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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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Eighteen
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Quantitative Inheritance
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BOX 18.1 CONTINUED
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then the three groups will have different geotactic scores. We can then conclude that the region of the chromosome that contains the RFLP also contains a quantitative trait locus. Finding the right RFLP is, of course, a tedious and time-consuming task. In a recent summary of the literature, Steven Tanksley reported that numerous quantitative trait loci have been mapped in tomatoes, corn, and other organisms. For example, ve quantitative trait loci have been mapped in tomatoes for fruit growth, and eleven quantitative trait loci have been mapped in corn for plant height. Enough data seem to be present to recognize an interesting generality. That is, our de nition of an additive model may need to be rethought because it appears that in almost every case studied so far, one or more of the quantitative trait loci account for a major portion of the phenotype, whereas most of the loci had very small effects. Thus, the additive model that assumes that all polygenes contribute equally to the phenotype may be wrong. However, additive models that allow different loci to contribute different degrees to the phenotype are still supported. Also of value from locating quantitative trait loci is a new ability to estimate the number of loci affecting a quantitative trait. In this chapter, we use an estimate of extreme F2 offspring to estimate the number of polygenes. There are other methods, including sophisticated statistical methods, that we will not develop here. Mapping quantitative trait loci gives us a third method, that is, simply counting the number of quantitative trait loci mapped. As the methods of mapping quantitative trait loci have been developed, they have also been re ned. High-resolution techniques under development will help us determine whether quantitative trait loci are, in fact, individual polygenes or clusters of polygenes.
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(We will get to why we use n 1 rather than n in the denominator in a moment.) Note, however, that the above measure is zero. By the de nition of the mean, the absolute value of the sum of deviations above it is equal to the absolute value of the sum of deviations below it one is negative and the other is positive. However, by squaring each deviation, as in equation 18.2, we create a relatively simple index the variance which is not zero and has useful properties related to the normal distribution.
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Ear length (in cm)
Normal distribution of ear lengths in corn. Data are given in table 18.2.
The ear lengths measured in table 18.2 are a sample of all ear lengths in the theoretically in nite population of ears in that variety of corn. Statisticians call sample values statistics (and use letters from the Roman alphabet to represent them), whereas they call population values parameters (and use Greek letters for them). The sample value is an estimate of the true value for the population. Thus, in the variance formula (equation 18.2), the sample value, V or s2, is an estimate of the population variance, 2. When sample values are used to estimate parameters, one degree of freedom is lost for each parameter estimated. To determine the sample variance, we divide not by the sample size, but by the degrees of freedom (n 1 in this case, as de ned in chapter 4). The variance for the entire population (assuming we know the population mean, , and all the data values) would be calculated by dividing by n. The sample variance is calculated in table 18.2. The variance has several interesting properties, not the least of which is the fact that it is additive. That is, if we can determine how much a given variable contributes to the total variance, we can subtract that amount of variance from the total, and the remainder is caused by whatever other variables (and their interactions) affect the trait. This property makes the variance extremely important in quantitative genetic theory. The standard deviation is also a measure of variation of a distribution. It is the square root of the variance: s V
(18.3)
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