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Chapter 18: Problem 22

In a selection experiment for increased plasma cholesterol levels in mice, parents with a mean level of \(2.37\) units were selected from a population with a mean of \(2.26\) units, and the progeny of the selected parents had an average level of \(2.33\) units. Estimate the narrow-sense heritability of this trait from these data,

Short Answer

Expert verified
The narrow-sense heritability (h^2) is approximately 0.636.

Step by step solution

01

Understand the Concepts

Narrow-sense heritability (h^2) is estimated as the proportion of phenotypic variance attributed to additive genetic variance. It can be calculated using the breeder's equation: \( h^2 = \frac{R}{S} \), where \( R \) is the response to selection and \( S \) is the selection differential.
02

Calculate the Selection Differential (S)

Selection differential \( S \) is the difference between the mean phenotype of the selected parents and the mean phenotype of the original population. Here, \( S = 2.37 - 2.26 = 0.11 \) units.
03

Calculate the Response to Selection (R)

Response to selection \( R \) is the change in the mean phenotype of the progeny relative to the original population mean. Thus, \( R = 2.33 - 2.26 = 0.07 \) units.
04

Calculate Narrow-Sense Heritability (h^2)

Using the breeder's equation, we substitute the known values: \( h^2 = \frac{0.07}{0.11} \approx 0.636 \). This result suggests that approximately 63.6% of the variation in plasma cholesterol levels can be attributed to additive genetic variance.

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Key Concepts

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

Exploring Additive Genetic Variance
Additive genetic variance is a crucial component when estimating narrow-sense heritability. It represents the part of the genetic variance that contributes to the offspring's phenotype in a predictable manner. Essentially, it consists of the sum of effects of individual genes that can be added up linearly.
Imagine each gene as an individual puzzle piece; the more pieces that fit together, the clearer the picture becomes. In the context of our exercise, additive genetic variance helps to explain how much of the change in traits, like plasma cholesterol levels, can be directly attributed to genetic factors rather than environmental influences.
  • Predictability: Additive genetic variance is what makes it possible to predict how traits will be passed from parents to offspring.
  • Importance in Breeding: In selective breeding, understanding additive genetic variance allows breeders to select parents with the desired traits, knowing these will likely be passed down.
Understanding the Selection Differential
Selection differential describes the difference in a trait's mean value between the selected parents and the entire population. This concept is central to artificial selection experiments where specific traits are chosen for breeding.
In our mouse experiment, it is calculated by subtracting the population's average from that of the selected parents. So, if selected parents have higher plasma cholesterol levels than the general population, the selection differential is positive.
  • Formula: Calculate selection differential as \( S = ext{mean of selected parents} - ext{mean of population}\).
  • Significance: A greater selection differential indicates a stronger selection pressure, as a larger difference shows more selective preference towards the trait.
Unpacking the Breeder's Equation
The breeder's equation is a fundamental principle in quantitative genetics. It is expressed as \( h^2 = \frac{R}{S} \), where \( R \) is the response to selection, and \( S \) is the selection differential. This equation allows us to calculate narrow-sense heritability, providing insights into the extent of genetic influence on a trait.
In our example with mice, understanding the breeder's equation helps us deduce how much change in cholesterol levels from parent to progeny is due to genetic factors. A high heritability close to one means that genetics plays a strong role, while a low value suggests environmental influences have more effect.
  • Response to Selection \( R \): Measures the shift in the progeny's mean trait value due to selection.
  • Application: The breeder's equation is pivotal in improving species through breeding, focusing on enhancing desirable traits systematically.

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Most popular questions from this chapter

A distribution has the feature that the standard deviation is equal to the variance. What are the possible values for the variance?

A mouse population has an average weight gain between ages 3 and 6 wecks of \(12 \mathrm{~g}\) and the narrow-sense heritatuility of the weight gain between 3 and 6 weeks is 20 percent. (a) What average weight gain would be expected among the offspring of parents whose average weight gain was \(16 \mathrm{~g}\) ? (b) What averake weight gain would be expected among the oftspring of parents whose average weight gain was \(8 \mathrm{~g}\) ?

When we compare a quantitative trait in the \(\mathrm{F}_1\) and \(F_2\) generations obtained by crossing two highly inbred sirains. Which set of progeny proyide's an estimate of the environmental variance? What determines the variance of the other set of progeny?

Ten female mice had the following numbers of liveborn offspring in theit first litters: \(11,9,13,10,9,8,10\). 11, 10, 13. Considering these females as representative of the total population from which they came, estimate the mean, variance, and standard deviation of size of the first litter in the entire population.

To estimate the heritability of maze-learning ability in rats, a selection experiment was carried aut. From a population in which the average number of trials riecessary to learn the maze was \(10.8\), with a variance of \(4.0\), animals were selected that managed to learn the maze in an average of \(5.8\) trials. Their offspring required an average of \(8.8\) triab io learn the maze. What is the estimated narrow-sense heritability of maze-learning ability in this population?
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