Question

Three gene pairs located on separate autosomes determine flower color and shape as well as plant height. The first pair exhibits incomplete dominance, where color can be red, pink (the heterozygote), or white. The second pair leads to the dominant personate or recessive peloric flower shape, while the third gene pair produces either the dominant tall trait or the recessive dwarf trait. Homozygous plants that are red, personate, and tall are crossed with those that are white, peloric, and dwarf. Determine the \(F_{1}\) genotype(s) and phenotype(s). If the \(F_{1}\) plants are inter. bred, what proportion of the offspring will exhibit the same phenotype as the \(\mathrm{P}_{1}\) plants?

Short answer

Answer: When the F1 plants are interbred, the proportion of offspring exhibiting the same phenotype as the P1 plants is 3/64.

Step-by-step solution

Determine the genotypes of the P1 plants

We have the following information about the P1 plants: 1. Homozygous red (incomplete dominance) 2. Dominant personate flower shape (dominant-recessive) 3. Dominant tall plant height (dominant-recessive) Based on this information, we can determine the genotypes of the P1 plants: - For flower color: Homozygous red, so RR - For flower shape: Dominant personate, so PP - For plant height: Dominant tall, so TT The P1 genotype is therefore RR PP TT. The cross is between plants that are red, personate, and tall (RR PP TT) and plants that are white, peloric, and dwarf. Based on the given information: - For flower color: white (incomplete dominance), so rr - For flower shape: recessive peloric, so pp - For plant height: recessive dwarf, so tt The other P1 genotype is thus rr pp tt.

Determine the potential genotype combinations of the F1 generation

To find the genotypes and phenotypes of the F1 generation, we will set up three separate Punnett squares, one for each gene pair. Flower color (RR x rr): R|r R|r -+-+-- R|r R|r Flower shape (PP x pp): P|p P|p -+-+-- P|p P|p Plant height (TT x tt): T|t T|t -+-+-- T|t T|t

Determine the F1 genotype(s) and phenotype(s)

From the step 2, we can see that the F1 genotypes are: - For flower color: All offspring will be Rr (pink). - For flower shape: All offspring will be Pp (personate). - For plant height: All offspring will be Tt (tall). So, the F1 genotype(s) are Rr Pp Tt, with the phenotype being pink, personate, and tall.

Find the proportion of offspring with the P1 phenotype when F1 plants are interbred

Now, let's assume the F1 plants are interbred. We need to determine the proportion of offspring that will exhibit the same phenotype as the P1 plants (red, personate, tall for one P1 plant and white, peloric, dwarf for the other P1 plant). First, we'll create Punnett squares for the F1 generation for each gene pair. Flower color (Rr x Rr): R | R| r| r --+--+--+ r | Rr|Rr|rr --+--+--+-- r | Rr|Rr|rr Flower shape (Pp x Pp): P | P| p --+--+-- p | Pp|pp Plant height (Tt x Tt): T | T| t --+--+-- t | Tt|tt Now, let's find the proportions for each phenotype. 1. For red, personate, and tall (RR PP TT): Flower color: 1/4 (RR) Flower shape: 1/2 (PP) Plant height: 1/4 (TT) The probability of the red, personate, and tall phenotype will be: \(\frac{1}{4}\times\frac{1}{2}\times\frac{1}{4}=\frac{1}{32}\) 2. For white, peloric, and dwarf (rr pp tt): Flower color: 1/4 (rr) Flower shape: 1/4 (pp) Plant height: 1/4 (tt) The probability of the white, peloric, and dwarf phenotype will be: \(\frac{1}{4}\times\frac{1}{4}\times\frac{1}{4}=\frac{1}{64}\) When the F1 plants are interbred, the proportion of offspring exhibiting the same phenotype as the P1 plants will be \(\frac{1}{32}+\frac{1}{64}=\frac{3}{64}\).

Key concepts

Incomplete Dominance

Imagine mixing red and white paint and ending up with pink—this is similar to the genetic concept of incomplete dominance. Incomplete dominance occurs when the progeny displays an intermediate phenotype, a mix between the traits of both parents.
This differs from complete dominance, where the dominant allele completely masks the recessive one. In the context of the given exercise, flower color exemplifies incomplete dominance. We have three genotypes:

• RR: Red Flowers
• Rr: Pink Flowers
• rr: White Flowers

The heterozygous condition (Rr) results in a phenotype that is neither red nor white but instead a blend—pink.

Understanding incomplete dominance helps in predictions about the appearance of offspring in genetic crosses, especially when you're accustomed to thinking in terms of complete dominance. By knowing that the F1 generation will be a blend, we can set expectations clearly, as seen in the exercise: Rr crosses leading to all pink offspring.

Punnett Squares

Punnett Squares serve as a handy visual tool that helps to predict the possible genetic outcomes of a cross-breeding experiment. In the exercise, they were used to figure out the genotypes of the F1 generation.

Each square segment represents a possible genotype for the offspring. We take the alleles from one parent and place them across one axis (usually horizontal) and do the same for the other parent vertically. The resulting squares inside show all potential combinations. For example, when dealing with one of the traits in the exercise like flower color, the Punnett Square would have R and r across the top and left, showcasing how they combine: - The R cut across the r from both axes can combine into Rr offspring. - Similarly, other combinations are RR and rr. What shines here is the prediction power of these squares. Once laid down, one can easily deduce the likelihood of each genotype appearing in the next generation.

In summary, a Punnett Square acts as a genetic map for breeding scenarios, compactly organizing information to facilitate easy understanding of genetic probabilities.

Phenotype

Phenotype refers to the observable traits of an organism arising from the interaction of its genotype with the environment. This can include physical appearance, physiological processes, and even behavior.

The exercise focuses on specific phenotypes: flower color, flower shape, and plant height. These traits are determined by the genetic combinations inherited from the parents. For example, let's take flower color. Even if the genetic makeup involves multiple alleles, what we see—red, pink, or white—is the phenotype. In the case of incomplete dominance, the mix of red and white alleles results in an intermediate pink phenotype. Phenotypes are essential to understanding genetics as they represent the endpoint of genetic coding. They are the final expression of the genetic information and often what breeders and researchers observe directly. Knowing the genotype might predict the phenotype under certain conditions, but remember that environmental factors can also play a role in how these phenotypic traits actually present themselves in the real world. In essence, while genotypes give us a code, phenotypes reveal how those codes play out visibly in nature.