barcode reader vb.net source code The Relationship Between Two in Software

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Table 18.3 The Relationship Between Two
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Variables, x and y (x = the midparent average of the two parents in wing length in fruit ies in millimeters; y = the offspring measurement)
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x 1.5 1.7 1.9 2 2 2 2.1 2.1 2.1 x x
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2 sx
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Thus equipped, if a cause-and-effect relationship does exist between the two variables, we can predict a y value given any x value. We can either use the formula y a bx or graph the regression line and directly determine the y value for any x value. We now continue our examination of the genetics of quantitative traits.
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y 2 2 2.2 2 2.2 2.2 1.9 2.2 2.5 92.7 x n (x n s2 x 2.51 x)2 1 0.44
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x 2.2 2.3 2.3 2.4 2.4 2.4 2.4 2.4 2.4
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y 2.3 2.2 2.6 2 2.3 2.4 2.6 2.6 2.6 n 37
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x 2.4 2.4 2.6 2.6 2.6 2.6 2.8 2.8 2.9 y y
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2 sy
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y 2.7 2.7 2.7 2.7 2.8 2.9 2.7 2.7 2.5 93.2 y n ( y n
2 sy
x 2.9 2.9 2.9 3 3 3 3.1 3.2 3.2 3.2
y 2.7 2.7 3 2.8 2.8 2.9 3 2.4 2.8 2.9
2.52 y )2 1 0.32
sy (x x ) (y n 1 y)
cov (x, y) r
0.11 0.78
cov(x, y) sx s y
0.11 (0.44)(0.32)
Source: Data from D. S. Falconer, Introduction to Quantitative Genetics, 2d ed. (London: Longman, 1981). Note: Data are graphed in gure 18.11.
Figure 18.12 Plots showing varying degrees of correlation within data sets.
Tamarin: Principles of Genetics, Seventh Edition
IV. Quantitative and Evolutionary Genetics
18. Quantitative Inheritance
The McGraw Hill Companies, 2001
Selection Experiments
Table 18.4 Johannsen s Findings of Relationship Between Bean Weights of Parents and Their Progeny
Weight of Parent Beans 15 65 75 55 65 45 55 35 45 25 35 15 25 Totals 5 8 5 6 2 1 4 11 13 1 30 Weight of Progeny Beans (centigrams) 20 25 30 2 9 20 36 37 3 107 35 3 14 37 139 58 12 263 40 16 51 101 278 133 29 45 37 79 204 498 189 61 50 71 103 287 584 195 38 55 104 127 234 372 115 25 977 60 105 102 120 213 71 11 622 306 135 52 24 9 2 65 75 66 76 69 20 70 45 34 34 20 2 75 19 12 17 4 80 12 6 3 3 85 3 5 1 90 2 n Mean SE 0.43 0.41 0.27 0.18 0.30 0.52 0.13
494 58.47 609 54.37 1,138 51.45 2,238 48.62 835 46.83 180 46.53 5,491 50.39
608 1,068 1,278
P O L Y G E N I C I N H E R I TA N C E IN BEANS
In 1909, W. Johannsen, who studied seed weight in the dwarf bean plant (Phaseolus vulgaris), demonstrated that polygenic traits are controlled by many genes. The parent population was made up of seeds (beans) with a continuous distribution of weights. Johannsen divided this parental group into classes according to weight, planted them, self-fertilized the plants that grew, and weighed the F1 beans. He found that the parents with the heaviest beans produced the progeny with the heaviest beans, and the parents with the lightest beans produced the progeny with the lightest beans (table 18.4). There was a signi cant correlation coef cient between parent and progeny bean weight (r 0.34 0.01). He continued this work by beginning nineteen lines (populations) with beans from various points on the original distribution and sel ng each successive generation for the next several years. After a few generations, the means and variances stabilized within each line. That is, when Johannsen chose, within each line, parent plants with heavier-than-average or lighter-than-average seeds, the offspring had the parental mean with the parental variance for seed size. For example, in one line, plants with both the lightest average bean weights (24 centigrams) and plants with the heaviest average bean weights (47 cg) produced offspring with average bean weights of 37 cg. By sel ng the plants each generation, Johannsen had made them more and more homozygous, thus lowering the number of segregating polygenes. Therefore, the lines became homozygous for certain of the polygenes (different in each line), and any variation in bean weight was then caused only by the environment. Johannsen thus showed that quantitative traits were under the control of many segregating loci.
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