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A distribution (see g. 18.5, bottom) can be described in several ways. One is the formula for the shape of the curve formed by the frequencies within the distribution. A more functional description of a distribution starts by de ning its center, or mean ( g. 18.8). As we can see from the gure, the mean is not itself enough to describe the distribution. Variation about this mean determines the actual shape of the curve. (We con ne our discussion to symmetrical, bellshaped curves called normal distributions. Many distributions approach a normal distribution.)
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Survival of Drosophila in the presence of DDT. Numbers and arrangements of DDT-resistant and susceptible chromosomes vary. (Reproduced with permission from the Annual
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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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Table 18.2 Hypothetical Data Set of Ear Lengths
(x) Obtained When Corn Is Grown from an Ear of Length 11 cm
x 7 8 9 9 10 10 10 10 10 10 11 11 11 11 11 11 12 12 12 13 13 13 14 14
Figure 18.8 Two normal distributions (bell-shaped curves) with the same mean.
x )2
4.12 3.12 2.12 2.12 1.12 1.12 1.12 1.12 1.12 1.12 0.12 0.12 0.12 0.12 0.12 0.12 0.88 0.88 0.88 1.88 1.88 1.88 2.88 2.88 4.88 (x 278 25 (x n x)
16.97 9.73 4.49 4.49 1.25 1.25 1.25 1.25 1.25 1.25 0.01 0.01 0.01 0.01 0.01 0.01 0.77 0.77 0.77 3.53 3.53 3.53 8.29 8.29 23.81 96.53
16 x n x s2 s 278 25 x n V s
Mean, Variance, and Standard Deviation
The mean of a set of numbers is the arithmetic average of the numbers and is de ned as x in which x x n the mean the summation of all values the number of values summed x n
(18.1)
11.12 x)2 1 96.53 24 2.0 4.02
In table 18.2, the mean is calculated for the distribution shown in gure 18.9.The variation about the mean is calculated as the average squared deviation from the mean: s2 V (x n x)2 1
(18.2)
This value (V or s2) is called the variance. Observe that the atter the distribution is, the greater the variance will be. The variance is one of the simplest measures we can calculate of variation about the mean. You might wonder why we simply don t calculate an average deviation from the mean rather than an average squared deviation. For example, we could calculate a measure of variation as (x n x) 1
Tamarin: Principles of Genetics, Seventh Edition
IV. Quantitative and Evolutionary Genetics
18. Quantitative Inheritance
The McGraw Hill Companies, 2001
Population Statistics
BOX 18.1
apping the location of a standard locus is conceptually relatively easy, as we saw in the mapping of the fruit y genome. We look for associations of phenotypes that don t segregate with simple Mendelian ratios and then map the distance between loci by the proportion of recombinant offspring. However, with quantitative loci we have a problem: We can t do simple mapping because genes contributing to the phenotype are often located across the genome. Thus, a particular continuous phenotype will be controlled by loci linked to numerous other loci, many unlinked to each other. However, with the advent of molecular techniques, it has become feasible to map polygenes.
Experimental Methods
Mapping Quantitative Trait Loci
In chapter 13, we showed how a locus can be discovered and mapped in the human genome (and other genomes) by association with molecular markers. That is, as the Human Genome Project has progressed, we have discovered restriction fragment length polymorphisms (RFLPs) that mark every region of all the chromosomes. Conceptually, there is not
Mapping a quantitative trait locus (QTL) to a particular chromosomal region using a restriction fragment length polymorphism (RFLP) marker. A hypothetical chromosome pair in the fruit y is shown. The ies have been selected for a geotactic score; QTL1 is the locus in the high line, and QTL2 is the locus in the low line. RFLP1 is homozygous in the high line and RFLP2 is homozygous in the low line.
much difference between nding the gene for cystic brosis and nding the gene that contributes to a quantitative trait. In theory, we look at a population of organisms and note various RFLPs or other molecular markers. We then look for the association of a marker and a quantitative trait. If an association exists, we can gain confidence that one or more of the polygenes controlling the trait is located in the chromosomal region near the marker. The closer the polygenes are to the markers, the more reliable our estimates are, because they depend on few crossovers taking place in that population. With many crossovers, the association between a particular marker and a particular effect diminishes. Since we don t know immediately from this method whether the region of interest has one or more polygenic loci, a new term has been coined to indicate that ambiguity. Instead of talking about polygenic loci directly, we talk of quantitative trait loci. For example, consider the search for polygenes associated with geotactic behavior in fruit ies (see g. 18.13). As selection proceeds, ies in the high and low lines diverge in their geotactic scores. The lines are also becoming homozygous for many loci since only a few parents are chosen to begin each new generation (see chapter 19). Thus, quantitative trait loci can become associated with different molecular markers in each line ( g. 1). If ies from each line are crossed, heterozygotes will be produced of both the markers and the quantitative trait loci. If there is very little crossing over between the two, three classes of F2 offspring will be produced. These offspring can be grouped according to their RFLPs and then tested for their geotactic scores. If, as gure 1 suggests, a relationship exists between a locus in uencing geotactic score and an RFLP,
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