Textbook Question
How many different types of gametes can be formed by individuals of the following genotypes:
(a) AaBb
(b) AaBB
(c) AaBbCc
(d) AaBBcc
(e) AaBbcc
(f) AaBbCcDdEe
What are the gametes in each case?
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Ch. 3 - Mendelian Genetics
Klug10th EditionEssentials of GeneticsISBN: 9780135588789
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Table of contents
- Ch. 1 - Introduction to Genetics16
- Ch. 2 - Mitosis and Meiosis28
- Ch. 3 - Mendelian Genetics37
- Ch. 4 - Modification of Mendelian Ratios53
- Ch. 5 - Sex Determination and Sex Chromosomes32
- Ch. 6 - Chromosome Mutations: Variation in Number and Arrangement37
- Ch. 7 - Linkage and Chromosome Mapping in Eukaryotes36
- Ch. 8 - Genetic Analysis and Mapping in Bacteria and Bacteriophages24
- Ch. 9 - DNA Structure and Analysis38
- Ch. 10 - DNA Replication29
- Ch. 11 - Chromosome Structure and DNA Sequence Organization22
- Ch. 12 - The Genetic Code and Transcription36
- Ch. 13 - Translation and Proteins27
- Ch. 14 - Gene Mutation, DNA Repair, and Transposition34
- Ch. 15 - Regulation of Gene Expression in Bacteria22
- Ch. 16 - Regulation of Gene Expression in Eukaryotes37
- Ch. 17 - Recombinant DNA Technology27
- Ch. 18 - Genomics, Bioinformatics, and Proteomics30
- Ch. 19 - The Genetics of Cancer21
- Ch. 20 - Quantitative Genetics and Multifactorial Traits37
- Ch. 21 - Population and Evolutionary Genetics45
Chapter 3, Problem 16
In assessing data that fell into two phenotypic classes, a geneticist observed values of 250:150. She decided to perform a ² analysis by using the following two different null hypotheses:
(a) the data fit a 3:1 ratio, and
(b) the data fit a 1:1 ratio.
Calculate the ² values for each hypothesis. What can be concluded about each hypothesis?
Verified step by step guidance1
Step 1: Identify the observed values and total number of observations. Here, the observed counts are 250 and 150, so the total is 250 + 150 = 400.
Step 2: For hypothesis (a), where the expected ratio is 3:1, calculate the expected counts by dividing the total according to this ratio. The expected count for the first class is \(\frac{3}{4} \times 400\), and for the second class is \(\frac{1}{4} \times 400\).
Step 3: For hypothesis (b), where the expected ratio is 1:1, calculate the expected counts by dividing the total equally. Each class is expected to have \(\frac{1}{2} \times 400\) individuals.
Step 4: Use the chi-square formula to calculate the chi-square value for each hypothesis:
\(\chi^{2} = \sum \frac{(O - E)^2}{E}\)
where \(O\) is the observed count and \(E\) is the expected count for each phenotypic class. Calculate this sum separately for each hypothesis using their respective expected counts.
Step 5: Compare the calculated chi-square values to the critical chi-square value from the chi-square distribution table at the appropriate degrees of freedom (df = number of classes - 1) and significance level (commonly 0.05). If the calculated value is less than the critical value, the hypothesis fits the data well; if greater, the hypothesis is rejected.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Chi-Square (χ²) Test
The chi-square test is a statistical method used to compare observed data with expected data based on a specific hypothesis. It calculates a χ² value that measures the difference between observed and expected frequencies. A higher χ² value indicates a greater deviation from the expected ratio, helping to determine if the null hypothesis can be rejected.
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Null Hypothesis in Genetic Ratios
In genetics, the null hypothesis often states that observed phenotypic ratios fit a predicted Mendelian ratio, such as 3:1 or 1:1. This hypothesis assumes no significant difference between observed and expected data. Testing different null hypotheses helps identify which genetic model best explains the observed data.
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Interpreting Chi-Square Results
After calculating the χ² value, it is compared to a critical value from the chi-square distribution table based on degrees of freedom and significance level. If χ² is less than the critical value, the null hypothesis is accepted; if greater, it is rejected. This interpretation determines whether observed deviations are due to chance or indicate a different genetic pattern.
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Related Practice
Textbook Question
Mendel crossed peas having round green seeds with peas having wrinkled yellow seeds. All F₁ plants had seeds that were round and yellow. Predict the results of testcrossing these F₁ plants.
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Textbook Question
The following are F₂ results of two of Mendel's monohybrid crosses.
For each cross, state a null hypothesis to be tested using x² analysis. Calculate the x² value and determine the p value for both. Interpret the p-values. Can the deviation in each case be attributed to chance or not? Which of the two crosses shows a greater amount of deviation?
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Textbook Question
The basis for rejecting any null hypothesis is arbitrary. The researcher can set more or less stringent standards by deciding to raise or lower the p value used to reject or not reject the hypothesis. In the case of the chi-square analysis of genetic crosses, would the use of a standard of p = 0.10 be more or less stringent about not rejecting the null hypothesis? Explain.
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