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Table 20.5 Selection Model of Heterozygote Advantage: The A Locus with A1 and A2 Alleles
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Genotype A1 A1 Initial genotypic frequencies Fitness (W ) Ratio after selection Genotypic frequencies after selection 1 p2(1 p2 s1 s1) A1 A2 2pq 1 2pq 2pq W 1 q2(1 q2(1 W A2 A2 q2 s2 s2) s2) 1 1 s1 p2 s2q2 W Total 1
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IV. Quantitative and Evolutionary Genetics
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20. Population Genetics: Process that Change Allelic Frequencies
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The McGraw Hill Companies, 2001
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BOX 20.1
t is surprising how much insight we can gain into the processes of population genetics by modeling them on a computer. The simple computer program presented here calculates changing allelic frequencies due to random mating when alleles at a locus are under a heterozygoteadvantage selection regime. The program is written in the Microsoft Visual Basic language. You can simulate any of the selection models described in chapter 20 by simply changing the variables. Also, this program can model many of the other processes discussed in this and the
Experimental Methods
A General Computer Program to Simulate the Approach to Allelic Equilibrium Under Heterozygote Advantage
last chapter; usually, only a few lines need to be changed to look at an entirely different process. Other com-
puter programs can substitute. Output should be graphed. The program should be rerun several times with various sets of values for the allelic frequencies and tnesses. If the outcome isn t clear by twenty- ve generations, the number of generations can be increased with a few small changes in the program. In the computer program ( g. 1), p is set to 0.9, q is 1 p (0.1), and the three tnesses are named w11, w12, and w22 for the AA, Aa, and aa genotypes, respectively. In this case, w11 is set to 0.4, w12 to 1, and w22 to 0.6, a model of heterozygote advantage;
continued
Sub Command1_Click () Static q(25) Static p(25) Picture1.Cls 'Set variables p(1) = .9 w11 = .4 w12 = 1 w22 = .6 q(1) = 1 - p(1) 'Calculate p and q values For i = 2 To 25 wbar = p(i - 1) ^ 2 * w11 + 2 * p(i - 1) * q(i - 1) * w12 + q(i - 1) ^ 2 * w22 q(i) = (q(i - 1) ^ 2 * w22 + p(i - 1) * q(i - 1) * w12) / wbar p(i) = 1 - q(i) Next i 'Draw axes and grid Picture1.Scale (-1, 1.1)-(26, -.1) Picture1.Line (0, 0)-(0, 1) For i = 0 To 10 Picture1.Line (0, .1 * i)-(25, .1 * i) Next i For i = 5 To 25 Step 5 Picture1.Line (i, 0)-(i, 1) Next i 'Draw q values Picture1.DrawWidth = 5 For i = 1 To 25 Picture1.PSet (i, q(i)) Next i End Sub Figure 1 A Microsoft Visual Basic computer program for the simulation of heterozygote advantage. The rst statement
indicates that the program is run by clicking a command button. Twenty- ve values of q and p are calculated and stored for printing. The program also prints a grid of lines at increments of q 0.1 and generations 5.
Tamarin: Principles of Genetics, Seventh Edition
IV. Quantitative and Evolutionary Genetics
20. Population Genetics: Process that Change Allelic Frequencies
The McGraw Hill Companies, 2001
Twenty
Population Genetics: Processes That Change Allelic Frequencies
BOX 20.1 CONTINUED
the number of generations is twenty ve. The program calculates the mean tness of the population, wbar, as p2(w11) 2pq(w12) q2(w22); it then calculates the new allelic frequencies after one generation of se1.0 0.9 0.8 0.7 0.6
lection (the new proportion of aa homozygotes plus half the proportion of heterozygotes). The program then repeats this process twenty- ve times, storing each new q in the array q(i). The graphic output shown in g-
ure 2 results. As you can see, q is approaching 0.6. If you would like to see the values generated by the program, appropriate print statements can be added.
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