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Ch. 14 - Mendel and the Gene Idea
Chapter 14, Problem 5

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

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Identify the genotypes for each trait: Let's denote the dominant alleles as A, B, C and the recessive alleles as a, b, c. For a plant that is heterozygous for all three characters, the genotype for each trait will be Aa, Bb, and Cc.
Determine the gamete combinations: Since each gene assort independently, the plant can produce gametes with all combinations of alleles. The possible gametes are ABC, ABc, AbC, Abc, aBC, aBc, abC, abc, each with equal probability of 1/8.
Calculate the probability for each case: a. Homozygous for the three dominant traits (AAA, BBB, CCC) - The probability of forming an AA, BB, and CC genotype from Aa x Aa, Bb x Bb, and Cc x Cc respectively is (1/4) * (1/4) * (1/4) = 1/64. b. Homozygous for the three recessive traits (aaa, bbb, ccc) - Similarly, the probability is (1/4) * (1/4) * (1/4) = 1/64. c. Heterozygous for all three characters (Aa, Bb, Cc) - The probability for each heterozygous pairing is (1/2) * (1/2) * (1/2) = 1/8. d. Homozygous for axial and tall, heterozygous for seed shape (AA, BB, Cc) - The probability is (1/4) * (1/4) * (1/2) = 1/32.
Summarize the expected proportions: a. 1/64 for homozygous dominant for all traits, b. 1/64 for homozygous recessive for all traits, c. 1/8 for heterozygous for all traits, d. 1/32 for homozygous axial and tall, heterozygous for seed shape.
Apply the results to predict offspring distribution: When the heterozygous plant self-fertilizes, the offspring will have the following proportions based on the calculated probabilities: 1/64 will be homozygous dominant for all traits, 1/64 will be homozygous recessive for all traits, 1/8 will be heterozygous for all traits, and 1/32 will be homozygous for axial and tall, heterozygous for seed shape.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 traits mask the expression of recessive ones. Mendel's laws of segregation and independent assortment explain how alleles segregate during gamete formation and how different traits are inherited independently.
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Genotype and Phenotype

The genotype refers to the genetic makeup of an organism, specifically the alleles it carries for a particular trait, while the phenotype is the observable expression of those traits. For example, a plant may have a genotype of 'Tt' for tallness (where 'T' is tall and 't' is short), resulting in a phenotype of tall. Understanding the relationship between genotype and phenotype is crucial for predicting the traits of offspring.
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Probability in Genetics

Probability in genetics is used to predict the likelihood of certain genotypes and phenotypes in offspring based on parental genotypes. By applying the rules of probability, such as the multiplication and addition rules, one can calculate the expected ratios of different genetic combinations without constructing a full Punnett square. This approach simplifies the analysis of multiple traits, especially when dealing with independent assortment.
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