Problem box answer

For hypothesis 1 the observed frequency of the bb genotype is given by:

Expanding the second term gives:

The 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:

Then subtracting fB from each side gives:

Squaring both sides gives:

The left side of which can be expanded to:

(fA + fO)2 = (fA + fO)(fA + fO) = fO2 + 2fAfO + fA2

And then:

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.

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