Additional STR allele frequency information can be added to improve the analysis in Problem 8. The frequency of D8S1179₁₂ = 0.12. The frequency of D16S539₁₈ = 0.08 and of D16S539₂₀ = 0.21. Lastly, D18S51₁₉ = 0.13 and D18S51₂₀ = 0.10. Combine the allele frequency information for these three STR genes with the information used in Problem 8 to calculate the frequency of the genotype for six of the STR genes.

Verified step by step guidance

1. Identify the alleles for each of the three STR loci given: D8S1179 with allele 12 (frequency 0.12), D16S539 with alleles 18 (frequency 0.08) and 20 (frequency 0.21), and D18S51 with alleles 19 (frequency 0.13) and 20 (frequency 0.10).
2. Recall the allele frequencies from Problem 8 for the other three STR loci to have a total of six STR loci for the genotype frequency calculation.
3. Determine the genotype frequencies for each locus by applying the Hardy-Weinberg principle: for homozygous genotypes, use $p^2$ where $p$ is the allele frequency; for heterozygous genotypes, use $2pq$ where $p$ and $q$ are the frequencies of the two different alleles.
4. Calculate the genotype frequency for each of the six STR loci separately using the allele frequencies, including the new alleles provided for the three loci in this problem.
5. Multiply the genotype frequencies of all six STR loci together to obtain the combined genotype frequency for the six STR genes, assuming independence between loci.

Key Concepts

Short Tandem Repeats (STRs)

STRs are repeating sequences of 2-6 base pairs of DNA that vary in length among individuals. They are highly polymorphic markers used in genetic profiling and forensic analysis. Each STR locus can have multiple alleles, and their frequencies in a population help calculate genotype probabilities.

Allele Frequency and Genotype Frequency

Allele frequency is the proportion of a specific allele among all alleles at a genetic locus in a population. Genotype frequency refers to the proportion of individuals with a particular combination of alleles. Calculating genotype frequency often involves combining allele frequencies, assuming Hardy-Weinberg equilibrium.

Multiplying Independent Loci Frequencies

When calculating the combined genotype frequency across multiple STR loci, the frequencies at each locus are multiplied together if loci are independent. This product gives the overall probability of observing a specific multi-locus genotype, which is essential in forensic and population genetics analyses.