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Modern Genetic Analysis Chapter 18. Quantitative Genetics
Problems

1. | Distinguish between continuous and discontinuous variation in a population, and give some examples of each.

2.

In a large herd of cattle, three different characters showing continuous distribution are measured, and the variances in the following table are calculated:

a. Calculate the broad- and narrow-sense heritabilities for each character.
b. In the population of animals studied, which character would respond best to selection? Why?
c. A project is undertaken to decrease mean fat content in the herd. The mean fat content is currently 10.5 percent. Animals of 6.5 percent fat content are interbred as parents of the next generation. What mean fat content can be expected in the descendants of these animals?

3.

Suppose that two triple heterozygotes A / a ; B / b ; C / c are crossed. Assume that the three loci are in different chromosomes.
a. What proportions of the offspring are homozygous at one, two, and three loci, respectively?
b. What proportions of the offspring carry 0, 1, 2, 3, 4, 5, and 6 alleles (represented by capital letters), respectively?

4. | In Problem 3, suppose that the average phenotypic effect of the three genotypes at the A locus is A / A= 4, A / a= 3, a / a= 1 and that similar effects exist for the B and C loci. Moreover, suppose that the effects of loci add to each other. Calculate and graph the distribution of phenotypes in the population (assuming no environmental variance).

5. | In Problem 4, suppose that there is a threshold in the phenotypic character so that, when the phenotypic value is above 9, the individual Drosophila has three bristles; when it is between 5 and 9, the individual has two bristles; and when the value is 4 or less, the individual has one bristle. Describe the outcome of crosses within and between bristle classes. Given the result, could you infer the underlying genetic situation?

6.

Suppose that the general form of a distribution of a trait for a given genotype is

over the range of x where f is positive.
a. On the same scale, plot the distributions for three genotypes with the following means and environmental variances:

b. Plot the phenotypic distribution that would result if the three genotypes were equally frequent in a population. Can you see distinct modes? If so, what are they?

7. | The following table shows a distribution of bristle number in Drosophila: Calculate the mean, variance, and standard deviation of this distribution.

8.

The following sets of hypothetical data represent paired observations on two variables (x, y). Plot each set of data pairs as a scatter diagram. Look at the plot of the points, and make an intuitive guess about the correlation between x and y. Then calculate the correlation coefficient for each set of data pairs, and compare this value with your estimate.
a. (1, 1); (2, 2); (3, 3); (4, 4); (5, 5); (6, 6).
b. (1, 2); (2, 1); (3, 4); (4, 3); (5, 6); (6, 5).
c. (1, 3); (2, 1); (3, 2); (4, 6); (5, 4); (6, 5).
d. (1, 5); (2, 3); (3, 1); (4, 6); (5, 4); (6, 2).

9.

A book on the problem of heritability of IQ makes the following three statements. Discuss the validity of each statement and its implications about the authors' understanding of h2 and H2.
a. "The interesting question then is...'How heritable?' The answer [0.01] has a very different theoretical and practical application from the answer [0.99]." [The authors are talking about H2.]
b. "As a rule of thumb, when education is at issue, H2 is usually the more relevant coefficient, and when eugenics and dysgenics (reproduction of selected individuals) are being discussed, h2 is ordinarily what is called for."
c. "But whether the different ability patterns derive from differences in genes...is not relevant to assessing discrimination in hiring. Where it could be relevant is in deciding what, in the long run, might be done to change the situation."

(From J. C. Loehlin, G. Lindzey, and J. N. Spuhler, Race Differences in Intelligence. Copyright © 1975 by W. H. Freeman and Company.)

10. | Using the concepts of norms of reaction, environmental distribution, genotypic distribution, and phenotypic distribution, try to restate the following statement in more exact terms: "80 percent of the difference in IQ performance between the two groups is genetic." What would it mean to talk about the heritability of a difference between two groups?

11. | Describe an experimental protocol for studies of relatives that could estimate the broad heritability of alcoholism. Remember that you must make an adequate observational definition of the trait itself.

12.

A line selected for high bristle number in Drosophila has a mean of 25 sternopleural bristles, whereas a low-selected line has a mean of only 2. Marker stocks involving the two large autosomes II and III are used to create stocks with various mixtures of chromosomes from the high (h) and low (l) lines. The mean number of bristles for each chromosomal combination is as follows:

What conclusions can you reach about the distri-bution of genetic factors and their actions from these data?

13.

Suppose that number of eye facets is measured in a population of Drosophila under various temperature conditions. Further suppose that it is possible to estimate total genetic variance (S28) as well as the phenotypic distribution. Finally, suppose that there are only two genotypes in the population. Draw pairs of norms of reaction that would lead to the following results:
a. An increase in mean temperature decreases the phenotypic variance.
b. An increase in mean temperature increases H2.
c. An increase in mean temperature increases S28 but decreases H2.
d. An increase in temperature variance changes a unimodal into a bimodal phenotypic distribution (one norm of reaction is sufficient here).

14.

Francis Galton compared the heights of male undergraduates with the heights of their fathers, with the results shown in the graph on the following page:

(Graph after W. F. Bodmer and L. L. Cavalli-Sforza, Genetics, Evolution, and Man. Copyright © 1976 by W. H. Freeman and Company.)

The average height of all fathers is the same as the average height of all sons, but the individual height classes are not equal across generations. The very tallest fathers had somewhat shorter sons, whereas the very short fathers had somewhat taller sons. As a result, the best line that can be drawn through the points on the scatter diagram has a slope of about 0.67 (solid line) rather than 1.00 (dashed line). Galton used the term regression to describe this tendency for the phenotype of the sons to be closer than the phenotype of their fathers to the population mean.
a. Propose an explanation for this regression.
b. How are regression and heritability related here?

© 1999 by W. H. Freeman and Company. All rights reserved.