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Chapter 18: Problem 23

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 \(8 \mathrm{~g}\) ?

Short Answer

Expert verified
(a) 12.8 g, (b) 11.2 g.

Step by step solution

01

Understanding the Problem

The problem gives us the average weight gain (12 g) of a mouse population between 3 and 6 weeks and specifies that the narrow-sense heritability of this trait is 20% (or 0.2). We need to find the expected average weight gain of the offspring based on the parents' average weight gain.
02

Understanding Heritability

Narrow-sense heritability is a measure of how much of the variance in a trait is due to additive genetic factors. It indicates the proportion of the phenotype that can be passed from parents to offspring. Given heritability (\( h^2 = 0.2 )\), we can use it to predict offspring traits from selected parents.
03

Expected Offspring Formula

The expected weight gain of the offspring (\( \bar{y} )\) can be calculated using the formula: \[ \bar{y} = \bar{p} + h^2(\bar{P} - \bar{p}) \] where \( \bar{p} )\) is the population mean, \( \bar{P} )\) is the mean gain of the selected parents, and \( h^2 )\) is the heritability.
04

Calculate for Parent Gain of 16g

Using the formula, with \( \bar{P} = 16 \ g )\), \( \bar{p} = 12 \ g )\), and \( h^2 = 0.2 )\): \[ \bar{y} = 12 + 0.2(16 - 12) = 12 + 0.8 = 12.8 \ g \]
05

Calculate for Parent Gain of 8g

Using the formula, with \( \bar{P} = 8 \ g )\), \( \bar{p} = 12 \ g )\), and \( h^2 = 0.2 )\): \[ \bar{y} = 12 + 0.2(8 - 12) = 12 - 0.8 = 11.2 \ g \]

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Key Concepts

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

Genetic Variance
Genetic variance refers to the diversity of genetic information within a population. It encompasses differences in gene frequencies, which affect traits like weight gain in mice. Understanding genetic variance is crucial because it helps us predict changes in populations over time, especially when considering traits passed from parents to offspring.
  • Genetic variance is determined by different genetic factors.
  • It directly impacts how much potential a trait has to evolve under selection.
  • High genetic variance means more options for population adaptability.
Genetic variance is a key component in the study of heritability, as it determines how reliably a trait can be predicted in descendants, offering essential insights into evolutionary processes in populations.
Additive Genetic Factors
Additive genetic factors are the genetic effects where the overall phenotype results from the sum of individual gene contributions. These factors are fundamental in predicting the responser of a trait to selection because they represent how traits are inherited.
  • Each gene contributes a piece to the overall trait.
  • Additive effects are predictable and stable over generations.
  • They allow for the calculation of narrow-sense heritability.
The concept of additive genetic factors is applied to determine narrow-sense heritability, which focuses on traits directly passed down from parents. This aspect of genetics allows breeders and geneticists to forecast changes within populations due to selective breeding.
Phenotypic Traits
Phenotypic traits are observable features of an organism, such as weight gain in mice. These traits result from the interaction of genetic information with the environment. Understanding phenotypic traits involves examining how genes express themselves physically.
  • They include physical characteristics, such as size or color.
  • Phenotypic expression can be influenced by environmental factors.
  • They are the basis of natural selection.
Examining phenotypic traits allows researchers to connect the genetic makeup of organisms to their physical forms. This knowledge is crucial in fields like evolutionary biology and inheritance studies because it helps explain how different genes contribute to the visible characteristics of a population.
Heritability Calculation
Heritability calculation quantifies how much of the variation in a trait is heritable from parents to offspring. It's expressed as a percentage or a fraction and helps indicate the influence of genetic factors on phenotypic variation. Narrow-sense heritability in particular focuses solely on additive genetic variance.
  • Narrow-sense heritability (\(h^2\)) is key for predicting offspring traits.
  • Allows breeders to select for desired traits.
  • Calculated using the formula: \( \bar{y} = \bar{p} + h^2(\bar{P} - \bar{p}) \).
Using narrow-sense heritability, researchers and breeders can predict offspring traits with considerable confidence, helping in the deliberate selection of desirable traits in breeding programs. For instance, in the mouse population, knowing heritability helps anticipate weight changes based on parental characteristics.

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Most popular questions from this chapter

A flock of broiler chickens has a mean weight gain of \(700 \mathrm{~g}\) between ages 5 and 9 weeks, and the narrow-sense heritahility of weight gain in this flock is \(0.80\). Selection for increased weight gain is carried out for five consecutive generations, and in each generation the average of the parents is 50 g preater than the average of the population from which the parents were derived. Assuming that the heritability of the trait remains constant at 80 percent. what is the expected mean weight gain after the five gencrations?

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,

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

In terms of the narrow-sense heritability, what is the theoretical correlation coefficient in phenotype between tirst cousins who are the offspring of monozygotic twins?

A quantitative trait is determined by three independently segregating. completely additive genes in a randomly mating population. Alleles \(A, B\), and \(C\) are tavorable for the trait. Genotype aa bb or has a phenorype of 0 , and in every other genotype one unit in phenotype is added for each tavorable allele that is present. Consider a random-mating population in which the allele trequencies are \(0.5\) for the favorable allele and the uniavorable allele at each locus. (a) What is the mean phenotype in the population? (b) If arificial selection is carried out such that the selected parents have a phenotype of cither 5 of 6 . what is the mean phenotype among the selected parents? (c) What are the allele frequencies among the selected parents? (d) If the selected parents are mated at randets, what is the expected mean phenotype among the offspring? (a) Do these results conform to the formula \(M^{\prime}=M+\) \(h^2\left(M^*-A h\right.\) ? (1) What is the value of \(h^2\) ? Is this value unexpected?
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