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Chapter 6: Problem 59

A plant of phenotype 1 was selfed, and, in the progeny, there were 100 plants of phenotype 1 and 60 plants of an alternative phenotype \(2 .\) Are these numbers compatible with expected ratios of 9: 7,\(13: 3,\) and \(3: 1 ?\) Formulate a genetic hypothesis on the basis of your calculations.

Short Answer

Expert verified
The observed ratio fits the expected 9:7 ratio.

Step by step solution

01

Understand the Problem

The problem involves comparing observed progeny ratios of two phenotypes, 1 and 2, against expected genetic ratios: 9:7, 13:3, and 3:1. We'll use the chi-square test for statistical analysis to see if the observed offspring fits these expected ratios.
02

Calculate the Total Number of Plants

Add the number of plants of phenotype 1 and phenotype 2. \[ 100 + 60 = 160 \]There are 160 plants in total.
03

Determine the Expected Numbers for Ratio 9:7

For a 9:7 ratio, divide 160 into 9 parts for phenotype 1 and 7 parts for phenotype 2.The total parts is 9 + 7 = 16.\[ \text{Expected } \text{Phenotype } 1 = \frac{9}{16} \times 160 = 90 \]\[ \text{Expected } \text{Phenotype } 2 = \frac{7}{16} \times 160 = 70 \]
04

Determine the Expected Numbers for Ratio 13:3

For a 13:3 ratio, divide 160 into 13 parts for phenotype 1 and 3 parts for phenotype 2.The total parts is 13 + 3 = 16.\[ \text{Expected } \text{Phenotype } 1 = \frac{13}{16} \times 160 = 130 \]\[ \text{Expected } \text{Phenotype } 2 = \frac{3}{16} \times 160 = 30 \]
05

Determine the Expected Numbers for Ratio 3:1

For a 3:1 ratio, divide 160 into 3 parts for phenotype 1 and 1 part for phenotype 2.The total parts is 3 + 1 = 4.\[ \text{Expected } \text{Phenotype } 1 = \frac{3}{4} \times 160 = 120 \]\[ \text{Expected } \text{Phenotype } 2 = \frac{1}{4} \times 160 = 40 \]
06

Perform Chi-Square Test for each Ratio

Calculate the chi-square value for each ratio using:\[ \chi^2 = \sum \frac{(O - E)^2}{E} \]Where \(O\) is the observed frequency, and \(E\) is the expected frequency.**For 9:7 ratio:**\[ \chi^2 = \frac{(100 - 90)^2}{90} + \frac{(60 - 70)^2}{70} = \frac{10^2}{90} + \frac{10^2}{70}\]\[ \chi^2 \approx 1.23 \]**For 13:3 ratio:**\[ \chi^2 = \frac{(100 - 130)^2}{130} + \frac{(60 - 30)^2}{30} = \frac{30^2}{130} + \frac{30^2}{30}\]\[ \chi^2 \approx 20.77 \]**For 3:1 ratio:**\[ \chi^2 = \frac{(100 - 120)^2}{120} + \frac{(60 - 40)^2}{40} = \frac{20^2}{120} + \frac{20^2}{40}\]\[ \chi^2 \approx 6.67 \]
07

Compare Chi-Square Values to Critical Values

The critical value for 1 degree of freedom at the 5% significance level is approximately 3.84.- For the 9:7 ratio: \(\chi^2 \approx 1.23\) (Less than 3.84; fit the data)- For the 13:3 ratio: \(\chi^2 \approx 20.77\) (Greater than 3.84; does not fit the data)- For the 3:1 ratio: \(\chi^2 \approx 6.67\) (Greater than 3.84; does not fit the data)

