# barcode reader vb.net source code The change in allelic frequency is then calculated as q qn+1 q q 1 q q in Software Printer QR in Software The change in allelic frequency is then calculated as q qn+1 q q 1 q q

The change in allelic frequency is then calculated as q qn+1 q q 1 q q
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To solve this equation, q is multiplied by (1 q)/(1 q) so that both parts of the expression are over a common denominator: q q q(1 q) 1 q
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(20.18)
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q2 1 q
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This is the expression for the change in allelic frequency caused by selection. Since selection will not act again until the same stage in the life cycle during the next generation, equation 20.18 is also an expression for the change in allelic frequency between generations. Two facts should be apparent from equation 20.18. First, the frequency of the recessive allele (q) is declining, as indicated by the negative sign of the fraction.This fact should be intuitive because of the way selection was de ned in the model (eliminating aa homozygotes). Second, the change in allelic frequency is proportional to q2, which appears in the numerator of the expression. In other words, allelic frequency is declining as a relative function of the number of homozygous recessive individuals in the population. This fact is consistent with the premise of the selection model (with selection against the homozygous recessive genotype). This nal formula supports the methodology of the model.
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Equilibrium Conditions
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Next we calculate the equilibrium q by setting the q equation equal to zero, since a population in equilibrium will show no change in allelic frequencies from one generation to the next: q2 1 q 0
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(20.19)
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Figure 20.11 Decline in q (the frequency of the a allele) under different intensities of selection against the aa homozygote. Note that the loss of the a allele is asymptotic in both cases, but the drop in allelic frequency is more rapid with the larger selection coef cient.
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Tamarin: Principles of Genetics, Seventh Edition
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IV. Quantitative and Evolutionary Genetics
20. Population Genetics: Process that Change Allelic Frequencies
The McGraw Hill Companies, 2001
Natural Selection
Table 20.3 Relative Occurrence of Heterozygotes
and Homozygotes as Allelic Frequency Declines: q f(a); p f(A)
f(Aa) (2pq) 0.50 0.32 0.18 0.0198 0.001998 f(aa) (q2) 0.25 0.04 0.01 0.0001 0.000001
from selection will just balance the change from mutation. Thus, p q sq2(1 q) 1 sq2 sq2(1 q) 1 sq2 0
q 0.5 0.2 0.1 0.01 0.001
f(Aa)/f(aa) 2 8 18 198 1,998
and p q
(20.21)
Now, some judicious simplifying is justi ed, because in a real situation, q will be very small because the a allele is being selected against. Thus, q will be close to zero, and 1 sq2 will be close to unity. Equation 20.21, therefore, becomes: p sq2(1 sq (1 /s s
(20.22)
q) q)
q 0.001, there are almost two thousand heterozygotes per aa homozygote. Remember, only the recessive homozygote is selected against. Natural selection cannot distinguish the dominant homozygote from the heterozygote.
q) q
In the case of a recessive lethal, s would be unity, so
Selection-Mutation Equilibrium
Although a deleterious allele is eliminated slowly from a population, the time frame is so great that there is opportunity for mutation to bring the allele back. Given a population in which alleles are removed by selection and added by mutation, the point at which no change in allelic frequency occurs, the selection-mutation equilibrium, may be determined as follows.The new frequency (qn 1) of the recessive a allele after nonlethal selection (s 1) against the recessive homozygote is obtained by equation 20.15: qn+1 q(1 sq) 1 sq2
^ and q
If a recessive homozygote has a tness of 0.5 (s 0.5) and a mutation rate, , of 1 10 5, the allelic frequency at selection-mutation equilibrium will be
s 0.004
If the recessive phenotype were lethal, then
s 0.003
These are very low equilibrium values for the a allele.
Change in allelic frequency under this circumstance will thus be q qn+1 q q sq2 (1 q(1 sq) (1 sq2) q sq3 sq2)
(20.20)
Types of Selection Models
In view of the limited ways that tnesses can be assigned, only a limited number of selection models are possible. Table 20.4 lists all possible selection models if we assume that tnesses are constants and the highest tness is one. (You might now go through the list of models and determine the equilibrium conditions for each.) Note that two possible tness distributions are missing.There is no model in which tnesses are 1 s, 1, and 1 for the A1A1, A1A2, and A2 A2 genotypes, respectively (remembering that p f[A1] and q f[A2]).That model is for selection against the A1A1 homozygote. Some re ection should show that this is the same model as model 1 of table 20.4, except that the A1 allele is acting like a recessive allele. In other words, natural selection acts against A1A1 homozygotes, but not against the A1A2 and A2 A2 genotypes. Thus, the model reduces to model 1 if we treat A1 as the recessive allele and A2 as the
q(1 (1
sq ) sq2)