Question

If you know that a population is 75% the dominant phenotype and 25% is the recessive phenotype, can you determine approximately how many of the dominant phenotype are homozygous dominant and how many are heterozygous dominant? Try this mathematically. B) talk is dominant over short in pea plants. In a population of pea plants, 60 were tall and 40 were short. What is the frequency (%) of short plants in the population? Using your answer, calculate the frequency of the short gene. What is the frequency of the tall gene?

Answer 1

1. If you know that a population is 75% the dominant phenotype and 25% is the recessive phenotype, can you determine approximately how many of the dominant phenotypes are homozygous dominant and how many are heterozygous dominant? 

This problem should be solved using Hardy-Weinberg equilibrium formula. Note that the dominant phenotype is the sum of heterozygous and homozygous dominant genotype. If the population consist of 75% dominant phenotype 25% recessive phenotype, then it should be:
AA+2Aa= 0.75
aa=0.25

You can find the frequency of the recessive genotype by square root the homozygous recessive.
aa=0.25
a=√0.25=0.5

Sum of dominant and recessive genotype should be 1.
a+A=1
A= 1-a 
A= 1-0.5= 0.5

dominant genotype= AA = 0.5 * 0.5= 0.25
heterozygous genotype= 2Aa = 2 * 0.5 * 0.5= 0.50

2. tall is dominant over short in pea plants. In a population of pea plants, 60 were tall and 40 were short. What is the frequency (%) of short plants in the population?

The population has 60 tall and 40 short plants, so the total plant would be: 60+40= 100 plants.
There is 40 short plants, so the frequency (%) of short plants in the population would be:
short plant count / total plant count= 40/100= 40%
The frequency of dominant phenotype(tall) is 60% while the recessive phenotype(short) is 40%.

3. Using your answer, calculate the frequency of the short gene.

Short gene is recessive so the plant that expresses the phenotype is only homozygous recessive which represented as aa. The question asking for the frequency of the genes which represented as a.
The calculation to find the frequency of the gene would be:
aa=0.4
a=√0.4= 0.6324= 63.24%

4. What is the frequency of the tall gene?
There is only two possible gene for the plant, tall(dominant) and short(recessive). From that information, you can conclude that the sum of the tall and short gene frequency would be 1.
The calculation would be:
dominant + recessive=1
A+ a= 1
A+0.6324 = 1
A= 1- 0.6324= 0.3676= 36.75%