Question

Asked Oct 20, 2019

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Common blood types are determined genetically by three alleles A, B, and O. (An allele is any of a group of possible mutational forms of a gene.) A person whose blood type is AA, BB, or OO is homozygous. A person whose blood type is AB, AO, or BO is heterozygous. The Hardy-Weinberg Law states that the proportion P of heterozygous individuals in any given population is

P(p, q, r) = 2pq + 2pr + 2qr

where p represents the percent of allele A in the population, q represents the percent of allele B in the population, and r represents the percent of allele O in the population. Use the fact that

p + q + r = 1

to show that the maximum proportion of heterozygous individuals in any population is

2

3

.

The maximum possible proportion of heterozygous individuals occurs when

(p, q, r) =

.

Step 1

Given:

Step 2

Solve p + q + r = 1 and put the value of this in above equation:

Step 3

Differentiate with respect to &ls...

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