The allele for the hair pattern widow's peak is dominant. In a population of 1000 individuals, 510 show the dominant phenotype. How many individuals would you expect of each of the possible 3 genotypes for this trait?

How do you answer this?

Question

The allele for the hair pattern widow's peak is dominant. In a population of 1000 individuals, 510 show the dominant phenotype. How many individuals would you expect of each of the possible 3 genotypes for this trait?

How do you answer this?

Daniel Allen · Accepted Answer

For the homozygous dominant genotype there will be #90# individuals. For the heterozygous genotype there will be #420# individuals and for the homozygous recessive genotype there will be #490# individuals.

To respond to this, apply the Hardy-Weinberg Equation. From the #1000# individuals, we know that #510# show dominant phenotype but we don't know how many of those individuals are homozygous dominant or heterozygous because both show dominant trait. But we can infer that the remaining #490# individuals show recessive trait and therefore have homozygous recessive genotype. #490/1000 = 0.49 = q^2# #0.7 = q# #p + q = 1# #p = 1 - q# #p = 0.3# Next #p^2 = 0.09# #q^2 = 0.49# #2pq = 2(0.7)(0.3) = 0.42# Verify Again: #p^2 + 2pq + q^2 = 1# #0.09 + 0.42 + 0.49 = 1# Consequently, you have #0.09(1000) = 90 -># with homozygous dominant genotype #0.42(1000) = 420 -># with heterozygous genotype #0.49(1000) = 490 -># with homozygous recessive genotype Verify Again: #90 + 420 + 490 = "1000 individuals"# #90 + 420 = "510 individuals " -># with dominant phenotype

Elias Aboujaoude · Answer

undefined For a dominant trait, the genotypes can be DD (homozygous dominant) or Dd (heterozygous dominant). The frequency of the dominant allele (D) is calculated using the given dataFor a dominant trait, the genotypes can be DD (homozygous dominant) or Dd (heterozygous dominant). The frequency of the dominant allele (D) is calculated using the given  510 dominant individuals / 1000 total individuals = 0.51. The square root of this frequency gives the proportion of homozygous dominant individuals (DD), and the remaining proportion represents heterozygous dominant individuals (Dd). Calculate the expected numbers accordingly.