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Chapter 4: Problem 6

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 \(P_{1}\) genotype(s) and phenotype(s). If the \(F_{1}\) plants are interbred, what proportion of the offspring will exhibit the same phenotype as the \(F_{1}\) plants?

Short Answer

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Answer: 9/32

Step by step solution

01

Define genotype and phenotype symbols

Let's assign symbols to each gene and phenotype: Flower color: Incomplete dominance - Red (R鈧丷鈧�) - Pink (R鈧丷鈧�) - White (R鈧俁鈧�) Flower shape: Dominant personate and recessive peloric - Personate (P鈧�) - Peloric (P鈧�) Plant height: Dominant tall and recessive dwarf - Tall (T鈧�) - Dwarf (T鈧�)
02

Identify the P鈧� genotypes and phenotypes

The problem states that the two parent plants have the following phenotypes: - Red, personate, and tall - White, peloric, and dwarf Using the symbols we defined earlier for genotypes and phenotypes, the \(P_{1}\) genotypes and phenotypes will be: Red, personate, and tall plant: R鈧丷鈧丳鈧丳鈧乀鈧乀鈧� White, peloric, and dwarf plant: R鈧俁鈧侾鈧侾鈧俆鈧俆鈧�
03

Find F鈧� genotypes after the cross

To find the genotypes of the \(F_{1}\) generation after the cross, we will perform a cross-pollination between the two \(P_{1}\) plants: R鈧丷鈧丳鈧丳鈧乀鈧乀鈧� x R鈧俁鈧侾鈧侾鈧俆鈧俆鈧� For each gene pair, the \(F_{1}\) offspring will inherit one allele from each parent, so the \(F_{1}\) genotype will be: Flower color: R鈧丷鈧� (Pink) Flower shape: P鈧丳鈧� (Personate) Plant height: T鈧乀鈧� (Tall) The \(F_{1}\) genotype is: R鈧丷鈧侾鈧丳鈧俆鈧乀鈧� The \(F_{1}\) phenotype is: Pink, personate, and tall
04

Interbreed F鈧� plants and find proportions

When we interbreed the \(F_{1}\) plants, we will be performing the following genetic cross: R鈧丷鈧侾鈧丳鈧俆鈧乀鈧� x R鈧丷鈧侾鈧丳鈧俆鈧乀鈧� To find the proportion of offspring that have the same phenotype as the \(F_{1}\) plants (Pink, personate, and tall), we need to consider each gene pair separately: - Flower color: R鈧丷鈧� x R鈧丷鈧� Proportion of offspring with pink flowers: 2/4 (Only heterozygotes will be pink) - Flower shape: P鈧丳鈧� x P鈧丳鈧� Proportion of offspring with personate shape: 3/4 (Personate is the dominant trait) - Plant height: T鈧乀鈧� x T鈧乀鈧� Proportion of offspring with tall height: 3/4 (Tall is the dominant trait)
05

Determine the overall proportion

Now, we need to find the proportion of offspring that have all three required traits: pink flower color, personate flower shape, and tall height. We can find this by multiplying the proportions for each trait together: \(Proportion = \frac{2}{4} \times \frac{3}{4} \times \frac{3}{4} = \frac{9}{32}\) Thus, \(9/32\) of the offspring of the \(F_{1}\) plants will exhibit the same phenotypes as the \(F_{1}\) plants (Pink, personate, and tall).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Incomplete Dominance
Understanding incomplete dominance is essential to grasping some unique genetic outcomes. Incomplete dominance occurs when neither allele in a gene pair completely dominates the other, resulting in a blending of traits. This happens notably in flower color, where a mix creates a new phenotype.
For example, if a plant with red flowers (\( R_1R_1 \)) is crossed with one that has white flowers (\( R_2R_2 \)), their offspring will be pink (\( R_1R_2 \)).
Here, pink is the intermediate trait because neither the red nor the white allele is completely dominant.
  • Red Allele (\( R_1 \)): Produces red pigment.
  • White Allele (\( R_2 \)): Results in no pigment.
This partial dominance becomes evident in the heterozygous condition (\( R_1R_2 \)), producing pink flowers. Such outcomes highlight how incomplete dominance allows us to see a spectrum of traits in offspring, rather than just the traits of the dominant allele.
Genotype and Phenotype
Genotype and phenotype are foundational concepts in genetics. A genotype is the actual genetic makeup of an organism, consisting of various alleles received from its parents. In this context, genotypes dictate the potential physical traits an organism can express.
Phenotypes, on the other hand, are the visible or expressible attributes that are manifested. For instance, the flower color genotype (\( R_1R_2 \)) results in the phenotype of pink flowers.
It's important to connect genotype with the way traits are expressed in an organism:
  • Genotype Example: \( R_1R_2P_1P_2T_1T_2 \) indicates pink, personate, and tall traits.
  • Phenotype Example: Pink flowers (result of \( R_1R_2 \)), personate shape (due to dominant \( P_1 \)), and tall height (from dominant \( T_1 \)).
Ultimately, understanding the distinction between genotype and phenotype is crucial in decoding the organism's physical expression and is a fundamental concept in predicting genetic cross outcomes.
Genetic Cross
Performing a genetic cross involves breeding individuals to study how traits pass from one generation to the next. For plants, a genetic cross helps understand inheritance patterns by combining characteristics from different genotypes.
Consider a genetic cross between a red, personate, tall plant (\( R_1R_1P_1P_1T_1T_1 \)) and a white, peloric, dwarf plant (\( R_2R_2P_2P_2T_2T_2 \)). Their \( F_1 \) offspring would inherit alleles for each trait, forming a new combination (\( R_1R_2P_1P_2T_1T_2 \)), expressed as pink, personate, and tall.
Studying such genetic crosses involves using:
  • Punnett Squares: Visualize all possible allele combinations.
  • Probability Calculations: Determine the likelihood of specific traits appearing in offspring.
By examining these crosses, we can discern not only the possible genotypes but also predict the appearance and behavior of future generations. Genetic crosses are vital for breeders and botanists to determine trait distribution and inheritance in hybrid populations.

