Population Genetics. Matthew B. Hamilton
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Название: Population Genetics

Автор: Matthew B. Hamilton

Издательство: John Wiley & Sons Limited

Жанр: Биология

Серия:

isbn: 9781118436899

isbn:

СКАЧАТЬ other allele frequencies can be obtained by similar steps. This must be true under Mendel's second law if the two loci are truly independent.

      For hypothesis 2, the frequency of the B allele can be obtained from the fact that all the allele frequencies must sum to 1:

equation

      Then subtracting pB from each side gives:

equation

      Squaring both sides gives:

equation

      The left side of which can be expanded to:

equation

      And then:

equation

      The last expression on the right is identical to the sum of the first and second expected genotype frequencies for hypothesis 2 in Table 2.3. Expressions for the frequency of the A and O alleles can also be obtained in this fashion.

      Problem box 2.3 answer

      The first step is to hypothesize genotypes under the two models of inheritance, as shown in Tables 2.6 and 2.7 for blood groups. Then, these genotypes can be used to estimate allele frequencies (here, p indicates probability or frequency). For the hypothesis of two loci with two alleles each:

equation

      For the hypothesis of one locus with three alleles:

equation

      The expected numbers of each genotype as well as the differences between the observed and expected genotype frequencies are worked out in the tables. For the hypothesis of two loci with two alleles each, χ2 = 0.266, whereas χ2 = 19 688 for the hypothesis of one locus with three alleles. Both of these tests have one degree of freedom (4 genotypes −2 for estimated allele frequencies −1 for the test), giving a critical value of χ20.05,1 = 3.84 from Table 2.5. The deviations between observed and expected genotype frequencies could easily be due to chance under the hypothesis of two loci with two alleles each. However, the observed genotype frequencies are extremely unlikely under the hypothesis of three alleles at one locus since the deviations between observed and expected genotype frequencies are very large.

Phenotype Genotype Observed Expected number of genotypes Observed − expected (Observed − expected)2/expected
Hypothesis 1: two loci with two alleles each
Purple/smooth A_B_ 2058 3816 (1–0.522)(1–0.512) = 2060.0 2.0 0.002
Purple/wrinkled A_bb 728 3816 (1–0.522)(0.51)2 = 724.2 3.8 0.020
Yellow/smooth aaB_ 769 3816 (0.52)2(1–0.512) = 763.5 5.5 0.040
Yellow/wrinkled Aabb 261 3816 (0.52)2(0.51)2 = 268.4 −7.4 0.204
Hypothesis 2: one locus with three alleles
Purple/smooth AB 2058 3816 (2(0.48)(0.49)) = 1795 63.0 38.5
Purple/wrinkled AA, AC 728 3816 ((0.48)2 + 2(0.48)(0.03)) = 989.1 −261.1 68.9
Yellow/smooth BB, BC 769 3816 ((0.49)2 + 2(0.49)(0.03)) = 1028.4 − 259.4 63.7
Yellow/wrinkled CC 261 3816 (0.03)2 = 3.4 257.6 19 517.0

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