An organism of the genotype AaBbCc was testcrossed to a triply recessive organism (aabbcc). The genotypes of the progeny are presented in the following table.

If these three genes were all assorting independently, how many genotypic and phenotypic classes would result in the offspring, and in what proportion, assuming simple dominance and recessiveness in each gene pair?

Verified step by step guidance

1. Step 1: Identify the number of genes and their alleles involved. Here, there are three genes (A, B, and C), each with two alleles: dominant (A, B, C) and recessive (a, b, c). The testcross is between AaBbCc and aabbcc.
2. Step 2: Determine the number of possible genotypic classes if the genes assort independently. Since each gene has two possible alleles from the heterozygous parent (A or a, B or b, C or c), the total number of genotypic combinations is \$2^3 = 8$.
3. Step 3: Determine the number of phenotypic classes. Because each gene exhibits simple dominance, each gene locus can produce two phenotypes: dominant (presence of at least one dominant allele) or recessive (homozygous recessive). Therefore, the total number of phenotypic classes is also \$2^3 = 8$.
4. Step 4: Calculate the expected proportion of each genotypic class in the offspring. Since the testcross parent is homozygous recessive for all genes, the genotype of each offspring depends solely on the allele contributed by the heterozygous parent. Each gene segregates independently with a 1:1 ratio of dominant to recessive alleles, so the expected frequency of each genotype is \(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}\).
5. Step 5: Calculate the expected proportion of each phenotypic class. Since each gene shows dominance, the phenotype depends on whether the dominant allele is present. The probability of showing the dominant phenotype for each gene is \(\frac{1}{2}\), and recessive is \(\frac{1}{2}\). Thus, the expected frequency of each phenotypic class is also \(\frac{1}{8}\).

Key Concepts

Independent Assortment

Independent assortment is a principle stating that genes for different traits segregate independently during gamete formation. For three gene pairs, this means each gene's alleles combine randomly, producing offspring with all possible genotype combinations in predictable ratios.

Testcross and Genotypic Classes

A testcross involves crossing an organism with a homozygous recessive individual to reveal the genotype of the first organism. The number of genotypic classes in offspring reflects the combinations of alleles inherited, which can be counted to determine genetic variation.

Phenotypic Ratios and Dominance

Phenotypic ratios depend on dominant and recessive allele interactions. With simple dominance, heterozygous and homozygous dominant genotypes show the dominant phenotype, while only homozygous recessive shows the recessive phenotype, affecting the number of observable phenotypic classes.