Flower position, stem length, and seed shape are three characters that Mendel studied. Each is controlled by an independently assorting gene and has dominant and recessive expression as indicated in Table 14.1.





If a plant that is heterozygous for all three characters is allowed to self-fertilize, what proportion of the offspring would you expect to be each of the following? (Note: Use the rules of probability instead of a huge Punnett square.)
a. Homozygous for the three dominant traits
b. Homozygous for the three recessive traits
c. Heterozygous for all three characters
d. Homozygous for axial and tall, heterozygous for seed shape

Verified step by step guidance

1. Identify the genotypes for each trait: For flower position, axial (A) is dominant over terminal (a). For stem length, tall (T) is dominant over dwarf (t). For seed shape, round (R) is dominant over wrinkled (r). A heterozygous plant for all three traits would have the genotype AaTtRr.
2. Use the rules of probability to determine the proportion of offspring for each scenario. For each trait, calculate the probability of being homozygous dominant, homozygous recessive, or heterozygous. Since the genes assort independently, multiply the probabilities for each trait to find the overall probability for the combination of traits.
3. For part a, calculate the probability of being homozygous dominant (AA, TT, RR). The probability of AA is 1/4, TT is 1/4, and RR is 1/4. Multiply these probabilities together to find the overall probability for homozygous dominant.
4. For part b, calculate the probability of being homozygous recessive (aa, tt, rr). The probability of aa is 1/4, tt is 1/4, and rr is 1/4. Multiply these probabilities together to find the overall probability for homozygous recessive.
5. For part c, calculate the probability of being heterozygous for all three characters (Aa, Tt, Rr). The probability of Aa is 1/2, Tt is 1/2, and Rr is 1/2. Multiply these probabilities together to find the overall probability for heterozygous for all three characters.

Key Concepts

Mendelian Genetics

Mendelian genetics refers to the principles of heredity discovered by Gregor Mendel, which include the laws of segregation and independent assortment. These laws explain how traits are inherited through dominant and recessive alleles, and how genes for different traits segregate independently during gamete formation, leading to genetic variation.

Independent Assortment

Independent assortment is a key principle of Mendelian genetics stating that genes for different traits are inherited independently of each other. This occurs during meiosis when homologous chromosomes are randomly distributed to gametes, allowing for various combinations of traits in offspring, which is crucial for calculating probabilities in genetic crosses.

Probability in Genetics

Probability in genetics involves using mathematical principles to predict the likelihood of specific genotypes and phenotypes in offspring. By applying the rules of probability, such as multiplication and addition rules, one can calculate the expected proportions of different genetic combinations without constructing extensive Punnett squares, especially in complex crosses.