Question

Male Trinidadian guppies use bright red patches of color to attract mates. Your colleague has recently sequenced 400 individual guppies at the opsin gene that controls sensitivity to red wavelengths in light. He has found a new variant of this gene that increases sensitivity to red in his samples. Unfortunately, a computer malfunction has scrambled his data and he no longer knows which alleles come from heterozygotes or homozygotes. Based on his recods, 80 of the 800 alleles sequenced are the new variant. If this gene is in H-W equilibrium in this population, how many individuals from his sample of 400 should be homozygous for the new allele?

Answer 1

According to Hardy-Weinberg equilibrium sum of all the allelic frequency of a gene is always 1 and sum of all the genotypic frequency of all the genotype is always 1.

So p+q =1

p2+ 2pq+q2 =1

here p = frequency of old allele

q is the frequency of the new variant allele.

p2 frequency of the homozygous old variant

q2 frequency of homozygous for the new variant

2pq frequency of heterozygous.

Each organism has two alleles of the same gene in the homologous chromosomes. So in the population of 400, there are 400*2 = 800 alleles.

Given that  80 of the 800 alleles sequenced are the new variant. it means the frequency of the new variant in the population is 80/800 = 0.1.

So q = 0.1.

Also p+q =1

so p = 1-q

or p = 1-0.1

Hence p =0.9.

Frequency of homozygous for new variant = 0.1*0.1 = 0.01

The number of individuals homozygous for the new allele = 400*0.01 = 4

Frequency of heterozygous or carrier will be 2pq

= 0.9*0.1*2 = 0.18

Number of heterozygous individual = 0.18*400 = 72

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