Solved Problems
Part 1
- Two homozygous varieties of Nicotiana longiflora have mean corolla lengths of 5 and 93.3 mm. The average of the F1 hybrids from these two varieties was of intermediate length. Among 444 F2 plants, none were found to have flowers either as long as or as short as the average of the parental varieties. Estimate the minimal number of pairs of alleles segregating from the F1.
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2- A representative sample of lamb weaning weights is shown below. Determine the weight limits within which 95% of all lambs from this population are expected to be found at weaning time.
81 | 81 | 83 | 101 | 86 |
65 | 68 | 77 | 66 | 92 |
94 | 85 | 105 | 60 | 90 |
94 | 90 | 81 | 63 | 58 |
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3- Two pairs of independently segregating genes with two alleles each, A/a and B/b, determine plant height additively in a population. The homozygote AA BB is 50cm tall, and the homozygote aa bb is 30cm tall.
- What is your prediction of the F1 height in a cross between the two homozygous stocks?
- What genotypes in the F2 will show a height of 40cm after an F1 * F1 cross?
- What will be the F2 frequency of the 40-cm plants?
- What assumptions have you made in answering this question?
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4- Assume that the difference between a corn plant 10 dm (decimeters) high and one 26 dm high results from four pairs of equal and cumulative multiple alleles, with the 26-dm plants being AA BB CC DD and the 10-dm plants being aa bb cc dd. For this problem, two 14-dm corn plants, when crossed, give nothing but 14-dm offspring (case A). Two other 14-dm plants give one 18-dm, four 16-dm, six 14-dm, and six 14-dm, four 12-dm, and one 10-dm offspring (case B). What genotypes for each of these 14-dm parents (cases A and B) would explain these results?
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5- The data shown below are from a series of crosses between two homozygous rodent lines to study hair length. All animals were grown under the same uniform environmental conditions. Line A has a hair length of 20 mm and Line B has a length of 36 mm. All the F1 progeny had hair length of 28 mm. The following results were obtained in the F2 generation. Assume that all the contributing alleles have equal and additive effects.
Hair length (mm) | # of animals |
36 | 2 |
34 | 14 |
32 | 60 |
30 | 108 |
28 | 140 |
26 | 114 |
24 | 52 |
22 | 18 |
20 | 2 |
a) Determine the number of polygene loci at which the parents carry different alleles
b) Provide the genotype for the parents and F1
c) What is the phenotypic value of each contributing allele?
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6- A random sample of lambs from a large flock was weighed at weaning at 100 days. The weight in kilograms for each of the 20 Lambs is shown in the accompanying table.
37 | 37 | 38 | 46 | 39 |
30 | 31 | 35 | 30 | 42 |
43 | 39 | 48 | 27 | 41 |
43 | 41 | 37 | 29 | 26 |
a) Estimate the mean, the variance, and the standard deviation of 100-day weaning weight in this population.
b) What range of weaning weights will be expected to include 68% of the Lambs?
c) What the range of weaning weights would be expected to include 95% of the Lambs?
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7- The following questions pertain to a normal distribution.
- What term applies to the value along the x-axis that corresponds to the peak of the distribution?
- If two normal distributions have the same mean but different variances, which is the broader?
- What proportion of the population is expected to lie within one standard deviation of the mean?
- What proportion of the population is expected to lie within two standard deviations of the mean?
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8- Consider a complex trait in which the phenotypic values in a large population are distributed approximately according to a normal distribution with mean 100 and standard deviation 15. What proportion of the population has a phenotypic value
- above 130
- below 85
- above 85
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9- The study of development time in a sample of pure breeding variety of self-fertilizing pea plants indicates that the time from planting to maturity follows a normal distribution with a mean of 77 days and a standard deviation of 2.39 days.
a. How much of the phenotypic variance shown for this trait is due to genetics? Explain.
b. What is the environmental variance for this trait?
c. What is the broad sense heritability of this trait?
d. Assume that a plant breeder selects plants that mature in 69 days to be the parents of the next generation. Estimate the time required for the next generation to mature.
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10- Pea plants of the variety described in the previous problem are crossed with pea plants from another pure breeding line. The time from planting to maturity of the F1 and F2 progeny is determined. The variances for this trait shown by the F1 and F2 are 4.85 and 9.67 days, respectively.
