

,)|(

)|()|,(

2

121 HGP

HGPLRGHHL

Individual likelihood often summarized as:

-log10(P(G|Hn))

Low numbers mean higher probability of Hn

Likelihoods can be plotted against each other

Carmichael et al. 2001 Mol Ecol 10:2787

Population Assignment Example: Wolf Populations in Northwest Territories Wolf populations sampled on island and

mainland populations in Canadian Northwest Territories

Immigrants detected on mainland (black circles) from Banks Island (white circles)

-log likelihood from Banks Island

-log

likel

ihoo

d fr

om M

ainl

and

Population Assignment Example:Fish Stories

Fishing competition on Lake Saimaa in Southeast Finland

Contestant allegedly caught a 5.5 kg salmon, much larger than usual for the lake

Officials 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

-

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

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

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

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

A series of little NBA prospects are born to ardent basketball fans in every city with an NBA team. The mothers regularly allege that the fathers are NBA stars from visiting teams. The “players” deny this

allegation.

Can this be resolved using molecular markers and population genetics methodologies?

Paternity Exclusion Analysis

Determine multilocus genotypes of all mothers, offspring, and potential fathers

Determine paternal gamete by “subtracting” maternal genotype from that of each offspring.

Infer paternity by comparing the multilocus genotype of all gametes to those of all potential males in the population

Assign paternity if all potential males, except one, can be excluded on the basis of genetic incompatibility with the observed pollen gamete genotype

Unsampled males must be considered

Locus 1

Locus 2

Locus 3

YES NO YES YES NO

NO

NO YES YES YES

YES YESNONO

NO

First step is to determine paternal contribution based on seedling alleles that do not match mother

Notice for locus 3 both alleles match mother, so there are two potential paternal contributions

Male 3 is the putative father because he is the only one that matches paternal contributions at all loci

Paternity Exclusion

Parentage Analysis: Paternity Exclusion

Determine multilocus genotypes of all mothers, offspring, and potential fathers

Determine paternal gamete by “subtracting” maternal genotype from that of each offspring.

Infer paternity by comparing the multilocus genotype of all gametes to those of all potential males in the population

Assign paternity if all potential males, except one, can be excluded on the basis of genetic incompatibility with the observed pollen gamete genotype

Unsampled males must be considered

Paternity Exclusion Analysis

Only one male cannot be excluded

More than one male cannot be excluded

All males are excluded

Possible outcomes:

Paternity is assigned

Analyze more loci

Conclude there is migration from external sources

Consequences:Male

Female

Male

MaleFemale

Male

Male

MaleFemale

Male

?

Probabilities of Paternity Exclusion, Single Locus, 2 alleles, codominant The paternity exclusion probability is the sum of the probability of all exclusionary combinations

)1(Pr: 2121 ppppSum k

m

kk

1

)Pr1(1Pr

See Chakraborty et al. 1988 Genetics 118:527 for a more general calculation of exclusion power

Probability of a falsely accused male of not matching for at least one of m loci:

Hedrick 2005

Alleles versus Loci For a given number of alleles: one locus with many alleles provides more exclusion

power than many loci with few alleles

10 loci, 2 alleles, Pr = 0.875

1 locus, 20 alleles, Pr=0.898

Uniform allele frequencies provide more power

Characteristics of an ideal genetic marker for paternity analysis

Highly polymorphic, (i.e. with many alleles)

Codominant

Reliable

Low cost

Easy to use for genotyping large numbers of individuals

Mendelian or paternal inheritance

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

2345678910

23

45

67

Shortcomings of Paternity Exclusion

Requiring exact matches for potential fathers is excessively stringent

Mutation

Genotyping error

Multiple males may match, but probability of match may differ substantially

No built-in way to deal with cryptic gene flow: case when male matches, but unsampled male may also match

Type I error: wrong father assigned paternity)

Advantages and Disadvantages of Likelihood

Advantages:

Flexibility: can be extended in many ways

- Compensate for errors in genotyping- Incorporate factors influencing mating success: fecundity,

distance, and directionCompensates for lack of exclusion power

- Fractional paternity Disadvantages

Often results in ambiguous paternities

Difficult to determine proper cutoff for LOD score

Summary

Direct assessment of movement is best way to measure gene flow

Parentage analysis is powerful approach to track movements of mates retrospectively

Paternity exclusion is straightforward to apply but may lack power and is confounded by genotyping error

Likelihood-based approaches can be more flexible, but also provide ambiguous answers when power is lacking