Question

You are studying a population of geese in which there are two color phases, brown and gray. Color in this species is controlled by a single gene, with brown dominant to gray. A random sample of 500 geese shows that 45 are gray. What percentage of the brown geese are heterozygous?

Answer 1

Answer-

According to the given question-

We know that according to Hardy-Weinberg Equilibrium question:
? + ? = 1
?² + 2?? + ?² = 1

Where ?= dominant allele frequency.
?=   recessive allele frequency.
?² = frequency of offspring having homozygous dominant genotype.
2?? = frequency of offspring having heterozygous genotype.
?² = frequency of offspring having homozygous recessive genotype.

Here we have total 500 geese of two color . one is brown which is dominant over the second color gray.

Out of 500 individuals of geese we have 45 which have gray color which means that gray color is recessive.

Frequency of gray geese = ?² = Number of geese / total population

?² = 45 / 500 = 0.09

So ? =0.3

we know that ? + ? = 1 so ? = 0.7

So ?² = (0.7)2 = 0.49

according to Hardy-Weinberg Equilibrium question:

?² + 2?? + ?² = 1

0.49 + 2?? + 0.09 = 1

2?? = 1- 0.58 = 0.42

dominant alleles frequency = ? = 0.7
recessive alleles frequency = ? = 0.3

frequency of offspring having homozygous dominant genotype.= ?² = 0.49

frequency of offspring having heterozygous genotype = 2?? =0.42

frequency of offspring having homozygous recessive genotype= ?² = 0.09

Population of Brown = ?² total population= 0.49 500 = 245 (Brown geese)

Population of heterozygous = 2?? total population = 0.42 500 = 210

So total 210 out of 500 are heterozygous = 210 / 500 100 = 42 % are heterozygous in the geese population which are brown

So total 245 out of 500 are Dominant black homozygous = 245 / 500 100 = 49 % are homozygous dominant in the geese population and are brown

So total 45 out of 500 are recessive gray homozygous = 45 / 500 100 = 9 % are homozygous recessive in the geese population and are gray.