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Key Concepts

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

Phenotypic Ratios
Phenotypic ratios help us understand how different traits are inherited in organisms. These ratios express the relationship among phenotypes we observe. For example, in genetics, phenotypic ratios commonly explored include 9:7, 13:3, and 3:1. Each of these ratios represents a possible distribution of visible traits among offspring.
For instance, the 9:7 ratio suggests that nine parts of the population exhibit one trait, and seven parts exhibit another. This might be seen in a situation where two different genes are interacting with one another, possibly in epistasis, where one gene affects the expression of another one.
Meanwhile, a 3:1 ratio is typically linked to a simple Mendelian cross, where one genetic trait is dominant over another. Calculating expected phenotypic numbers from these ratios involves using proportions to predict how many of each phenotype should appear in a group, based on known parental traits.
  • The goal of using phenotypic ratios is to establish what is expected under certain genetic conditions.
  • They provide a powerful way to hypothesize genetic outcomes in populations.
Genetic Hypothesis
A genetic hypothesis serves as a prediction of genetic outcomes based on known genetic principles. It is crucial to determine whether observations align with Mendelian inheritance or other genetic models.
A basic genetic hypothesis might begin with observing certain dominant and recessive traits in a set of parents, predicting their offspring's phenotypes, and comparing these predictions against observed results.
The hypothesis in this scenario involves predicting which phenotypic ratio best fits the observed 100 phenotype 1 plants and 60 phenotype 2 plants. The expected traits are calculated using ratios like 9:7, 13:3, and 3:1, as shown in the step-by-step method.
  • Formulating a genetic hypothesis requires understanding dominant and recessive traits.
  • It helps predict the observed versus expected outcomes in genetic experiments.
Assuming the chi-square test results align, our hypothesis could be: 'The phenotypic ratio of the progeny primarily follows a 9:7 genetic model.' This reflects that both traits observed in the plant progeny fit into this specific genetic prediction pattern.
Statistical Analysis
Statistical analysis allows us to rigorously assess whether observed genetic data fits expected models. One crucial tool in genetics for this purpose is the chi-square test. This statistical measure evaluates how well observed experimental data matches the expected result.
The chi-square test for genetic studies is relatively straightforward. We calculate a chi-square value using the formula: \[\chi^2 = \sum \frac{(O - E)^2}{E}\]where \(O\) represents observed frequencies, and \(E\) represents expected frequencies. Through this formula, we derive a numerical \( \chi^2\) value, which can be compared against a critical value from the chi-square distribution table to conclude whether our genetic model is a good fit.
  • If the calculated \(\chi^2\) value is less than the critical value, the genetic hypothesis is a good fit.
  • If greater, it indicates a poor fit, suggesting another genetic hypothesis may be more appropriate.
The application of statistical analysis, including understanding significance levels and degrees of freedom, is key to accurately interpreting genetic experiments. This way, we reliably predict phenotypic ratios in offspring based on parental genetic makeup.

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Most popular questions from this chapter

In a maternity ward, four babies become accidentally mixed up. The ABO types of the four babies are known to be \(\mathrm{O}, \mathrm{A}, \mathrm{B},\) and \(\mathrm{AB}\). The \(\mathrm{ABO}\) types of the four sets of parents are determined. Indicate which baby belongs to each set of parents: (a) \(A B \times O,(b) A \times O,(c) A x\) \(\mathrm{AB},(\mathrm{d}) \mathrm{O} \times \mathrm{O}\).

In common wheat, Triticum aestivum, kernel color is determined by multiply duplicated genes, each with an \(R\) and an \(r\) allele. Any number of \(R\) alleles will give red, and a complete lack of \(R\) alleles will give the white phenotype. In one cross between a red pure line and a white pure line, the \(\mathrm{F}_{2}\) was \(\frac{63}{64}\) red and \(\frac{1}{64}\) white. a. How many \(R\) genes are segregating in this system? b. Show the genotypes of the parents, the \(\mathrm{F}_{1}\), and the \(\mathrm{F}_{2}\). c. Different \(\mathrm{F}_{2}\) plants are backcrossed with the white parent. Give examples of genotypes that would give the following progeny ratios in such backcrosses: (1) 1 red : 1 white, (2) 3 red : 1 white, (3) 7 red: 1 white. d. What is the formula that generally relates the number of segregating genes to the proportion of red individuals in the \(\mathrm{F}_{2}\) in such systems?

In sweet peas, the synthesis of purple anthocyanin pigment in the petals is controlled by two genes, \(B\) and \(D\) The pathway is a. What color petals would you expect in a purebreeding plant unable to catalyze the first reaction? b. What color petals would you expect in a purebreeding plant unable to catalyze the second reaction? c. If the plants in parts \(a\) and \(b\) are crossed, what color petals will the \(F_{1}\) plants have? d. What ratio of purple:blue:white plants would you expect in the \(\mathrm{F}_{2}\) ?

A woman who owned a purebred albino poodle (an autosomal recessive phenotype) wanted white puppies; so she took the dog to a breeder, who said he would mate the female with an albino stud male, also from a pure stock. When six puppies were born, all of them were black; so the woman sued the breeder, claiming that he replaced the stud male with a black dog, giving her six unwanted puppies. You are called in as an expert witness, and the defense asks you if it is possible to produce black offspring from two pure-breeding recessive albino parents. What testimony do you give?

A dominant allele \(H\) reduces the number of body bristles that Drosophila flies have, giving rise to a "hairless" phenotype. In the homozygous condition, \(H\) is lethal. An independently assorting dominant allele \(S\) has no effect on bristle number except in the presence of \(H\) in which case a single dose of \(S\) suppresses the hairless phenotype, thus restoring the hairy phenotype. However, \(S\) also is lethal in the homozygous (S/S) condition. a. What ratio of hairy to hairless flies would you find in the live progeny of a cross between two hairy flies both carrying \(H\) in the suppressed condition? b. When the hairless progeny are backcrossed with a parental hairy fly, what phenotypic ratio would you expect to find among their live progeny?
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