In a line of cherry tomatoes, the average fruit weight is 16 g. A plant producing tomatoes with an average weight of 12 g is used in one self-fertilization cross to produce a line of smaller tomatoes, and a plant producing tomatoes of 24 g is used in a second cross to produce larger tomatoes. What is the selection differential (S) for fruit weight in each cross?
Table of contents
- 1. Introduction to Genetics51m
- 2. Mendel's Laws of Inheritance3h 37m
- 3. Extensions to Mendelian Inheritance2h 41m
- 4. Genetic Mapping and Linkage2h 28m
- 5. Genetics of Bacteria and Viruses1h 21m
- 6. Chromosomal Variation1h 48m
- 7. DNA and Chromosome Structure56m
- 8. DNA Replication1h 10m
- 9. Mitosis and Meiosis1h 34m
- 10. Transcription1h 0m
- 11. Translation58m
- 12. Gene Regulation in Prokaryotes1h 19m
- 13. Gene Regulation in Eukaryotes44m
- 14. Genetic Control of Development44m
- 15. Genomes and Genomics1h 50m
- 16. Transposable Elements47m
- 17. Mutation, Repair, and Recombination1h 6m
- 18. Molecular Genetic Tools19m
- 19. Cancer Genetics29m
- 20. Quantitative Genetics1h 26m
- 21. Population Genetics50m
- 22. Evolutionary Genetics29m
20. Quantitative Genetics
Heritability
Problem 18
Textbook Question
In a population of tomato plants, mean fruit weight is 60 g and h² is 0.3. Predict the mean weight of the progeny if tomato plants whose fruit averaged 80 g were selected from the original population and interbred.

1
Understand the problem: This is a quantitative genetics problem involving heritability (h²) and selection. Heritability is the proportion of phenotypic variance that is due to genetic variance. The goal is to predict the mean weight of the progeny after selection and interbreeding.
Identify the formula to use: The breeder's equation is appropriate here. It is expressed as: , where R is the response to selection, h² is heritability, and S is the selection differential.
Calculate the selection differential (S): The selection differential is the difference between the mean phenotype of the selected parents and the mean phenotype of the original population. Use the formula: . Here, is 80 g and is 60 g.
Determine the response to selection (R): Plug the values of h² and S into the breeder's equation. Use the formula: . Here, h² is 0.3, and S is the difference calculated in the previous step.
Predict the mean weight of the progeny: Add the response to selection (R) to the mean phenotype of the original population. Use the formula: . This will give the predicted mean weight of the progeny.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Heritability (h²)
Heritability (h²) is a measure of how much of the variation in a trait, such as fruit weight, can be attributed to genetic differences among individuals in a population. A heritability value of 0.3 indicates that 30% of the variation in fruit weight is due to genetic factors, while the remaining 70% is influenced by environmental factors. This concept is crucial for predicting how traits will be passed on to future generations.
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Selection Differential
The selection differential is the difference between the mean trait value of the selected individuals and the mean trait value of the entire population. In this case, the selected tomato plants have an average fruit weight of 80 g, while the population mean is 60 g. This differential helps in estimating the expected change in the trait in the next generation due to selection.
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Response to Selection
Response to selection refers to the expected change in the mean trait value of a population after selection and breeding. It can be calculated using the formula R = h² × S, where R is the response, h² is heritability, and S is the selection differential. This concept allows us to predict how the mean fruit weight of the progeny will change based on the selected parent plants.
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