Question

Hardy-Weinberg problem:

There are 500 German Shepherds found in California. They are all free to interbreed without restriction. Floppy ears are recessive to Upright ears and 100 of the German Shepherds in this population are floppy-eared. What are the percentages of floppy-eared and upright-eared German Shepherds (phenotypic)? What are the percentages of each genotype for this group of dogs?

Answer 1

Answer: Percentage of floppy-eared (phenotypic) = 100/500 = 0.2 × 100 =20%

and upright-eared German Shepherds (phenotypic) = 400/500 = 0.8 × 100 = 80%

The population is in Hardy-Weinberg equilibrium.

The HW equation is given as p2 + 2pq + q2 =1 i.e. (p+q)2 = 1

Let the allele for floppy ear be ‘e’ and for upright ear be ‘E’

Here p2 = EE = frequency of the homozygous dominant genotype.

q2 = ee = frequency of the recessive genotype.

2pq = Ee = frequency of heterozygotes in the population.

p = frequency of the dominant allele

q = frequency of the recessive allele.

Since floppy eared is recessive phenotype hence the frequency of the genotype and phenotype will be the same i.e 100/500 = 0.2 i.e.   q2 = 0.2

Hence q = 0.447

Since p + q = 1 hence p = 1- 0.447 = 0.553

Therefore p2= 0.305

And 2pq = 2 × 0.553 × 0.447 = 0.494.

Therefore percentage of the genotype EE = p2 = 0.305 × 100 = 30.5%

Percentage of the genotype ee = q2 = 0.2 × 100 = 20%

Percentage of the genotype Ee = 2pq = 0.494 × 100 = 49.4%