In humans the presence of chin and cheek dimples is dominant to the absence of dimples, and the ability to taste the compound PTC is dominant to the inability to taste the compound. Both traits are autosomal, and they are unlinked. The frequencies of alleles for dimples are D = 0.62 and d = 0.38. For tasting, the allele frequencies are T = 0.76 and t = 0.24.
Determine the frequency of genotypes for each gene and the frequency of each phenotype.

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with calculating the genotype frequencies for two unlinked autosomal traits (dimples and PTC tasting) using the given allele frequencies. Then, we will use these genotype frequencies to determine the phenotype frequencies for each trait.
2. Step 2: Use the Hardy-Weinberg principle to calculate the genotype frequencies for each gene. For dimples, the allele frequencies are D = 0.62 and d = 0.38. The Hardy-Weinberg equation is p² + 2pq + q² = 1, where p and q are the allele frequencies. Calculate the following: (1) Frequency of homozygous dominant (DD) = p² = (0.62)², (2) Frequency of heterozygous (Dd) = 2pq = 2(0.62)(0.38), and (3) Frequency of homozygous recessive (dd) = q² = (0.38)².
3. Step 3: Similarly, calculate the genotype frequencies for the PTC tasting gene. The allele frequencies are T = 0.76 and t = 0.24. Again, use the Hardy-Weinberg equation: (1) Frequency of homozygous dominant (TT) = p² = (0.76)², (2) Frequency of heterozygous (Tt) = 2pq = 2(0.76)(0.24), and (3) Frequency of homozygous recessive (tt) = q² = (0.24)².
4. Step 4: Determine the phenotype frequencies for each trait. For dimples, the dominant phenotype (presence of dimples) is expressed by both DD and Dd genotypes, while the recessive phenotype (absence of dimples) is expressed by the dd genotype. Add the frequencies of DD and Dd to find the frequency of the dominant phenotype, and use the frequency of dd for the recessive phenotype. Similarly, for PTC tasting, the dominant phenotype (ability to taste PTC) is expressed by TT and Tt genotypes, while the recessive phenotype (inability to taste PTC) is expressed by the tt genotype. Add the frequencies of TT and Tt for the dominant phenotype, and use the frequency of tt for the recessive phenotype.
5. Step 5: Summarize the results. You now have the genotype frequencies (DD, Dd, dd for dimples; TT, Tt, tt for PTC tasting) and the phenotype frequencies (presence vs. absence of dimples; ability vs. inability to taste PTC). These frequencies represent the genetic and phenotypic distribution in the population under Hardy-Weinberg equilibrium.

Key Concepts

Mendelian Genetics

Mendelian genetics is the study of how traits are inherited through generations based on the principles established by Gregor Mendel. It involves understanding dominant and recessive alleles, where dominant alleles mask the expression of recessive ones. This framework is essential for predicting genotype and phenotype frequencies in a population, particularly for traits governed by single genes.

Hardy-Weinberg Principle

The Hardy-Weinberg principle provides a mathematical model to calculate allele and genotype frequencies in a population under ideal conditions. It states that allele frequencies will remain constant from generation to generation in the absence of evolutionary influences. This principle is crucial for determining expected genotype frequencies based on known allele frequencies, especially for traits that are autosomal and unlinked.

Phenotype and Genotype Frequencies

Phenotype frequencies refer to the proportion of individuals in a population exhibiting a particular trait, while genotype frequencies refer to the proportion of different genetic combinations present. For traits governed by two alleles, these frequencies can be calculated using the allele frequencies and the principles of Mendelian inheritance, allowing for the prediction of how traits will manifest in a population.