A. To determine the value of p (and q), we can use the equation p + q = 1, where p represents the frequency of the recessive allele (white flowers) and q represents the frequency of the dominant allele (purple flowers). We are given that there are 18 plants with white flowers and 142 plants with purple flowers. This gives us a total of 160 plants.
We can set up two equations:
p + q = 1
p = 18/160
We can solve for q:
q = 1 - p
q = 1 - (18/160)
q = 142/160
q = 0.8875
So the value of p is 0.1125.
B. The value of q is 0.8875.
C. The frequency of heterozygous plants in the field can be determined using the equation 2pq, where p and q are as defined in part A.
2pq = 2(0.1125)(0.8875)
2pq = 0.1997
So the frequency of heterozygous plants in the field is 0.1997 or approximately 20%.
D. To check our work, we can use the equation p' + 2pq + q' = 1, where p' is the frequency of homozygous recessive plants (p' = p^2), q' is the frequency of homozygous dominant plants (q' = q^2), p and q are the frequencies of the two alleles as defined in part A.
p' + 2pq + q' = (0.1125)^2 + 2(0.1125)(0.8875) + (0.8875)^2
p' + 2pq + q' = 0.01266 + 0.1997 + 0.7875
p' + 2pq + q' = 1
So our value checks out, and indeed, the sum of the frequencies of all three genotypes (homozygous dominant, heterozygous, homozygous recessive) adds up to 1.