Chapter Questions
How does a quantitative characteristic differ from a discontinuous characteristic?
Briefly explain why the relation between genotype and phenotype is frequently complex for quantitative characterist ics.
Why do polygenic characterist ics have many phenotypes?
Explain the relation between a population and a sample. What characteristics should a sample have to be representative of the population?
What information do the mean and variance provide about a distribution?
How is the standard deviation related to the variance?
What information does the correlation coefficient provide about the association between two variables?
What is regression? How is it used?
List all the components that contribute to the phenotypic variance and define each component.
How do broad-sense and narrow-sense heritabilities differ?
Briefly out line some of the ways in which heritability can be calculated.
Briefly describe common misunderstandings or misapplications of the concept of heritability.
Briefly explain how genes affecting a polygen ic characteristic are located with the use of QTL mapping.
How is the response to selection related to narrow sense heritability and the selection different ial? What information does the response to selection provide?
Why does the response to selection often level off after many generations of selection?
For each of the following characteristics, indicate whether it would be considered a discontinuous characteristic or a quantitative characteristic. Briefly justify your answer.a. Kernel color in a strain of wheat, in which two codominant alleles segregating at a single locus determine the color. Thus, there are three phenotypes present in this strain: white, light red, and medium red.b. Body weight in a family of Labrador retrievers. An autosomal recessive allele that causes dwarfism is present in this family. Two phenotypes are recognized:dwarf (less than $13 \mathrm{kg}$ ) and normal (greater than $23 \mathrm{kg}$ ).c. Presence or absence of leprosy. Susceptibility to leprosy is determined by multiple genes and numerous environmental factors.d. Number of toes in guinea pigs, which is influenced by genes at many loci.e. Number of fingers in humans. Extra (more than five) fingers are caused by the presence of an autosomal dominant allele.
Assume that plant weight is determined by a pair of alleles at each of two independently assorting loci $(A \text { and } a, B$ and $b$ ) that are additive in the ir effects. Further assume that each allele represented by an uppercase letter contributes $4 \mathrm{g}$ to weight and that each allele represented by a lowercase letter contributes $1 \mathrm{g}$ to weight. a. If a plant with genotype $A A B B$ is crossed with a plant with genotype aa $b b,$ what weights are expected in the$\mathrm{F}_{1}$ progeny?b. What is the dist ribution of weight expected in the $\mathrm{F}_{2}$ progeny?
Assume that three loci, each with two alleles $(A \text { and } a, B$ and $b, C \text { and } c),$ determine the differences in height between two homozygous strains of a plant. These genes are additive and equal in their effects on plant height. One strain (aa bb $\alpha$ ) is $10 \mathrm{cm}$ in height. The other strain $(A A B B C C)$ is $22 \mathrm{cm}$ in height. The two strains are crossed, and the resulting $\mathrm{F}_{1}$ are interbred to produce $\mathrm{F}_{2}$ progeny. Give the phenotypes and the expected proportions of the $\mathrm{F}_{2}$ progeny.
A farmer has two homozygous varieties of tomatoes. One variety, called Little Pete, has fruits that average only $2 \mathrm{cm}$ in diameter. The other variety, Big Boy, has fruits that average a whopping $14 \mathrm{cm}$ in diameter. The farmer crosses Little Pete and Big Boy; he then intercrosses the $\mathrm{F}_{1}$ to produce $\mathrm{F}_{2}$ progeny. He grows $2000 \mathrm{F}_{2}$ tomato plants and doesn't find any $\mathrm{F}_{2}$ offspring that produce fruits as small as Little Pete or as large as Big Boy. If we assume that the differences in fruit size of these varieties are produced by genes with equal and additive effects, what can we condude about the minimum number of loci with pairs of alleles detemining the differences in fruit size of the two varieties?