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Most popular questions from this chapter

In this chapter, we focused on many extensions and modifications of Mendelian principles and ratios, In the process, we encountered many opportunities to consider how this information was acquired. Answer the following fundamental questions: (a) How were early geneticists able to ascertain inheritance patterns that did not fit typical Mendelian ratios? (b) How did geneticists determine that inheritance of some phenotypic characteristics involves the interactions of two or more gene pairs? How were they able to determine how many gene pairs were involved? (c) How do we know that specific genes are located on the sexdetermining chromosomes rather than on autosomes? (d) For genes whose expression seems to be tied to the sex of individuals, how do we know whether a gene is X-linked in contrast to exhibiting sex-limited or sex-influenced inheritance? (e) How was extranuclear inheritance discovered?

In goats, development of the beard is due to a recessive gene. The following cross involving true-breeding eoats was made and carried to the \(\mathrm{F}_{2}\) generation: \(\mathrm{P}_{1}=\) bearded female \(\times\) beardless male \(\mathrm{F}_{1}:\) all bearded males and beardless females \\[ \mathbf{F}_{1} \times \mathbf{F}_{1} \rightarrow\left\\{\begin{array}{l} 1 / 8 \text { beardless males } \\ 3 / 8 \text { bearded males } \\ 3 / 8 \text { beardless females } \\ 1 / 8 \text { bearded females } \end{array}\right. \\] Offer an explanation for the inheritance and expression of this trait, diagramming the cross. Propose one or more crosses to test your hypothesis.

Three autosomal recessive mutations in yeast, all producing the same phenotype \((m 1, m 2, \text { and } m 3),\) are subjected to complementation analysis, Of the results shown below, which, if any, are alleles of one another? Predict the results of the cross that is not shown-that is, \(m 2 \times m 3\) Cross \(1: \quad m I \times m 2 \longrightarrow P_{1}=\) all wild-type progeny Cross \(2: \quad m I \times m 3 \longrightarrow P_{1}:\) all mutant progeny

A geneticist from an alien planet that prohibits genetic research brought with him two true-breeding lines of frogs. One frog line croaks by uttering "rib-it rib-it" and has purple eyes. The other frog line croaks by muttering "knee- deep knee-deep" and has green eyes. He mated the two frog lines, producing \(\mathrm{P}_{1}\) frogs that were all utterers with blue eyes. A large \(\mathrm{F}_{2}\) generation then yielded the following ratios: \(27 / 64\) blue, utterer \(12 / 64\) green, utterer \(9 / 64\) blue, mutterer \(9 / 64\) purple, utterer \(4 / 64\) green, mutterer \(3 / 64\) purple, mutterer (a) How many total gene pairs are involved in the inheritance of both eye color and croaking? (b) Of these, how many control eye color, and how many control croaking? (c) Assign gene symbols for all phenotypes, and indicate the genotypes of the \(P_{1}, F_{1},\) and \(F_{2}\) frogs. (d) After many years, the frog geneticist isolated true-breeding lines of all six \(\mathrm{F}_{2}\) phenotypes. Indicate the \(\mathrm{F}_{1}\) and \(\mathrm{P}_{2}\) phenotypic ratios of a cross between a blue, mutterer and a purple, utterer.

A husband and wife have normal vision, although both of their fathers are red- green color-blind, inherited as an X-linked recessive condition. What is the probability that their first child will be (a) a normal son, (b) a normal daughter, (c) a color-blind \(\operatorname{son},(d)\) a color-blind daughter?
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