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Selection Against the Recessive Homozygote
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We can analyze selection by using our standard modelbuilding protocol of population genetics namely, de-
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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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Natural Selection
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Table 20.2 Selection Against the Recessive
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Homozygote: One Locus with Two Alleles, A and a
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Genotype AA Initial genotypic frequencies Fitness (W ) Ratio after selection Genotypic frequencies after selection p2 1 p2 p2 W Aa 2pq 1 2pq 2pq W aa q2 1 s q2(1 s) q2(1 s) W 1 sq2 1 W Total 1
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individuals that survive to reproduce, only six aa individuals would survive to reproduce. The total of the three genotypes after selection is 1 sq2. That is, p2 1 2pq sq2 q2(1 s) p2 2pq q2 sq2
Mean Fitness of a Population
The value (1 sq2) is referred to as the mean tness of the population, W, because it is the sum of the tnesses of the genotypes multiplied (weighted) by the frequencies at which they occur. Thus, it is a weighted mean of the tnesses, weighted by their frequencies. The new ratios of the three genotypes can be returned to genotypic frequencies by simply dividing by the mean tness of the population,W, as in the last line of table 20.2. (Remember that a set of numbers can be converted to proportions of unity by dividing them by their sum.) The new genotypic frequencies are thus the products of their original frequencies times their tnesses, divided by the mean tness of the population. After selection, the new allelic frequency (qn 1) is the proportion of aa homozygotes plus half the proportion of heterozygotes, or qn
Disruptive selection in Drosophila melanogaster. After twelve generations of selection for ies with either many or few bristles (chaetae) on the sternopleural plate, the population was bimodal. In other words, many ies in the population had either few or many bristles, but few ies had an intermediate bristle number. (Reprinted with permission from Nature,
Vol. 193, J. M. Thoday and J. B. Gibson, Isolation by Disruptive Selection. Copyright 1962 Macmillan Magazines Limited.)
the same tness (W 1). Natural selection cannot differentiate between the two genotypes because they both have the same phenotype.The recessive homozygote, however, is being selected against, which means that it has a lower tness than the two other genotypes (W 1 s). After selection, the ratio of the different genotypes is determined by multiplying their frequencies (HardyWeinberg proportions) by their tnesses. The procedure follows from the de nition of tness, which in this case is a relative survival value. Thus, only 1 s of the aa genotype survives for every one of the other two genotypes. For example, if s were 0.4, then the tness of the aa type would be 1 s, or 0.6. For every ten AA and Aa
q2(1 s) 1 sq2
pq sq2
q(q sq p) 1 sq2 q(1 sq) 1 sq2 (20.15)
This model can be simpli ed somewhat if we assume that the aa genotype is lethal. Its tness would be zero,
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
and s, the selection coef cient, would be one. Equation 20.15 would then change to qn
q(1 q) 1 q2 q)(1
(20.16)
Since (1 q2) is factorable into (1 20.16 becomes qn
q), equation
For a fraction to be zero, the numerator must equal zero. ^ Thus, q2 0, and q 0. At equilibrium, the a allele should be entirely removed from the population. If the aa homozygotes are being removed, and if there is no mutation to return a alleles to the population, then eventually the a allele disappears from the population.
(1 (1
q(1 q) q)(1 q) q q)
(20.17)
Time Frame for Equilibrium
One shortcoming of this selection model is that it is not immediately apparent how many generations will be required to remove the a allele.The de ciency can be compensated for by using a computer simulation or by introducing a calculus differential into the model. Either method would produce the frequency-time graph of gure 20.11. This gure clearly shows that the a allele is removed more quickly when selection is stronger (when s is larger) and that the curves appear to be asymptotic the a allele is not immediately eliminated and would not be entirely removed until an in nitely large number of generations had passed. There is a reason for the asymptotic behavior of the graph: As the a allele becomes rarer and rarer, it tends to be found in heterozygotes (table 20.3). Since selection can remove only aa homozygotes, an a allele hidden in an Aa heterozygote will not be selected against.When q 0.5, there are two heterozygotes for every aa homozygote. When
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