Seed size in a plant is a polygenic characteristic. A grower crosses two pure-breeding varieties of the plant and measures seed size in the $\mathrm{F}_{1}$ progeny. She then backcrosses the $\mathrm{F}_{1}$ plants to one of the parental varieties and measures seed size in the backcross progeny. The grower finds that seed size in the backcross progeny has a higher variance than does seed size in the $\mathrm{F}_{1}$ progeny. Explain why the backcross progeny are more variable.
The following data are the numbers of digits per foot in 25 guinea pigs. Construct a frequency distribution for these data.4,4,4,5,3,4,3,4,4,5,4,4,3,2,4,4,5,6,4,4,3,4,4,4,5.
Ten male Harvard students were weighed in $1916 .$ Their weights are given here in kilograms. Calculate the mean, variance, and standard deviation for these weights. $$51,69,69,57,61,57,75,105,69,63$$
Among a population of tadpoles, the correlation coefficient for size at metamorphosis and time required for metamorphosis is $-0.74 .$ On the basis of this correlation, what condusions can you make about the relative sizes of tadpoles that metamorphose quickly and those that metamorphose more slowly?
A researcher studying alcohol consumption in North American cities finds a significant, positive cor relation between the number of Baptist preachers and alcohol consumption. Is it reasonable for the researcher to conclude that the Baptist preachers are consuming most of the alcohol? Why or why not?
Body weight and length were measured on six mosquito fish; these measurements are given in the following table. Calculate the correlation coefficient for weight and length in these fish.(IMAGE CAN'T COPY).Wet" $\begin{array}{lc}\text { weight }(g) & \text { Length }(m m) \\ 115 & 18 \\ 130 & 19 \\ 210 & 22 \\ 110 & 17 \\ 140 & 20 \\ 185 & 21\end{array}$
The heights of mothers and daughters are given in the following table:(TABLE CAN'T COPY)a. Calculate the correlation coefficient for the heights of the mothers and daughters.b. Using regression, predict the expected height of a daughter whose mother is 67 inches tall.
Phenotypic variation in the tail length of mice has the following components: (TABLE CAN'T COPY)a. What is the narrow-sense heritability of tail length?b. What is the broad-sense heritability of tail length?
The narrow-sense heritability of ear length in Reno rabbits is $0.4 .$ The phenotypic variance $\left(V_{p}\right)$ is $0.8,$ and the environmental variance $\left(V_{\mathrm{E}}\right)$ is $0.2 .$ What is the additive genetic variance $\left(V_{A}\right)$ for earlength in these rabbits?
Assume that human ear length is influenced by multiple genetic and environmental factors. Suppose you measured ear length on three groups of people, in which group A consists of five unrelated persons, group B consists of five siblings, and group C consists of five first cousins. a. With the assumption that the environment for each group is similar, which group should have the highest phenotypic variance? Explain why.b. Is it realistic to assume that the environmental variance for each group is similar? Explain your answer.
A characteristic has a nar row-sense heritability of 0.6.a. If the dominance variance $\left(V_{0}\right)$ increases and all other variance components remain the same, what will happen to the narrow-sense heritability? Will it increase, decrease, or remain the same? Explain.b. What will happen to the broad-sense heritability? Explain.c. If the environmental variance $\left(V_{\mathrm{E}}\right)$ increases and all other variance components remain the same, what will happen to the narrow-sense heritability? Explain.d. What will happen to the broad-sense heritability? Explain.
Flower color in the varieties of pea plants studied by Mendel is controlled by alleles at a single locus. A group of peas homozygous for purple flowers is grown. Careful study of the plants reveals that all their flowers are purple, but there is some variability in the intensity of the purple color. What would the estimated heritability be for this variation in flower color? Explain your answer.
A graduate student is studying a population of bluebonnets along a roadside. The plants in this population are genetically variable. She counts the seeds produced by 100 plants and measures the mean and variance of seed number. The variance is $20 .$ Selecting one plant, the student takes cuttings from it and cultivates them in the greenhouse, eventually producing many genetically identical clones of the same plant. She then transplants these clones into the roadside population, allows them to grow for 1 year, and then counts the number of seeds produced by each of the cloned plants. The student finds that the variance in seed number among these cloned plants is $5 .$ From the phenotypic variance of the gen etically variable and genetically identical plants, she calculates the broad-sense heritability. a. What is the broad-sense heritability of seed number for the roadside population of bluebonnets?b. What might cause this estimate of heritability to be inaccurate?
