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

Last Time Principal Components Analysis Genotype likelihoods Population assignment Forensic identification

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

Recent Article on Forensic DNA “The Dark Side of DNA Databases” in The Atlantic October 8, 2015 http://www.theatlantic.com/science/archive/2015/10/the-dark-side-of-dna-databases/408709/ 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

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?

Today Population structure and gene flow Introduction to paternity analysis

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

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:

Differentiation of Subpopulations qm 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:

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!

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

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?

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 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

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

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!

Loci

Mother and Child Maternal Alleles Paternal Alleles Mom Child skittle jellybean

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. 1988 Genetics 118:527 for a more general calculation of exclusion power

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

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 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

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