Question

A new kind of tulip is produced that develops only purple or pink flowers. Assume that flower color is controlled by a single-gene locus, and that the purple allele (C) is dominant to the pink allele (c). A random sample of 1000 tulips from a large cultivated field yields 847 purple flowers, and 153 pink flowers. a. Determine the frequency of the purple and pink alleles in this field population. b. Estimate the proportion of all purple flowering plants that are heterozygotes and homozygotes.

Answer 1

a) The frequency of the purple allele, C, is 0.61 and the frequency of the pink allele,c, is 0.39.

b) The proportion of all purple flowering plants that are heterozygotes is 0.4758 x 1000 = 475

The proportion of all purple flowering plants that are homozygotes is

0.372 x 1000 = 372

Step-by-step explanation:

According to Hardy-Weinberg, the allelic frequencies in a locus are represented as p and q, referring to the allelic dominant or recessive forms. The genotypic frequencies after one generation are p² (Homozygous dominant), 2pq (Heterozygous), q² (Homozygous recessive). Populations in H-W equilibrium will get the same allelic frequencies generation after generation. The sum of these allelic frequencies equals 1, this is p + q = 1.

In the same way, the sum of genotypic frequencies equals 1, this is

p²+ 2pq + q² = 1

Available data:

• Flower color is controlled by a single-gene locus,

• The purple allele (C) is dominant to the pink allele (c).

• Sample of 1000 tulips

• 847 purple flowers, and 153 pink flowers.

a. Determine the frequency of the purple and pink alleles in this field population.

We know that:

• 847 CC + Cc individuals are purple

• 153 cc individuals are pink

In order to get the allelic frequencies, we need to calculate the genotypic frequencies first. We will calculate the genotypic frequency for the recessive allele, F(cc), first:

F (cc)= 153/1000

F (cc) = 0.153

F (cc) =q²= 0.153. So now we need to calculate the allelic frequency for this recessive allele. This is, q²=0.153

q=√0.153

q= 0.39

If the recessive allelic frequency f(c) equals 0.39, then by clearing tue equation p + q = 1 we can know the dominant allelic frequency, f(C). This is:

p + q = 1

p + 0.39 = 1

p = 1 - 0.39

p = 0.61

b. Estimate the proportion of all purple flowering plants that are heterozygotes and homozygotes.

• Purple flowering plants are CC + Cc

• There are 847 CC + Cc individuals in the population

The phenotypic frequency of purpled-individuals C- is 847/1000=0.847

If the dominant allelic frequency is f (C) = 0.61

Then, the purple homozygous genotype frequency is F(CC)=p²=0.372

And If the recessive allelic frequency is f (c)= 0.39

Then, the purple heterozygous genotype frequency is F(Cc)= 2 x p x q = 2 x 0.61 x 0.39 = 0.4758

We can verify these results by applying the following formula:

p2 + 2pq + q2 = 1

0.372+ 0.476 + 0.153= 1

• The proportion of all purple flowering plants that are heterozygotes is 0.4758 x 1000 = 475

• The proportion of all purple flowering plants that are homozygotes is

0.372 x 1000 = 372

• The proportion of all white flowering plants that are homozygotes is

0.153 x 1000 = 153