Many researchers have estimated the heritability of human traits by comparing the correlation coefficients of monozygotic and dizygotic twins (see pp. $148-149)$ One of the assumptions in using this method is that two monozygotic twins experience environments that are no more similar to each other than those experienced by two dizygotic twins. How might this assumption be violated? Give some specific examples of how the environments of two monozygotic twins might be more similar than the environments of two dizygotic twins.
What conclusion can you draw from Figure 24.18 about the proportion of phenotypic variation in shell breadth that is due to genetic differences? Explain your reasoning.
A genetics researcher determines that the broad-sense heritability of height among Southwestern University undergraduate students is 0.90. Which of the following conclusions would be reasonable? Explain your answer. a. Since Sally is a Southwestern University undergraduate student, $10 \%$ of her height is determined by nongenetic factors.b. Ninety percent of variation in height among all undergraduate students in the United States is due to genetic differences.c. Ninety percent of the height of Southwestern University undergraduate students is determined by genes.d. Ten percent of the variation in height among Southwestern University undergraduate students is determined by variation in nongenetic factors.e. Because the heritability of height among Southwestern University students is so high, any change in the students' environment will have minimal effect on their height.
The length of the middle joint of the right index finger was measured on 10 sets of parents and their adult offspring. The mean parental lengths and the mean offspring lengths for each family are listed in the following table. Calculate the regression coefficienMean parental length $(m m)$ for regression of mean offspring Iength against mean parental length and estimate the narrow-sense heritability for this characteristic. (TABLE CAN'T COPY)
Assume that in Figure $24.14, x$ equals the mean phenotype of the parents and $y$ equals the mean phenotype of the offspring. Which line represents the highest heritability? Explain your answer.
Drosophila buzzatii is a fruit fly that feeds on the rotting fruits of cacti in Australia. Timothy Prout and Stuart Barker calculated the heritabilities of body size, as measured by thorax length, for a natural population of $D .$ buzzatii raised in the wild and for a population of $D .$ buzzatii collected in the wild but raised in the laboratory (T. Prout and J. S. F. Barker. 1989. Genetics $123: 803-813) .$ They found the following heritabilities.(EQUATION CAN'T COPY)Why do you think that the heritability measured in the laboratory-reared population is higher than that measured in the natural population raised in the wild?
Mr. Jones is a pig farmer. For many years, he has fed his pigs the food left over from the local university cafeteria, which is known to be low in protein, deficient in vitamins, and downright untasty. However, the food is free, and his pigs don't complain. One day a salesman from a feed company visits Mr. Jones. The salesman claims that his company sells a new, high-protein, vitamin-enriched feed that enhances weight gain in pigs. Although the food is expensive, the salesman claims that the increased weight gain of the pigs will more than pay for the cost of the feed, increasing Mr. Jones's profit. Mr. Jones responds that he took a genetics class at university and that he has conducted some genetic experiments on his pigs; specifically, he has calculated the narrow-sense heritability of weight gain for his pigs and found it to be 0.98. Mr. Jones says that this heritability value indicates that $98 \%$ of the variance in weight gain among his pigs is determined by genetic differences, and therefore the new pig feed can have little effect on the growth of his pigs. He concludes that the feed would be a waste of his money. The salesman doesn't dispute $\mathrm{Mr}$. Jones' heritability estimate, but he still claims that the new feed can significantly increase weight gain in Mr. Jones' pigs. Who is correct and why?
