Question

genetics problem:

3. For each of the Cepea nemoralis populations below, assuming H-W equilibrium, calculate the frequencies of the brown, pink, and yellow alleles: NUMBER WITH COLOR TOTAL HABITAT BROWN PINK YELLOW Deciduous wood 83 1018 407 1508 Rough Herbage 212 755 971 (the dominance relationships are: CB>CPCY where B, P, and Y are the brown, pink, and yellow alleles respectively)

Answer 1

For a tri-allelic system, the Hardy-Weinberg Equations are:

p + q + r = 1
p² + q² + r² + 2pq + 2pr + 2qr = 1

Where,

p, q, r are the allelic frequencies of the three alleles, and p², q², r², 2pq, 2pr, and 2qr are the respective genotypic frequncies.

Now, since C^B>C^P>C^Y; if p = Freq(C^B), q = Freq(C^P), and r = Freq(C^Y)

Frequency of the Brown phenotype = p² + 2pq + 2pr
Frequency of the Pink phenotype = q² + 2qr
Frequency of the Yellow phenotype = r²

i) Decidious Wood Population:

Frequency of the Brown phenotype = p² + 2pq + 2pr = 83/1508 = 0.055
Frequency of the Pink phenotype = q² + 2qr = 1018/1508 = 0.675
Frequency of the Yellow phenotype = r² = 407/1508 = 0.27

Now,

      r² = 0.27
=> r = 0.5196

      q² + 2qr = 0.675
=> q² + 2q*(0.5196) = 0.675
=> q² + 1.0392 q - 0.675 = 0
=> (q - 0.452503) (q + 1.4917) = 0

Since q cannot be negative, q = 0.4525

Now, p + q + r = 1
=> p + 0.4525 + 0.5196 = 1
=> p = 1 - 0.4525 - 0.5196 = 0.0279

Therefore, in the Decidious Wood the allelic frequencies are:

Frequency(C^B) = p = 0.0279
Frequency(C^P) = q = 0.4525
Frequency(C^Y) = r = 0.5196

ii) Rough Herbage Population:

Frequency of the Brown phenotype = p² + 2pq + 2pr = 4/971 = 0.004
Frequency of the Pink phenotype = q² + 2qr = 212/971 = 0.218
Frequency of the Yellow phenotype = r² = 755/971 = 0.778

Now,

      r² = 0.778
=> r = 0.882

      q² + 2qr = 0.218
=> q² + 2q*(0.882) = 0.218
=> q² + 1.764 q - 0.218 = 0
=> (q - 0.11596) (q + 1.87996) = 0

Since q cannot be negative, q = 0.116

Now, p + q + r = 1
=> p + 0.116 + 0.882 = 1
=> p = 1 - 0.116 - 0.882 = 0.002

Therefore, in the Rough Herbage population the allelic frequencies are:

Frequency(C^B) = p = 0.002
Frequency(C^P) = q = 0.116
Frequency(C^Y) = r = 0.882