The frequencies of the four alleles contributed to the child by possible father F1 in Problem 7 are 0.18, 0.23, 0.13, and 0.14. Calculate the Combined Paternity Index (CPI) for the four genes in this analysis.

Verified step by step guidance

1. Understand that the Combined Paternity Index (CPI) is the product of the Paternity Indices (PIs) for each gene or allele tested. The PI for each gene is calculated based on the allele frequency contributed by the alleged father.
2. Recall that the Paternity Index (PI) for a single allele is calculated as the reciprocal of the allele frequency if the alleged father is homozygous for that allele, or as 1 divided by twice the allele frequency if the alleged father is heterozygous. Since the problem only provides allele frequencies, assume the simplest case where PI = 1 / allele frequency for each allele.
3. Write down the allele frequencies given: $\mathrm{f\_1}=0.18,\mathrm{f\_2}=0.23,\mathrm{f\_3}=0.13,\mathrm{f\_4}=0.14$.
4. Calculate the PI for each allele using the formula $\mathrm{PI\_i}=\; 1\; /\mathrm{f\_i}$. This means you will compute $PI\_1\; =\; 1/0.18$, $PI\_2\; =\; 1/0.23$, $PI\_3\; =\; 1/0.13$, and $PI\_4\; =\; 1/0.14$.
5. Multiply all the individual PIs together to get the Combined Paternity Index: $CPI\; =\; PI\_1\; \backslash times\; PI\_2\; \backslash times\; PI\_3\; \backslash times\; PI\_4$. This product gives the overall likelihood ratio supporting paternity based on the four alleles.

Key Concepts

Allele Frequency

Allele frequency refers to how common a specific allele is within a population. It is expressed as a proportion or percentage and is crucial in genetic analyses to estimate the likelihood of an individual carrying a particular allele. In paternity testing, allele frequencies help calculate the probability that a random individual from the population could contribute the observed alleles.

Paternity Index (PI)

The Paternity Index is a likelihood ratio that compares the probability of the alleged father transmitting a specific allele to the child versus a random man from the population. It is calculated for each genetic marker and reflects how strongly the genetic evidence supports paternity. A higher PI indicates stronger evidence that the tested man is the biological father.

Combined Paternity Index (CPI)

The Combined Paternity Index is the product of individual Paternity Indices across multiple genetic loci. It aggregates the evidence from all tested markers to provide an overall likelihood ratio supporting paternity. The CPI is used to calculate the probability of paternity, with higher values indicating stronger genetic evidence that the tested man is the biological father.