Problem 8 - Biology: The Unity and Diversity of Life

Question

Assuming complete dominance, crosses between two dihybrid \(\mathrm{F}_{1}\) pea plants, which are offspring from a cross \(A A B B \times a a b b,\) result in \(F_{2}\) phenotype ratios of ___. a. 1: 2: 1 b. 3: 1 c. 1: 1: 1: 1 d. 9: 3: 3: 1

Step-by-Step Solution

Answer

The \(F_2\) phenotype ratio is 9:3:3:1.

Step 1: Define the P Generation

Start with the parent generation (P generation) cross. We have two plants: one with the genotype \(AA BB\) and another with \(aa bb\). This is a complete dominance situation, so the A allele is dominant to a, and B is dominant to b.

Step 2: Produce F1 Generation

The offspring from this cross would all be heterozygous for both traits. This means each \(F_1\) plant has the genotype \(AaBb\).

Step 3: Define the F2 Cross

The \(F_1\) dihybrid plants are crossed, i.e., \(AaBb \times AaBb\). According to Mendelian genetics, we rigorously follow the dihybrid cross to find the phenotypic ratio.

Step 4: Set Up the Punnett Square for F2

Each \(F_1\) parent can produce four types of gametes: \(AB, Ab, aB, ab\). We construct a 4x4 Punnett square to predict the offspring from these gamete combinations.

Step 5: Analyze Results from the Punnett Square

Fill in the Punnett square to see all possible genotypes for \(F_2\). This results in phenotypes for both traits being presented: dominant for both (A-B-), dominant for first (A-bb), dominant for second (aaB-), and recessive for both (aabb).

Step 6: Determine the Phenotypic Ratio

Count the phenotype combinations from the Punnett square. For a dihybrid cross with complete dominance, the phenotypic ratio of the \(F_2\) generation should be \(9:3:3:1\). The 9 corresponds to dominant for both traits, the 3s are for each trait being dominant in isolation, and 1 for recessive in both.

Key Concepts

Dihybrid Cross

A dihybrid cross is a fundamental concept in Mendelian genetics that dives into the inheritance patterns of two independent traits. Imagine, for example, a plant where seed shape and seed color are the traits of interest. Each trait can be traced back to specific alleles: dominant and recessive.
To understand dihybrid crosses, consider a parent generation (P) plant with round yellow seeds crossed with another plant having wrinkled green seeds, with genotypes such as \(AA BB\) and \(aa bb\), respectively. This cross results in offspring, termed \(F_1\), that are dihybrids. All \(F_1\) offspring are heterozygous for seed shape and color, with the phenotype of round yellow seeds represented by the genotype \(AaBb\).

• In a dihybrid cross, each \(F_1\) plant produces four types of gametes - combinations of alleles for both traits: \(AB, Ab, aB, ab\).
• When these gametes combine in a Punnett square, it creates a 4x4 grid illustrating all possible genotypes of the \(F_2\) generation.

By analyzing this square, the fascinating patters of inheritance reveal themselves, showcasing genetic variance and possibilities.

Phenotypic Ratio

Phenotypic ratio refers to the relative number of offspring manifesting each possible form of the traits under consideration in the \(F_2\) generation. In the dihybrid cross, each trait follows the complete dominance pattern, resulting in distinct phenotype combinations.

• The golden ratio for a dihybrid cross with complete dominance is \(9:3:3:1\).
• This ratio depicts the dominant phenotype for both traits appearing the most frequent, symbolized as \(9\) (e.g., round and yellow seeds).
• The \(3\)'s in the ratio indicate offspring dominant in only one trait, either round green or wrinkled yellow.
• The \(1\) represents the recessive phenotype in both traits, hence wrinkled green.

Through careful counting within a 4x4 Punnett square, you can discover this ratio emerges regularly in dihybrid crosses, a hallmark of Mendel's principles in action.

Complete Dominance

Complete dominance is a straightforward genetic phenomena where the presence of a single dominant allele in a gene pair masks the effect of a recessive allele. Using the pea plant traits as an example, the presence of an \(A\) (signifying round seeds) overshadowes the effect of an \(a\) (rats wrinkled seeds), ensuring the phenotype remains round.

• Complete dominance ensures that only one allele needs to be dominant for the trait to be expressed.
• This single dominant allele results in no blending, preserving distinct and separate trait manifestations between generations.

In the dihybrid cross, this principle ensures the consistent expression of combinations such as round over wrinkled and yellow over green, shaping the recognizable patterns in the 9:3:3:1 phenotypic ratio. Understanding this concept is key for deciphering genetic predictions and patterns.