- What are the environmental and genotypic variances for this trait?
- What is the broad sense heritability for this trait?
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11- Two highly inbred (means homozygous) strains of mice are crossed. The F1 generation has a mean tail length of 5 cm and a standard deviation of 1.5 cm. The F2 generation has a mean tail length of 5 cm and a standard deviation of 4 cm. What are the environmental variance, the genetic variance, and the broad-sense heritability of tail length in this population?
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12- Most population has an average weight gain between ages 3 and 6 weeks of 12 grams, and the narrow-sense heritability of the weight gain between 3 and 6 weeks is 20%.
- What average weight gain would be expected among the offspring of parents whose average weight gain was 16 gram?
- What average weight gain would be expected among the offspring of parents whose average weight gain was 8 gram?
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13- The following measurements of head width and wing length were made on a series of steamer ducks:
Specimen | Head Width (cm) | Wing Length(cm) |
1 | 2.75 | 30.3 |
2 | 3.20 | 36.2 |
3 | 2.86 | 31.4 |
4 | 3.24 | 35.7 |
5 | 3.16 | 33.4 |
6 | 3.32 | 34.8 |
7 | 2.52 | 27.2 |
8 | 4.16 | 52.7 |
a. Calculate the mean and the standard deviation of head width and of wing length for these eight birds.
b. Calculate the correlation coefficient for the relationship between head width and wing length in this series of ducks.
c. What conclusions can you make about the association between head width and wing length in steamer ducks?
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14- Two pairs of independently segregating genes with two alleles each, A/a and B/b, determine plant height additively in a population. The homozygote AA BB is 50cm tall, and the homozygote aa bb is 30cm tall.
a. What is your prediction of the F1 height in a cross between the two homozygous stocks?
b. What genotypes in the F2 will show a height of 40cm after an F1 x F1 cross?
c. What will be the F2 frequency of the 40-cm plants?
d. What assumptions have you made in answering this question?
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15- A quantitative geneticist determines the following variance components for leaf width in a population of wildflowers growing along a roadside in Kentucky:
Additive genetic variance (VA)=4.2
Dominance genetic variance (VD)=1.6
Interaction genetic variance (VI)=0.3
Environmental variance (VE)=2.7
Genetic-environmental variance (VG*E)=0.0
a. Calculate the broad-sense heritability and the narrow-sense heritability for leaf width in this population of wildflowers.
b. What do the heritabilities obtained in (a) indicate about the genetic nature of leaf width variation in this plant?
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16- In Kansas, a farmer is growing a variety of wheat called TK138. He calculates the narrow sense heritability for yield (the amount of wheat produced per acre) and finds that the heritability of yield for TK138 is 0.95. The next year, he visits a farm in Poland and observes that another variety of wheat, UG334, growing there has only about 40 percent as much yield as the TK138 grown on his farm in Kansas. Since he found the heritability of yield in his wheat to be very high, he concludes that the TK138 wheat is genetically superior to the UG334 wheat, and he tells the Polish farmers that they can increase their yield by using TK138. Is his conclusion correct? Why or why not?
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17- Dermatoglyphics are the patterns of the ridged skin found on the fingertips, toes, palms, and soles of the feet. (Fingerprints are dermatoglyphics.) Classification of dermatoglyphics frequently is based on the number of triradii: A triradius is a point from which three ridge systems separate at angels of 120 degree. The number of triradii on all 10 fingers was counted for each member of several families, and the results are tabulated here.
Family | Mean number of Triradii in the parents | Mean number of Triradii in the offspring |
1 | 14.5 | 12.5 |
2 | 8.5 | 10 |
3 | 13.5 | 12.5 |
4 | 9 | 7 |
5 | 10 | 9 |
6 | 9.5 | 9.5 |
7 | 11.5 | 11 |
8 | 9.5 | 9.5 |
9 | 15 | 17.5 |
10 | 10 | 10 |
a. Calculate the narrow-sense heritability for the number of triradii by the regression of the mean phenotype of the parents against the mean phenotype of the offspring.
b. What does your calculated heritability value indicate about the relative contributions of genetic variation and environmental variation to the differences observed in number of triradii?
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18- The heights of nine college-age males and the heights of their fathers are presented here.
