1. Lecture 15: Individual Identity and Paternity Analysis
October 16, 2015

2. Last Time Principal Components Analysis Genotype likelihoods
Population assignment
Forensic identification

3. 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

4. Recent Article on Forensic DNA
“The Dark Side of DNA Databases” in The Atlantic October 8, 2015
Or google “The Atlantic DNA Database”
A 70 yr old wheelchair-bound man was implicated in a 40-year old rape case based on matching 9 loci in a CODIS profile
Defense attorney obtained a screen of all 9-locus matches within the 65,000 person database: 122 matches observed

5. Recent Article on Forensic DNA
Based on probability of identity calculation, there is only a 1 in 754 million chance that two randomly-selected individuals would share the same 9-locus CODIS profile
Can the defense attorney legitimately claim that this exonerates her client?
Why were so many matches found in such a small database?

6. Today Population structure and gene flow
Introduction to paternity analysis

7. Island Model of Population Structure
Expected Identity by Descent at time t, no migration: qm q0 m
IBD due to prior inbreeding
IBD due to random mating
Incorporating migration:
If population size on islands is small, and/or gene flow (m) is low, drift will occur
where m is proportion of N that are migrants each generation

8. Migration-Drift Equilibrium
This aproach is VERY widely used to calculate number of migrants per generation
It is an APPROXIMATION of EQUILIBRIUM conditions under the ISLAND MODEL
Only holds for low Nm
FST=0.01, approximation is Nm = 24.8
If N=50, actual Nm is 14.6
At migration-drift equilibrium:
FST = ft = ft-1
Assuming m2 is small, and ignoring 2m in numerator and denominator:

9. Differentiation of Subpopulationsqm q0 m
Subpopulations will be more uniform with high levels of gene flow and/or high N
Nm>1 homogenizes populations
Nm<<1 results in fixation of alternate alleles and ultimate differentiation (FST=1)
At drift-migration equilibrium:

10. Limitations of FST
FST is a long, integrated look into the evolutionary/ecological history of a population: may not represent status quo
Assumptions of the model frequently violated:
Island model unrealistic
Selection is often an important factor
Mutation may not be negligible
Sampling error!

11. Alternatives to FST Direct measurements of movement: mark-recapture
Genetic structure of paternal and maternal gametes only
Chloroplast and mitochondrial DNA
Pollen gametes
Parentage analysis: direct determination of the parents of particular offspring through DNA fingerprinting

12. 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?

13. 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

14. Paternity Exclusion
YES NO
Locus 1
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
Locus 2
Locus 3

15. Paternity Exclusion Analysis
Possible outcomes:
Male
Female ?
Consequences:
Only one male cannot be excluded
More than one male cannot be excluded
All males are excluded
Paternity is assigned
Analyze more loci
Conclude there is migration from external sources

16. Sweet Simulation of Paternity Analysis
Collected seeds (baby) from a hermaphroditic, self-incompatible plant
Which of the candidate hermaphrodites (you) fathered the seeds?
Six loci with varying numbers of alleles
Organize candy into loci (next slide)
Determine paternal contribution to offspring by subtracting maternal alleles
Exclude potential fathers that don’t have paternal allele
Nonexcluded candidate is the father!

17. Loci

18. Mother and Child Maternal Alleles Paternal Alleles Mom Child skittle
jellybean

19. Probabilities of Paternity Exclusion, Single Locus, 2 alleles, codominant
The paternity exclusion probability is the sum of the probability of all exclusionary combinations
Hedrick 2005
Probability of a falsely accused male of not matching for at least one of m loci:
See Chakraborty et al Genetics 118:527 for a more general calculation of exclusion power

20. 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

21. 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

22. 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)

23. Advantages and Disadvantages of Likelihood
Flexibility: can be extended in many ways
Compensate for errors in genotyping
Incorporate factors influencing mating success: fecundity, distance, and direction
Compensates for lack of exclusion power
Fractional paternity
Disadvantages
Often results in ambiguous paternities
Difficult to determine proper cutoff for LOD score

24. 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