A plant line with reduced fertility comes to the attention of a plant breeder who observes that seed pods often contain a mixture of viable seeds that can be planted to produce new plants and withered seeds that cannot be sprouted. The breeder examines numerous seed pods in the reduced fertility line and counts 622 viable seeds and 204 nonviable seeds.
What single-gene mechanism best explains the breeder's observation?

Verified step by step guidance

1. The first step is to recognize that the problem involves a genetic mechanism that affects seed viability. The observation of both viable and nonviable seeds in the same seed pod suggests a genetic phenomenon related to segregation or lethality.
2. Next, consider the possibility of a single-gene mechanism. A likely explanation is that the reduced fertility is caused by a recessive lethal allele. This means that individuals homozygous for the lethal allele (genotype: $\mathrm{aa}$) do not survive, while heterozygous ($\mathrm{Aa}$) and homozygous dominant ($\mathrm{AA}$) individuals are viable.
3. To test this hypothesis, calculate the expected genotypic ratios from a heterozygous cross ($\mathrm{Aa}\times \mathrm{Aa}$). The Punnett square for this cross predicts the following genotypes: $\mathrm{AA}$, $\mathrm{Aa}$, $\mathrm{Aa}$, and $\mathrm{aa}$, with a ratio of 1:2:1.
4. Since the $\mathrm{aa}$ genotype is lethal, only the $\mathrm{AA}$ and $\mathrm{Aa}$ genotypes contribute to viable seeds. This results in a phenotypic ratio of 3 viable seeds (1 $\mathrm{AA}$ + 2 $\mathrm{Aa}$) to 1 nonviable seed ($\mathrm{aa}$).
5. Finally, compare the observed data (622 viable seeds and 204 nonviable seeds) to the expected 3:1 ratio. Use a chi-square test to determine if the observed data fits the expected ratio, which would confirm the hypothesis of a recessive lethal allele as the single-gene mechanism.

Key Concepts

Mendelian Inheritance

Mendelian inheritance refers to the principles of heredity established by Gregor Mendel, which describe how traits are passed from parents to offspring through discrete units called genes. In this context, the observation of viable and nonviable seeds suggests a single-gene trait, where one allele may be dominant and responsible for seed viability, while the other allele leads to nonviable seeds.

Genetic Ratio

The genetic ratio is a way to express the expected proportions of different genotypes or phenotypes resulting from a genetic cross. In this case, the ratio of viable to nonviable seeds (622:204) can be analyzed to determine if it aligns with a typical Mendelian ratio, such as 3:1, indicating a single-gene trait with one dominant and one recessive allele.

Allelic Interaction

Allelic interaction refers to how different alleles of a gene interact to influence a trait. In the scenario presented, the presence of both viable and nonviable seeds suggests that the gene in question may exhibit incomplete dominance or a simple dominant-recessive relationship, where the dominant allele produces viable seeds and the recessive allele results in nonviable seeds.