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Chapter 20: Problem 16

In a herd of dairy cows the narrow-sense heritability for milk protein content is \(0.76,\) and for milk butterfat it is \(0.82 .\) The cor- relation coefficient between milk protein content and butterfat is \(0.91 .\) If the farmer selects for cows producing more butterfat in their milk, what will be the most likely effect on milk protein content in the next generation?

Short Answer

Expert verified
Answer: The most likely effect on milk protein content in the next generation will be an increase, due to the strong positive genetic correlation of 0.719 between the two traits.

Step by step solution

01

Understand the given information

In this exercise, we are given the following information: - Narrow-sense heritability for milk protein content: \(0.76\) - Narrow-sense heritability for milk butterfat: \(0.82\) - Correlation coefficient between milk protein content and butterfat: \(0.91\) The narrow-sense heritability gives us an idea of how much the traits can be affected by selection, while the correlation coefficient tells us how these traits are related.
02

Determine genetic correlation

Genetic correlation is a measure of how the genetic factors affecting one trait are related to the genetic factors affecting another trait. We can use the correlation coefficient to determine the genetic correlation. Genetic correlation between milk protein content and milk butterfat can be given by: Genetic correlation = Correlation coefficient × √(Heritability of Trait 1 × Heritability of Trait 2)
03

Calculate the genetic correlation

To calculate the genetic correlation between milk protein content and milk butterfat, plug the given heritability and correlation coefficient values into the formula: Genetic correlation = \(0.91\) × √(\(0.76\) × \(0.82\)) Now, we can calculate the genetic correlation: Genetic correlation ≈ \(0.91\) × √(\(0.6232\)) Genetic correlation ≈ \(0.91\) × \(0.7894\) Genetic correlation ≈ \(0.719\)
04

Determine the effect on milk protein content

Now that we have calculated the genetic correlation, we can use this value to determine the most likely effect on milk protein content if the farmer selects cows producing more butterfat. Since the genetic correlation is positive, it suggests that an increase in milk butterfat will lead to an increase in milk protein content. The value of \(0.719\) implies a strong positive relationship between the two traits, meaning the increase in milk protein content is highly likely. In conclusion, if the farmer selects dairy cows for higher milk butterfat production, the milk protein content in the next generation is likely to increase as well due to the strong positive genetic correlation between the two traits.

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Most popular questions from this chapter

A dark-red strain and a white strain of wheat are crossed and produce an intermediate, medium-red \(\mathrm{F}_{1}\). When the \(\mathrm{F}_{1}\) plants are interbred, an \(\mathrm{F}_{2}\) generation is produced in a ratio of 1 dark-red: 4 medium-dark-red: 6 medium-red: 4 light-red: 1 white, Further crosses reveal that the dark-red and white \(\mathrm{F}_{2}\) plants are true breeding. (a) Based on the ratios in the \(\mathrm{F}_{2}\) population, how many genes are involved in the production of color? (b) How many additive alleles are needed to produce each possible phenotype? (c) Assign symhols to these alleles and list pnssible genotypes that give rise to the medium-red and light-red phenotypes. (d) Predict the outcome of the \(F_{1}\) and \(F_{2}\) generations in a cross between a true-breeding medium-red plant and a white plant.

In a population of tomato plants, mean fruit weight is \(60 \mathrm{g}\) and \(\left(h^{2}\right)\) 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.

List as many human traits as you can that are likely to be under the control of a polygenic mode of inheritance.

In an assessment of learning in Drosophila, flies were trained to avoid certain olfactory cues. In one population, a mean of 8.5 trials was required. A subgroup of this parental population that was trained most quickly (mean \(=6.0\) ) was interbred, and their progeny were examined. These flies demonstrated a mean training value of \(7.5 .\) Calculate realized heritability for olfactory learning in Drosophila.

Height in humans depends on the additive action of genes. Assume that this trait is controlled by the four loci \(R, S, T,\) and \(U\) and that environmental effects are negligible. Instead of additive versus nonadditive alleles, assume that additive and partially additive alleles exist. Additive alleles contribute two units, and partially additive alleles contribute one unit to height. (a) Can two individuals of moderate height produce offspring that are much taller or shorter than either parent? If so, how? (b) If an individual with the minimum height specified by these genes marries an individual of intermediate or moderate height, will any of their children be taller than the tall parent? Why or why not?
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