Sheep with the dominant wool color allele, W, are white, while sheep homozygous for the recessive allele w, are black. From a flock that is 50% black and 50% white, and at Hardy-Weinberg equilibrium, how many of the 200 lambs born next are black?2) Sheep with the dominant wool color allele, W, are white, while sheep homozygous for the recessive allele w, are black. From a flock that is 50% black and 50% white, and at Hardy-Weinberg equilibrium, how many of the 200 lambs born next are black?

Explanation:

Hardy Weinberg equilibrium states that the frequency of alleles and genotypes in a population will remain constant in the absences of evolutionary disturbances such as mutation gene flow, natural selection, and with random mating and infinite population size

the equation for the law is

p² + 2pq + q² and p + q = 1

where p² represent frequency of the homozygous dominant genotype WW, 2pq represent frequency of the heterozygous dominant genotype Ww  and q² represent the frequency of the recessive genotype ww. Also p represent the frequency of the dominant alleles while q represent frequency of the recessive alleles.

50% are black from the flock

q² = 0.5, q = √ 0.5 = 0.7071 and p = 1 - 0.7071 = 0.293

out of the 200 lambs, 0.5 × 200 will be black = 100 black

while p² = 0.293² = 0.085849

population that will be homozygous white (WW) =  0.085849 × 200 = 17.17 approx 17

and population that will be heterozygous white ( Ww) = 2 × 0.298 × 0.7071 × 200 = 84.29 approx 84

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