The proportion of the population with genotype Bb can be calculated using the two equations of the Hardy-Weinberg principle. These equations are: p + q = 1 where: p = frequency of the dominant allele (B) q = frequency of the recessive allele (b) p2 + 2pq + q2 = 1 where: p2 = frequency of the homozygous dominant genotype (BB) 2pq = frequency of the heterozygous genotype (Bb) q2 = frequency of the homozygous recessive genotype (bb) This principle works under the following assumptions about the population: there is no immigration; no emigration; no mutations; no natural selection; the population is large. It is useful to identify what information has been given already in the question, and what information the question is asking for. In this case, the frequency of genotype BB has been given, which is the homozygous dominant genotype as both alleles are dominant. We therefore know that p2 = 0.49. The question is asking for the frequency of genotype Bb. Individuals with this genotype carry two different alleles, which is the heterozygous genotype. This means the question is asking for the value of 2pq. We must first find the value of p, by taking the square root of our value for p2. √0.49 = 0.7, therefore p = 0.7. Now we know the value of p, we can substitute it into the equation ‘p + q = 1’ and rearrange to find the value of q. 0.7 + q = 1 q = 1 - 0.7 Therefore q = 0.3 The values found for p2 and q can then be substituted into the equation ‘p2 + 2pq + q2 = 1’ to find the value of 2pq. 0.49 + 2pq + (0.3)2= 1 0.49 + 2pq + 0.09 = 1 2pq + 0.58 = 1 2pq = 0.42 Your answer should then be stated clearly after your working out so it's easy for the examiner to see. For example: 'The frequency of genotype Bb in the population is 0.42.'
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