Height of Son (inches) | Height of Father (inches) |
70 | 70 |
72 | 76 |
71 | 72 |
64 | 70 |
66 | 70 |
70 | 68 |
74 | 78 |
70 | 74 |
73 | 69 |
a. Calculate the mean and the variance of height for the sons and for the fathers.
b. Calculate the correlation coefficient for the relationship between the height of father and height of son.
c. Determine the narrow-sense heritability of height in this group by regression of the son’s height on the height of father.
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19- A scientist wants to determine the narrow-sense heritability of tail length in mice. He measures tail length among the mice of a population and finds a mean tail length of 9.7 cm. He then selects the 10 mice in the population with the longest tail: Mean tail length in these selected mice is 14.3 cm. He interbreeds the mice with the long tails and examines tail length in their progeny. The mean tail length in the F1 progeny of the selected mice is 13 cm. Calculate the selection differential, the response to selection, and the narrow-sense heritability for tail length in these mice.
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20- Assume that all phenotypic variance in seed weight in beans is genetically determined and is additive. From a population in which the mean seed weight was 0.88 g, a farmer selected two seeds, each weighing 1.02g. He planted these and crossed the resulting plants to each other, then collected and weighed their seeds. The mean weight of their seeds was 0.96 g. What is the narrow-sense heritability of seed weight?
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21- The narrow-sense heritability of egg weight in a particular flock of chickens is 0.60. A farmer selects for increased egg weight in this flock. The difference in the mean egg weight of the unselected chickens and the selected chickens is 10 g. How much should egg weight increase in the offspring of the selected chickens?
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22- Assume that varieties of wheat are available in which kernel color is known to be determined by 3 loci, designated A, B, and C. Assume that each Locus has two alleles. Alleles A, B, and C, each add an equal quantity of red pigment to the phenotype while alleles a, b, and c contribute no pigment. Pure-breeding strains with white and dark red kernels are crossed to produce an F1 which is in turn selfed to form an F2. Pairs of F2 plants are then crossed to produce the F3 phenotypes in the following list. For each F3 phenotype, identify the genetic makeup of the F2 parents.
a. all white
b. 63/64 showing varying shades of red, and 1/64 white.
c. 15/16 showing varying shades of red, and 1/16 white
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23- Assume that tail length in white rats is a quantitative trait. In one pure-breeding line the tail averages 7 inches and in another it averages 4 inches. Progeny arising from the interbreeding of these two lines have tails which average 5.5 inches. When members of the F1 interbreed, the 496 offspring have tails which also average 5.5 in in length, but which vary much more than those of their parents, with the range between 4 and 7 inches. Two members of the F2 have 7-inch tails.
a. Based on these data, what can be concluded about the number of genes involved in determining tail length?
b. How many members of the F2 would be expected to have four-inch tails?
c. Assuming an equal contribution from each effective allele, how much does each allele contribute to the trait?
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24- The distribution of ear length for a sample of 60 adult rabbits approximates a normal curve. The mean ear length is 5.27 cm with a variance of 1.21 cm.
a. Determine the standard deviation for the sample
b. Within what range do 68% of the sample values fall?
c. Within what range do 99% of the sample values fall?
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25- Distinguish between a) broad-sense heritability and narrow-sense heritability. b) which of these two estimates of heritability is of greatest interest to plant and animal breeders? explain why?
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26- Egg weight in chickens is a quantitative trait. The average egg weight in a particular generation is 25.7 grams. The hens selected for this generation by the chicken breeder to give rise to the next generation produce eggs with an average weight of 29.1 grams, and their offspring produce eggs with an average weight of 28 grams.
a. Determine the realized heritability of this trait.
b. Is this trait likely to have a significant genetic basis? explain.
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27- Study indicates that litter size in swine has a realized heritability of 0.11. A generation of swine shows an average litter size of 9.2, and individuals selected from this generation to be the parents of the next generation have an average litter size of 11.1. Predict the average litter size that will be expected in the next generation.
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28- The number of tomatoes produced per plant was determined for the F2 generation of a cross between two varieties of tomato plants. This tomato production exhibited a normal distribution with a mean of 27 and a variance of 9. What percentage of the F2 plants would be expected to produce:
a. between 24 and 30 tomatoes
b. more than 30 tomatoes
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29- The F2 phenotypic ratio for a particular quantitative trait is 1:6:15:20:15:6:1. How many pairs of alleles are involved in determining this trait?
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