barcode reader vb.net source code The Wahlund Effect: Heterozygote in Software

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Table 20.1 The Wahlund Effect: Heterozygote
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Frequencies Are Below Expected in a Conglomerate Population
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Subgroup I p q p2 2pq q2 0.1 0.9 0.01 0.18 0.81 Subgroup 2 0.9 0.1 Expected 0.81 0.18 0.01 0.25 0.50 0.25 Conglomerate 0.5 0.5 Observed 0.41 0.18 0.41
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Note: In this example, the subgroups are of equal sizes.
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Tamarin: Principles of Genetics, Seventh Edition
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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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Small Population Size
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1.0 0.75 0.50 0.25 0 1 2 3 4 5 6 7 8 9 10
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Generations
Random genetic drift. Ten populations, each consisting of two individuals with initial q 0.5, all go to xation or loss of the a allele (four or zero copies) within ten generations due to the sampling error of gametes. Once the a allele has been xed or lost, no further change in allelic frequency will occur (barring mutation or migration). We show a population of only two individuals to exaggerate the effects of random genetic drift.
Initial conditions of random drift model. One thousand populations, each of size one hundred, and each with an allelic frequency (q) of 0.5.
present generation. The end result will be either xation or loss of any given allele (q 1 or q 0; g. 20.4), although which will be xed or lost depends on the original allelic frequencies. The rate of approach to reach the xation-loss endpoint depends on the size of the population.
Simulation of Random Genetic Drift
We can investigate the process of random genetic drift mathematically by starting with a large number of populations of the same nite size and observing how the distribution of allelic frequencies among the populations changes in time due only to random genetic drift. For example, we can start with one thousand hypothetical populations, each containing one hundred individuals, with the frequency of the a allele, q, 0.5 in each ( g. 20.5). We measure time in generations, t, as a function of the population size, N (one hundred in this example). For instance, t N is generation one hundred, t N/5 is generation twenty, and t 3N is generation three hundred. Then, by using computer simulation (or the Fokker-Planck equation, which physicists use to describe diffusion processes such as Brownian motion), we generate the series of curves shown in gure 20.6.These curves show that as the number of generations increases, the populations begin to diverge from q 0.5. Approximately the same number of populations go to q values above 0.5 as go to q values below 0.5.Therefore, the distribution spreads symmetrically. When the distribution of allelic frequencies reaches the sides of the graph, some populations become xed for the a allele and some lose it. In a sense, the sides act as sinks:
Genetic drift in small populations: q 0.5. After time passes, the populations of gure 20.5 begin to diverge in their allelic frequencies. Time is measured in population size (N), showing that the effects of random genetic drift are qualitatively similar in populations of all sizes; the only difference is the timescale. (From M. Kimura, Solution of a process of random
genetic drift with a continuous model, Proceedings of the National Academy of Sciences, USA, 41:144-50, 1955. Reprinted by permission.)
Any population that has the a allele lost or xed will be permanently removed from the process of random genetic drift. Without mutation to bring one or the other allele
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
Figure 20.7 Continued genetic drift in the one thousand populations, each numbering one hundred in size, shown in gures 20.5 and 20.6. After approximately 2N generations, the distribution is at, and populations are going to loss or xation of the a allele at a rate of 1/2N populations per generation. (From
S. Wright, Evolution in Mendelian Populations, Genetics, 97:114. Copyright 1931 Genetics Society of America.)
back into the gene pool, these populations maintain a constant allelic frequency of zero or 1.0. At a point between N (one hundred) and 2N (two hundred) generations, the distribution of allelic frequencies attens out and begins to lose populations to the edges ( xation or loss) at a constant rate, as shown in gure 20.7. The rate of loss is about 1/2N (1/200), or 0.5% of the populations per generation. If the initial allelic frequency was not 0.5, everything is shifted in the distribution ( g. 20.8), but the basic process is the same in all populations, sampling error causes allelic frequencies to drift toward xation or elimination. If no other factor counteracts this drift, every population is destined to eventually be either xed for or de cient in any given allele. The amount of time the process takes depends on population size. The example used here was based on small populations of one hundred. If we substitute one million for one hundred in gure 20.6, a at distribution of populations would not be reached for two million generations, rather than two hundred generations. Thus, a population experiences the effect of random genetic drift in inverse proportion to its size: Small populations rapidly x or lose a given allele, whereas large populations take longer to show the same effects. Genetic drift also shows itself in several other ways.
Random genetic drift in small populations with q 0.1. Compare this gure with gure 20.6. In this case, the probability of xation of the a allele is 0.1, and the probability of its loss is 0.9. (From M. Kimura, Solution of a process of random
genetic drift with a continuous model, Proceedings of the National Academy of Sciences, USA, 41:144 50, 1955. Reprinted by permission.)
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