Derive a general formula to give the ratio of the number of

Derive a general formula to give the ratio of the number of recessive alleles found in heterozygotes to the number of recessive alleles found in homozygotes as a function of the frequency of recessive alleles (q) in a population at Hardy-Weinberg equilibrium (hint: use the HW formulas for expected heterozygote and homozygote genotypes). The only variable in your formula should be q. Remember that homozygotes contain 2 alleles and heterozygotes contain 1. Using your formula, calculate this ratio for q = 0.5, q = 0.25, q = 0.1. What does this tell you about the expression of rare recessive alleles in a random mating population?

Solution

Derive a general formula to give the ratio of the number of recessive alleles found in heterozygotes to the number of recessive alleles found in homozygotes as a function of the frequency of recessive alleles (q) in a population at Hardy-Weinberg equilibrium (hint: use the HW formulas for expected heterozygote and homozygote genotypes). The only variable in your formula should be q. Remember that homozygotes contain 2 alleles and heterozygotes contain 1. Using your formula, calculate this ratio for q = 0.5, q = 0.25, q = 0.1. What does this tell you about the expression of rare recessive alleles in a random mating population?

p² + 2pq + q² = 1 and p + q = 1

p = frequency of the dominant allele in the population
q = frequency of the recessive allele in the population
p² = frequency of f homozygous dominant individuals
q² = frequency of homozygous recessive individuals
2pq= frequency of heterozygous individuals

for q = 0.5,

p + q = 1

p = 1-0.5=0.5

p = frequency of the dominant allele in the population =0.5
q = frequency of the recessive allele in the population=0.5
p² = frequency of homozygous dominant individuals=0.25
q² = frequency of homozygous recessive individuals=0.25
2pq = frequency of heterozygous individuals=0.50

ratio = ratio of the number of recessive alleles found in heterozygotes to the number of recessive alleles found in homozygotes

= 0.25 /0.25 =1 answer

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q = 0.25,

p + q = 1

p = 1-0.25=0.75

p = frequency of the dominant allele in the population =0.75
q = frequency of the recessive allele in the population=0.25
p² = frequency of of homozygous dominant individuals=0.75 x 0.75=0.5625
q² = frequency of homozygous recessive individuals=0.25 x0.25=0.0625
2pq = frequency of e of heterozygous individuals=2x 0.75x0.25=0.375

ratio = ratio of the number of recessive alleles found in heterozygotes to the number of recessive alleles found in homozygotes

= 0.1875/0.0625 =3 answer

q = 0.1.

p + q = 1

p = 1-0.1=0.9

p = frequency of the dominant allele in the population =0.9
q = frequency of the recessive allele in the population=0.1
p² = frequency of homozygous dominant individuals=0.81
q² = frequency of homozygous recessive individuals=0.01
2pq = frequency of heterozygous individuals=0.18

ratio = ratio of the number of recessive alleles found in heterozygotes to the number of recessive alleles found in homozygotes

0.09/0.01=9 answer