Question

Having correctly established the \(\mathrm{F}_{2}\) ratio in Problem 18 , predict the \(\mathrm{F}_{2}\) ratio of a "dihybrid" cross involving two independently assorting characteristics (e.g., \(\mathrm{P}_{1}=W W W W A A A A \times\) wwwwaaaa).

Short answer

Question: Predict the F2 ratio of a dihybrid cross involving two independently assorting characteristics. The P1 generation contains the genotypes WWWWAAAA and wwwwaaaa. Answer: The F2 ratio of the dihybrid cross involving two independently assorting characteristics is 9:3:3:1 (Dominant W and A phenotypes : Dominant W and Recessive a phenotypes : Recessive w and Dominant A phenotypes : Recessive w and a phenotypes).

Step-by-step solution

Determine the F1 genotypes

Cross the two P1 individuals to produce the F1 generation. For each characteristic, one allele from each parent will be passed onto their offspring. The F1 generation will be: WwAa (the offspring receives one W and one w allele for the W characteristic, and one A and one a allele for the A characteristic).

Determine the F2 genotypes

Cross two F1 individuals (WwAa x WwAa) to produce the F2 generation using the forked-line method or Punnett square method. Forked-line method: - For the W characteristic: Ww x Ww -> 1 WW : 2 Ww : 1 ww (in the ratio 1:2:1) - For the A characteristic: Aa x Aa -> 1 AA : 2 Aa : 1 aa (in the ratio 1:2:1) Combine both ratios in the F2 generation: 1(WWAA) : 2(WWAa) : 1(WWaa) : 2(WwAA) : 4(WwAa) : 2(Wwaa) : 1(wwAA) : 2(wwAa) : 1(wwaa) The F2 genotypes ratio is: 1:2:1:2:4:2:1:2:1

Determine the phenotypic ratio in F2

Based on the genotypes ratio in F2, we will deduce the phenotypic ratio. WW: Dominant W phenotype Ww: Dominant W phenotype ww: Recessive w phenotype AA: Dominant A phenotype Aa: Dominant A phenotype aa: Recessive a phenotype Dominant W and A phenotypes: 1(WWAA) + 2(WWAa) + 2(WwAA) + 4(WwAa) = 9 Dominant W and Recessive a phenotypes: 1(WWaa) + 2(Wwaa) = 3 Recessive w and Dominant A phenotypes: 1(wwAA) + 2(wwAa) = 3 Recessive w and a phenotypes: 1(wwaa) = 1 The F2 phenotypic ratio is: 9:3:3:1 (Dominant W and A phenotypes : Dominant W and Recessive a phenotypes : Recessive w and Dominant A phenotypes : Recessive w and a phenotypes).

Key concepts

F2 generation

The F2 generation refers to the second filial generation, or in simpler terms, the 'grandchildren' of the original breeding pair, known as the P1 or parental generation. In the context of a dihybrid cross, which follows two traits, the F2 generation results from crossing two F1 individuals that have heterozygous genotypes for both traits.

Continuing from the cited exercise example, when F1 plants with a genotype of WwAa (having one 'W' and one 'w' allele for the first trait, and one 'A' and one 'a' allele for the second trait) are crossed, the F2 generation exhibits a variety of genotypes and phenotypes dictated by the rules of Mendelian inheritance.

Punnett square

A Punnett square is a diagram that is used to predict the genotype and phenotype frequencies of offspring from a genetic cross. This tool allows students and geneticists to visualize how alleles from each parent combine and segregate. It's a grid that represents all possible combinations of the male's gametes on one side and the female's gametes on the other. For a dihybrid cross, which looks at two traits, the Punnett square becomes a 4x4 grid, showcasing all possible allele combinations for the F2 generation. It's particularly useful for visual learners as it organizes complex genetic information into an easy-to-understand format.

Forked-line method

The forked-line method, also known as the branch diagram, is an alternative to the Punnett square and tends to be more efficient for analyzing dihybrid crosses or when considering more than two traits. Starting with one trait and drawing branches for each allele combination, you then add branches for the next trait, essentially creating a 'family tree' for alleles. By multiplying the probabilities along each branch path, you can calculate the likelihood of specific genotypes and phenotypes occurring in the F2 generation without constructing a large Punnett square.

Phenotypic ratio

The phenotypic ratio describes the pattern of different visible traits (phenotypes) appearing in the F2 generation of a genetic cross. This ratio reflects the varying expressions of traits dictated by the underlying genotypes. In the exercise's dihybrid cross, the F2 phenotypic ratio of 9:3:3:1 results from the combination of dominant and recessive traits. Here, a 9:3:3:1 ratio indicates that nine individuals will have both dominant traits, three will have one dominant and one recessive trait of the first kind, three will have one recessive and one dominant trait of the second kind, and one will have both recessive traits. It's a signature ratio for dihybrid crosses with two unlinked genes where both genes have complete dominance.

Genotypic ratio

In contrast, the genotypic ratio provides insight into the genetic makeup (genotype) of the F2 generation. Instead of focusing on what traits appear, it's all about the combinations of alleles inherited. The genotypic ratio from the exercise's dihybrid cross is 1:2:1:2:4:2:1:2:1. This breakdown indicates how frequently each genotype occurs, from double dominant (WWAA) to double recessive (wwaa), demonstrating the diversity of genetic combinations that can result from a dihybrid cross involving independent assortment.

Mendelian inheritance

Finally, Mendelian inheritance is the way traits are passed down from parents to offspring through genes, as first described by Gregor Mendel through his work with pea plants. Mendelian inheritance emphasizes principles like the segregation of alleles and independent assortment. Allele segregation suggests that each parent's two alleles for each trait separate during reproductive cell formation, with each gamete receiving only one allele. Independent assortment means the alleles of one trait separate independently from the alleles of another trait. This concept perfectly encapsulates the exercise, where a dihybrid cross results in the 9:3:3:1 phenotypic ratio for the F2 generation, predicting the inheritance patterns of two traits controlled by two different gene pairs.