Question

In cultivated flowers, called "stocks," pigment is controlled by two independently assorting alleles. When the dominant allele \(\mathrm{A}\) is present at one locus, \(\mathrm{C}_{-}\) at the other locus leads to red; cc leads to cream. The double recessive aa at the first locus produces a white flower regardless of alleles at the second locus. (a) If a homozygous red stock is crossed with a white variety, what phenotypic and genotypic ratios are expected in the \(\mathrm{F}_{1}\) and \(\mathrm{F}_{2}\) generations? (b) If a cross between a red stock and a white stock produces progeny of all three phenotypes, what are the genotypes of the parents? (c) Come up with a possible mechanism to explain this phenotypic action.

Short answer

In summary: (a) When a homozygous red stock (AABB) is crossed with a white variety (aacc), the F1 generation has a phenotypic ratio of 1 red (AaCc) and a genotypic ratio of 1 AaCc. In the F2 generation, the phenotypic ratio is 3:1:3 (red: cream: white) and the genotypic ratio is 1:2:1:2:4:2:1:2:1. (b) In a cross between a red stock and a white stock that produces progeny of all three phenotypes, the genotypes of the parents are AaCc (red) and aaCc (white) and their progeny show the phenotypic ratio of 1:1:2 (red: cream: white). (c) A possible mechanism to explain the phenotypic action is that the A allele at the first locus activates the pigment pathway, and the C allele at the second locus determines pigment production (red or cream). In the absence of the A allele, no pigment pathway is activated, resulting in a white flower.

Step-by-step solution

Identify the genotype of the parents

A homozygous red stock would have the genotype AABB (with A being the allele for red). Since a white variety has aa for the first locus, its genotype must be aacc (with C- not affecting the phenotypes in this case).

Calculate the F1 generation's offspring genotypes

The cross between AABB and aacc can be represented as: Parent 1: AABB Parent 2: aacc In the F1 generation, all progeny will have the genotype AaCc, where the progeny inherited one allele from each parent: a red phenotype.

Calculate the F2 generation's offspring genotypes and phenotypes

Let's examine the cross between two F1 offspring (AaCc x AaCc). We will use the forked-line method to track each locus separately and then combine them: Locus 1: Aa x Aa - AA: 1/4 - Aa: 1/2 - aa: 1/4 Locus 2: Cc x Cc - CC: 1/4 - Cc: 1/2 - cc: 1/4 Let's combine the phenotypes, using the information given: - Red phenotype: AAC-, AaCC, AaCc = (1/4 + 1/2) * 1/4 + (1/4 * 1/2) = 3/8 - Cream phenotype: Aacc = (1/2) * 1/4 = 1/8 - White phenotype: aaC-, aacc = 1/4 * 3/4 = 3/16

Calculate the genotypic ratios

The genotypic ratio in F2 generation is: - AABB: 1/4 * 1/4 = 1/16 - AABb: 1/4 * 1/2 = 1/8 - AAbb: 1/4 * 1/4 = 1/16 - AaBB: 1/2 * 1/4 = 1/8 - AaBb: 1/2 * 1/2 = 1/4 - Aabb: 1/2 * 1/4 = 1/8 - aaBB: 1/4 * 1/4 = 1/16 - aaBb: 1/4 * 1/2 = 1/8 - aabb: 1/4 * 1/4 = 1/16 So, in the F2 generation, the phenotypic ratio is 3:1:3 (red: cream: white) and the genotypic ratio is 1:2:1:2:4:2:1:2:1. #b) Genotypes of the parents for all three phenotypes in the progeny#

Consider the phenotypes of the parents

Since the cross between a red stock and a white stock produces progeny of all three phenotypes, let one parent be red (Parent 1) and the other parent be white (Parent 2).

Identify the genotypes based on phenotypes

Given the available information, the genotype of Parent 1 must be AaCc or AaCC since both would result in a red phenotype. Parent 2 must have the genotype aaCc since it produces a white flower.

Check if the identified genotypes yield the expected phenotypes

Let's calculate the progeny genotypes and phenotypes of the cross between AaCc and aaCc: Locus 1: Aa x aa - Aa: 1 - aa: 0 Locus 2: Cc x Cc - CC: 1/4 - Cc: 1/2 - cc: 1/4 When combined, the phenotypes are: - Red: AaCC = 1/4 - Cream: Aacc = 1/4 - White: aaC-, aacc = 1/2 * 1 + 1/4 = 3/4 Thus, when Parent 1 is AaCc, and Parent 2 is aaCc, their progeny show all three phenotypes with the ratio 1:1:2 (red: cream: white). #c) Possible mechanism to explain the phenotypic action# One possible mechanism to explain this phenotypic action is that the A allele at the first locus is responsible for activating the pigment pathway, while the C allele at the second locus is responsible for the specific pigment production (red or cream). When the plant has at least one A allele, the pigment pathway is activated. If it also has at least one C allele, it produces a red pigment. When no C allele is present, the pathway produces a cream pigment. If the plant lacks the A allele (and has the double recessive aa), it does not activate the pigment pathway. In such a case, the presence or absence of the C allele doesn't matter as no pigment is produced, and the flower is white.

Key concepts

Mendelian Genetics

Mendelian genetics is the foundation for understanding how traits are inherited through generations. Named after the 'father of genetics', Gregor Mendel, who first discovered the principles through breeding experiments with pea plants, this area of genetics focuses on how genes and their associated traits are transmitted. It introduces key concepts such as alleles, where each gene has multiple forms, dominance, where one allele can mask the presence of another, and the difference between homozygous (same alleles) and heterozygous (different alleles).

In the context of the exercise, Mendelian genetics explains the inheritance of flower pigment, underscoring the importance of dominant and recessive alleles. For example, a dominant allele A results in red pigment while the dominant C allele when paired with A leads to a cream color. The white color is expressed only when both loci have recessive alleles (aa). Understanding these principles allows us to predict the floral color outcomes in stock flowers' progeny.

Genotypic and Phenotypic Ratios

The distinction between genotype and phenotype is fundamental in genetics. The genotype refers to the genetic makeup of an organism — the specific alleles an individual carries. On the other hand, the phenotype is the observable characteristic or trait, like flower color. Students need to grasp the concept of genotypic and phenotypic ratios to predict the outcomes of genetic crosses.

In our flower example, by crossing a homozygous red stock (AABB) with a homozygous white stock (aacc), the F1 generation will all have the genotype AaCc, thus all expressing red (phenotype). The F2 generation, however, will exhibit a variety of genotypes and phenotypes. The phenotypic ratio (3:1:3) results from the combination of genotypic outcomes and their corresponding phenotypes — 3 parts red, 1 part cream, and 3 parts white. Students can visualize these ratios to better understand the underlying genotypic combinations that result in the observed traits of the flowers.

Independent Assortment

Independent assortment is a principle described by Mendel stating that the genes for different traits can segregate independently during the formation of gametes. This means different traits are inherited separately from one another, allowing for a vast combination of genetic outcomes that contribute to the diversity we see in living organisms.

In our exercise, the inheritance of flower pigment is controlled by two independently assorting alleles, A/a and C/c. This independent assortment means that an allele of one gene (A/a) can combine randomly with an allele of another gene (C/c) during gamete formation. We can demonstrate this with the typical 9:3:3:1 phenotypic ratio seen in a dihybrid cross, like the one encountered when tracking the inheritance of flower color for the A and C loci. Understanding independent assortment clarifies how the combination of alleles from multiple genes can influence the phenotype, which, in the case of our flower genetics exercise, results in red, cream, or white flowers.