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Tamarin: Principles of Genetics, Seventh Edition
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IV. Quantitative and Evolutionary Genetics
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18. Quantitative Inheritance
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The McGraw Hill Companies, 2001
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Quantitative Inheritance
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STUDY OBJECTIVE 3: To de ne and measure heritability, the unit of inheritance of variation in traits controlled by many loci 542 547 Equipped with statistical tools, we analyzed the genetic control of continuous traits. The heritability estimates tell us how much of the variation in the distribution of a trait can be attributed to genetic causes. Heritability in the narrow sense is the relative amount of variance due to additive
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loci. Heritability in the broad sense is the relative amount of variance due to all genetic components, including dominance and epistasis. In practice, heritability can be calculated as realized heritability gain divided by selection differential. Estimates of human heritabilities can be constructed from correlations among relatives, concordance and discordance between twins, and studies of monozygotic twins reared apart.
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PROBLEM 1: In a certain stock of wheat, grain color is controlled by four loci acting according to an additive model. How many different gametes can a tetrahybrid produce How many different genotypes will result if tetrahybrids are self-fertilized What will be the phenotypic distribution of these genotypes Answer: Assume the A, B, C, and D loci with A and a, B and b, C and c, and D and d alleles, respectively. A tetrahybrid will have the genotype Aa Bb Cc Dd. A gamete can get either allele at each of four independently assorting loci, so there are 24 16 different gametes. Three genotypes are possible for each locus, two homozygotes and a heterozygote. Therefore, for four independent loci, there are 34 81 different genotypes. Phenotypes are distributed according to the binomial distribution. Thus, there will be a pattern of (A a)2n (A a)8; a ratio of 1:8:28:56:70:56:28:8:1 of phenotypes with decreasing red color from left to right, eight red colors plus white. PROBLEM 2: In horses, white facial markings are inher-
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P R O B L E M S
YO Y YP offspring yield 3.1 mean yield of the population parental yield 3.4 2.2
Substituting into equation 18.8: H YO YP Y Y 3.1 3.4 2.2 2.2 0.9 1.2 0.75
PROBLEM 3: Corn growing in a eld in Indiana had a lysine (amino acid) content of 2.0%, with a variance of 0.16. When grown in the greenhouse under controlled and uniform conditions, the mean lysine content was again 2.0%, but the variance was 0.09. What measure of heritability can you calculate
Answer: We use equation 18.9 for the calculation of heritability by partitioning of the variance (VPh VG VE). In this case: VPh VG VE total phenotypic variance 0.16 variance due to genotype 0.09 variance due to environment
ited in an additive fashion. These markings are scored on a scale that begins at zero. In a particular population, the average score is 2.2. A group of horses with an average score of 3.4 is selected to be parents of the next generation. The offspring of this group of selected parents have a mean score of 3.1. What is the realized heritability of white facial markings in this herd of horses Answer: This is a simple selection experiment; the data t our equation for realized heritability (equation 18.8). In this case:
In the greenhouse, we have minimized environmental variance, meaning the total genotypic variance 0.09. If we subtract this from the total variance, we get the original environmental variance: 0.16 0.09 0.7. Heritability in the broad sense is the genetic variance divided by the total phenotypic variance, or 0.09/0.16 0.56.
Tamarin: Principles of Genetics, Seventh Edition
IV. Quantitative and Evolutionary Genetics
18. Quantitative Inheritance
The McGraw Hill Companies, 2001
Exercises and Problems
E X E R C I S E S
TRAITS CONTROLLED BY MANY LOCI
A N D
P R O B L E M S *
1. A variety of squash has fruits that weigh about 5 pounds each. In a second variety, the average weight is 2 pounds. When the two varieties are crossed, the F1 produce fruit with an average weight of 3.5 pounds. When two of these are crossed, their offspring produce a range of fruit weights, from 2 to 5 pounds. Of two hundred offspring, three produce fruits weighing about 5 pounds and three produce fruits about 2 pounds in weight. Approximately how many allelic pairs are involved in the weight difference between the varieties, and approximately how much does each effective gene contribute to the weight 2. In rabbit variety 1, ear length averages 4 inches. In a second variety, it is 2 inches. Hybrids between the varieties average 3 inches in ear length. When these hybrids are crossed among themselves, the offspring exhibit a much greater variation in ear length, ranging from 2 to 4 inches. Of ve hundred F2 animals, two have ears about 4 inches long, and two have ears about 2 inches long. Approximately how many allelic pairs are involved in determining ear length, and how much does each effective gene seem to contribute to the length of the ear What do the distributions of P1, F1, and F2 probably look like 3. Assume that height in people depends on four pairs of alleles. How can two persons of moderate height produce children who are much taller than they are Assume that the environment is exerting a negligible effect. 4. How do polygenes differ from traditional Mendelian genes 5. If skin color is caused by additive genes, can matings between individuals with intermediate-colored skin produce light-skinned offspring Can such matings produce dark-skinned offspring Can matings be-
tween individuals with light skin produce darkskinned offspring (See also QUANTITATIVE INHERITANCE IN HUMAN BEINGS) 6. The tabulated data from Emerson and East ( The Inheritance of Quantitative Characters in Maize, 1913, Univ. Nebraska Agric. Exp. Sta. Bull, no. 2) show the results of crosses between two varieties of corn and their F2 offspring (see the table on ear length in corn). Provide an explanation for these data in terms of number of allelic pairs controlling ear length. Do all the genes involved affect length additively Explain. 7. In Drosophila, a marker strain exists containing dominant alleles that are lethal in the homozygous condition on both chromosome 2, 3, and 4 homologues. These six lethal alleles are within inversions, so there is virtually no crossing over. The strain thus remains perpetually heterozygous for all six loci and therefore all three chromosome pairs. (Geneticists use a shorthand notation in these balanced-lethal systems in which only the dominant alleles on a chromosome are shown, with a slash separating the two homologous chromosomes.) The markers are: chromosome 2, Curly and Plum (Cy/Pm, shorthand for CyPm /Cy Pm); chromosome 3, Hairless and stubble (H/S); and chromosome 4, Cell and Minute(4) (Ce/M[4]). With this strain, which allows you to follow particular chromosomes by the presence or absence of phenotypic markers, construct crosses to give the strains Crow used (see g. 18.7) to determine the location of polygenes for DDT resistance. 8. A red- owered plant is crossed with a yellow owered plant to produce F1 plants with orange owers. The F1 offspring are selfed, and they produce plants with owers in a range of seven different colors. How many genes are probably involved in color production
Ear Length in Corn (cm) 5 Variety P60 Variety P54 F1 F2(F1 F1) 4 6 21 7 24 8 8 1 19 12 26 12 47 14 73 3 17 68 11 9 68 12 4 39 15 25 26 15 15 9 10 1 7 2 9 10 11 12 13 14 15 16 17 18 19 20 21
* Answers to selected exercises and problems are on page A-20.
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