Joe is breeding cockroaches in his dorm room. He finds that the average wing length in his population of cockroaches is $4 \mathrm{cm} .$ He chooses six cockroaches that have the largest wings; the average wing length among these selected cockroaches is $10 \mathrm{cm}$. Joe interbreeds these selected cockroaches. From earlier studies, he knows that the narrow-sense heritability for wing length in his population of cockroaches is 0.6.a. Calculate the selection differential and expected response to selection for wing length in these cockroaches.b. What should be the average wing length of the progeny of the selected cockroaches?
Three characteristics in beef cattle-body weight, fat content, and tenderness-are measured, and the following variance components are estimated: (TABLE CAN'T COPY)In this population, which characteristic would respond best to sclection? Explain your reasoning.
A randier detemines that the average amount of wool produced by a sheep in her flock is 22 kg per year. In an attempt to increase the wool production of her flock, the rancher picks five male and five female sheep with the greatest wool production; the average amount of wool produced per sheep by those selected is $30 \mathrm{kg}$. She interbreeds these selected sheep and finds that the average wool production among the progeny of the selected sheep is $28 \mathrm{kg}$. What is the narrow -sense heritability for wool production among the sheep in the rancher's flock?
A strawberry famer determines that the average weight of individual strawberries produced by plants in his garden is $2 \mathrm{g}$. He selects the 10 plants that produce the largest strawberries; the average weight of strawberries among these selected plants is $6 \mathrm{g}$. He interbreeds these selected plants. The progeny of these sciected plants produce strawberries that weigh $5 \mathrm{g}$. If the farmer were to select plants that produce an average strawberry weight of 4 $\mathrm{g}$, what would be the predicted weight of strawberrics produced by the progeny of these selected plants?
Has the response to selection levaled off in the strain of corn selected for high oil content shown in Figure$24.22 ?$ What does this observation suggest about genetic variation in the strain selected for high oil content?
The narrow-sense heritability of wing length in a population of Drosophila melanogaster is $0.8 .$ The narmwsense heritability of head width in the same population is $0.9 .$ The genetic correlation between wing length and head width is - 0.86. If a geneticist selects for increased wing length in these flies, what will happen to head width?
Pigs have been domesticated from wild boars. Would you expect to find higher heritability for weight among domestic pigs or wild boars? Explain your answer.
Bipolar illness is a psychiatric disorder with a strong hereditary basis, but the exact mode of inheritance is not known. Research has shown that siblings of patients with bipolar illness are more likely to develop the disorder than are siblings of unaffected persons. Findings from one study demonstrated that the ratio of bipolar brothers to bipolar sisters is higher when the patient is male than when the patient is female. In other words, relatively more brothers of bipolar patients also have the disease when the patient is male than when the patient is female. What does this observation suggest about the inheritance of bipolar illness?
We have explored some of the difficulties in separating the genetic and environmental components of human behavioral characteristics. Considering these difficulties and what you know about calculating heritability, propose an experimental design for accurately measuring the heritability of musical ability.
A student who has just learned about quantitative genetics says, "Heritability est imates are worthless! They don't tell you anyth ing about the genes that affect a characteristic. They don't provide any infor mation about the types of offspring to expect from a cross. Heritability estimates measured in one population can't be used for other populations, so they don't even give you any general information about how much of a characterist ic is genetically determined. Heritabilities don't do anything but make undergraduate students sweat during tests." How would you respond to this statement? Is the student correct? What good are heritabilities, and why do geneticists bother to calculate them?
Eugene Eisen selected for increased 12 -day litter weight (total weight of a litter of offspring 12 days after birth) in a population of mice (E. I. Eisen. 1972. Genetics $72: 129-142) .$ The 12 -day litter weight of the population steadily increased but then leveled off after about 17 generations. At generation $17,$ Eisen took one family of mice from the selected population and reversed the selection procedure: in this group, he selected for decreased 12 -day litter weight. This group immediately responded to decreased selection; the 12 -day litter weight dropped $4.8 \mathrm{g}$ within one generation and dropped 7.3 g after 5 generations. On the basis of the results of the reverse selection, what is the most likely explanation for the leveling off of 12- day litter weight in the original population? (IMAGE CAN'T COPY)