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Two-Locus Control
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Now let us examine the same kind of cross using two other stocks of wheat with red and white kernels. Here, when the resulting intermediate (medium-red) F1 are self-fertilized, ve color classes of kernels emerge in a ratio of 1 dark red:4 medium dark red:6 medium red:4 light red:1 white ( g. 18.3). The offspring ratio, in sixteenths, comes from the self-fertilization of a dihybrid in which the two loci are unlinked. In this case, both loci affect the same trait in the same way. In gure 18.3, each capital
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Comparison of continuous variation (ear length in corn) with discontinuous variation (height in peas).
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Cross involving the grain color of wheat in which one locus is segregating.
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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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Another cross involving wheat grain color in which two loci are segregating.
letter represents an allele that produces one unit of color, and each lowercase letter represents an allele that produces no color. Thus, the genotype AaBb has two units of color, as do the genotypes AAbb and aaBB. All produce the same intermediate grain color. Recall from chapter 2 that a cross such as this produces nine genotypes in a ratio of 1:2:1:2:4:2:1:2:1. If these classes are grouped according to numbers of color-producing alleles, as shown in gure 18.3, the 1:4:6:4:1 ratio appears. This ratio is a product of a binomial expansion.
Three-Locus Control
In yet another cross of this nature, H. Nilsson-Ehle in 1909 crossed two wheat strains, one with red and the other with white grain, that yielded plants in the F1 generation with grain of intermediate color. When these plants were self-fertilized, at least seven color classes, from red to white, were distinguishable in a ratio of 1:6:15:20:15:6:1 ( g. 18.4). This result is explained by assuming that three loci are assorting independently, each with two alleles, so that one allele produces a unit of red color and the other allele does not. We then see seven color classes, from red to white, in the 1:6:15:20:15:6:1 ratio. This ratio is in sixty-fourths, directly from the 8 8 (trihybrid) Punnett square, and comes from grouping genotypes in accordance with the number of colorproducing alleles they contain. Again, the ratio is one that is generated in a binomial distribution.
Multilocus Control
From here, we need not go on to an example with four loci, then ve, and so on. We have enough information to draw generalities. It should not be hard to see how discrete loci can generate a continuous distribution ( g. 18.5). Theoretically, it should be possible to distinguish
One of Nilsson-Ehle s crosses involving three loci controlling wheat grain color. Within the Punnett square, only the number of color-producing alleles is shown in each box to emphasize color production.
Tamarin: Principles of Genetics, Seventh Edition
IV. Quantitative and Evolutionary Genetics
18. Quantitative Inheritance
The McGraw Hill Companies, 2001
Traits Controlled by Many Loci
The change in shape of the distribution as increasing numbers of independent loci control grain color in wheat. If each locus is segregating two alleles, with each allele affecting the same trait, eventually a continuous distribution will be generated in the F2 generation.
three color alleles, or it may belong to the medium-red class with only two color alleles ( g. 18.5). The variation within each genotype is due to the environment that is, two organisms with the same genotype may not necessarily be identical in color because nutrition, physiological state, and many other variables in uence the phenotype. Figure 18.6 shows that it is possible for the environment to obscure genotypes even in a one-locus, two-allele system. That is, a height of 17 cm could result in the F2 from either the aa or Aa genotype in the gure when there is excessive variation ( g. 18.6, column 3). In the other two cases in gure 18.6, there would be virtually no organisms 17 cm tall. Systems such as those we are considering, in which each allele contributes a small unit to the phenotype, are easily in uenced by the environment, with the result that the distribution of phenotypes approaches the bell-shaped curve seen at the bottom of gure 18.5. Thus, phenotypes determined by multiple loci with alleles that contribute dosages to the phenotype will approach a continuous distribution. This type of trait is said to exhibit continuous, quantitative, or metrical variation. The inheritance pattern is polygenic or quantitative. The system is termed an additive model because each allele adds a certain amount to the phenotype. From the three wheat examples just discussed, we can generalize to systems with more than three polygenic loci, each segregating two alleles. From table 18.1, we can predict the distribution of genotypes and phenotypes expected from an additive model with any number of unlinked loci segregating two alleles each.This table is useful when we seek to estimate how many loci are producing a quantitative trait, assuming it is possible to distinguish the various phenotypic classes. For example, when a strain of heavy mice was crossed with a lighter strain, the F1 were of intermediate weight. When these F1 were interbred, a continuous distribution of adult weights appeared in the F2 generation. Since only about one mouse in 250 was as heavy as the heavy parent stock, we could guess that if an additive model holds, then four loci are segregating. This is because we expect 1/(4)n to be as extreme as either parent; one in 250 is roughly 1/(4)4 1/256.
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