5b - Comprehensive Notes on Paternity Testing

Introduction to Paternity Testing

• Overview of the lecture content: Conceptual understanding of paternity index analysis.

• Upcoming lectures will involve practical calculations using numbers.

Paternity Index (PI)

• Definition: Paternity index (PI) is a ratio of two competing hypotheses regarding paternity denoted as hypothesis X (true biological father) and hypothesis Y (unrelated male).

Key Concepts in Paternity Testing

• Genotype Basics: Focus on genotypes at a single locus for analysis.

  • Example Genotype Configuration:

  • Mother: AB

  • Father: CD

  • Child: AC

• Paternal Obligate: The allele that must be provided by the biological father, which in the example, is allele C from father.

Calculation of Paternity Index

Numerator (X)

• Assumption: Assumes the trio (mother, father, child) is a true biological family.

• **Components:

1. Frequency of Mother’s Genotype** (AB) in population = $2PQ$ where P is frequency of allele A and Q is frequency of allele B.

2. Frequency of Father’s Genotype (CD) in population = $2PQ$ for alleles C and D.

   3. Transmission Probabilities:

   • 50% chance for each allele being passed from both parents (mother heterozygous AB, father heterozygous CD).

   • Mother passes A or B; father passes C or D.

   • Therefore, transmission probabilities for each parent = 0.5 for their respective alleles.

Denominator (Y)

• Changes: The child is unrelated to the presumed father.

• Components:

  1. Frequency of mother’s genotype (AB): $2PQ$.

  2. Frequency of father's genotype (CD): $2PQ$.

  3. Transmission probabilities remain the same.

  • Paternal allele frequency (allele C) in population is also included.

• Paternity Index Simplification: Results in a simplified calculation of the paternity index, which becomes:

  • $PI = rac{1}{2 imes (frequency ext{ of paternal obligate})}$ .

Variations in Paternity Testing Scenarios

Case: Suspected Father is Homozygous

• **Example Genotype Configuration:

  • Mother:** AB

  • Child: AC

  • Suspected Father: CC (homozygous for C).

• New Calculation for Numerator:

1. Mother’s genotype frequency: $2PQ.$

2. Child’s Genotype Frequency = $P^2$ (frequency of C since father is homozygous).

3. Transmission: 0.5 (mother) and 1 (father, since homozygous).

• Paternity Index Result:

  • $PI = rac{1}{(frequency ext{ of paternal obligate})}$.

Case: Mother and Child Share Genotype

• Example Genotype Configuration:

  • Mother: AB

  • Child: AB

  • Suspected Father: BC.

• Key Observations:

  • Mother must pass A; B must come from father.

  • Numerator Calculation: Similar to previous examples with 2PQ for both parents and transmission of 0.5.

Denominator Analysis

• Complications:

  • Uncertainty about which allele came from the father if both alleles are shared.

• Resulting Calculation:

  • Paternity index emerges as $PI = 0.5 imes (frequency A) imes (frequency B)$.

Mutation Rate Implications

Importance of Mutation Rates

• Context: Mutation events can complicate paternity analysis and indexing.

• Example:

  • Mother: AB

  • Father: CD

  • Child: AE.

• Assuming Mutation: The E allele is considered a paternal obligate due to a possible mutation.

Key Calculative Components for Mutations

1. Numerator:

   • Standard genotype frequencies (2PQ) multiplied by transmission probabilities.

2. Power of Exclusion (PoE):

   • Defined as the frequency of individuals in the population who lack the given allele.

3. Denominator Considerations:

   • Incorporates PoE alongside maternal transmission probabilities.

Final Calculation with Mutation

• Paternity Index adjust: $PI = rac{(mutation rate)}{(Power of Exclusion)}$.

• The mutation rate varies widely, typically for STRs, occurring 1 in 1000 to 1 in 10000 meiosis.

Conclusion and Future Lectures

• Discussion on Random Man Not Excluded (RMNE): Refers to the frequency of random men not being excluded as biological fathers, opposing the PoE.

• Culmination: The understanding of paternity index is critical for genetic testing, whether for human, wildlife, or domestic animals.

• Next Steps: Upcoming practical lecture on applying these concepts with data and working examples utilizing cheat sheets.