Question

Calculate the observed frequencies of genotypes CGCG, CGCY, and CYCY at day 21. Compare these frequencies to the expected frequencies calculated in question 2 and to the observed frequencies at day 7. Is the seedling population in Hardy-Weinberg equilibrium at day 21, or is evolution occurring? Explain your reasoning and identify which genotypes, if any, appear to be selected for or against.

Short answer

The observed genotypefrequencies of the genotypes\({C^G}{C^G}\),\({C^G}{C^Y}\), and\({C^Y}{C^Y}\)at day 21 are 0.27, 0.61, and 0.12, respectively.

The observed genotype frequencies at day 21 for each seedling differ from the observed and expected genotype frequencies at day seven. Thus, the allele frequencies have changed from day seven till day 21.

The seedling population is not in Hardy-Weinberg equilibrium at day 21 and is undergoing evolution.

The seedling population is not in Hardy-Weinberg equilibrium at day 21 because the observed and expected genotype frequencies for both the homozygous dominant and recessive genotypes are different from day 7. The genotype \({C^G}{C^G}\)is being selected for, and the \({C^Y}{C^Y}\)is being selected against evolution.

Step-by-step solution

Genotype selection

A Hardy-Weinberg population has a similar observed and expected genotype frequency throughout. If genotype frequency changes, it implies that selection is acting for or against a particular allele or genotype. Genotype selection causes certain genotypes to survive, reproduce, and flourish than the other genotypes in a population.

Explanation for part (a)

To calculate: Observed frequencies of genotypes \({C^G}{C^G}\),\({C^G}{C^Y}\), and\({C^Y}{C^Y}\)at day 21.

On day 21,

Number of homozygous dominant or green seedlings (\({C^G}{C^G}\))= 47

Number of heterozygous genotypes or green-yellow seedlings (\({C^G}{C^Y}\))= 106

Number of homozygous dominant or yellow seedlings (\({C^Y}{C^Y}\))= 20

Total number of seedlings= 173

The observed genotypic frequency of\({C^G}{C^G}\)(\({p^2}\)) is:

\({p^2} = \frac{{Number{\rm{ }}of{\rm{ }}homozygous{\rm{ }}dominant{\rm{ }}or{\rm{ }}green{\rm{ }}seedlings{\rm{ }}\left( {{C^G}{C^G}} \right)}}{{Total{\rm{ }}number{\rm{ }}of{\rm{ }}seedlings}}\)

\(\begin{aligned}{l}{p^2} &= \frac{{47}}{{173}}\\{p^2} &= 0.27\end{aligned}\)

The observed genotypic frequency of\({C^G}{C^Y}\)(\(2pq\)) is:

\(2pq = \frac{{Number{\rm{ }}of{\rm{ }}homozygous{\rm{ }}dominant{\rm{ }}or{\rm{ }}green{\rm{ }}seedlings{\rm{ }}\left( {{C^G}{C^Y}} \right)}}{{Total{\rm{ }}number{\rm{ }}of{\rm{ }}seedlings}}\)

\(\begin{aligned}{l}2pq &= \frac{{106}}{{173}}\\2pq &= 0.61\end{aligned}\)

The observed genotypic frequency of\({C^Y}{C^Y}\)(\({q^2}\)) is:

\({q^2} = \frac{{Number{\rm{ }}of{\rm{ }}homozygous{\rm{ }}recessive{\rm{ }}or{\rm{ }}yellow{\rm{ }}seedlings{\rm{ }}\left( {{C^Y}{C^Y}} \right)}}{{Total{\rm{ }}number{\rm{ }}of{\rm{ }}seedlings}}\)

\(\begin{aligned}{l}{q^2} &= \frac{{20}}{{173}}\\{q^2} &= 0.115\\{q^2} &= 0.12\end{aligned}\)

Thus, the observed genotypefrequencies of the genotypes\({C^G}{C^G}\),\({C^G}{C^Y}\), and\({C^Y}{C^Y}\)at day 21 are 0.27, 0.61, and 0.12, respectively.

Explanation for part (b)

To compare the observed genotypefrequencies at day 21 to the observed andexpected frequencies of genotypes \({C^G}{C^G}\),\({C^G}{C^Y}\), and\({C^Y}{C^Y}\)at day 7.

The observed genotypefrequencies of the genotypes\({C^G}{C^G}\),\({C^G}{C^Y}\), and\({C^Y}{C^Y}\)at day 21 are 0.27, 0.61, and 0.12, respectively.The observed genotypefrequencies of the genotypes\({C^G}{C^G}\),\({C^G}{C^Y}\), and\({C^Y}{C^Y}\)at day 7are 0.23, 0.51, and 0.26, respectively.

The expected frequencies of the genotypes\({C^G}{C^G}\),\({C^G}{C^Y}\), and\({C^Y}{C^Y}\)are 0.23, 0.50, and 0.26, respectively.

The observed genotype frequencies at day 21 for each seedling are different from the observed and expected genotype frequencies at day seven. Thus, the allele frequencies have changed from day 7 to day 21.

Explanation for part (c)

The comparison between theobservedgenotypefrequencies at day 21 and observed and expected frequencies of genotypes \({C^G}{C^G}\), \({C^G}{C^Y}\), and \({C^Y}{C^Y}\)at day seven suggests that the seedling population is not in Hardy-Weinberg equilibrium at day 21 and is undergoing evolution.

Explanation for part (d)

The seedling population is not in Hardy-Weinberg equilibrium at day 21 because the observed genotype frequency for each seedling is different compared to the observed and expected genotype frequencies at day 7.

The genotype frequency for\({C^G}{C^G}\)has increased to 0.27 on day 21 from 0.23 as observed on day seven. On the other hand, thegenotype frequency for\({C^Y}{C^Y}\)has decreased at day 21 from 0.26 to 0.12.

On day 27, many \({C^Y}{C^Y}\)plants were not surviving. The population of \({C^Y}{C^Y}\)plants fell from 56 to 20 while \({C^G}{C^G}\) plants were decreased slightly and were stable. Thus, the genotype \({C^G}{C^G}\)is being selected for, and the \({C^Y}{C^Y}\)is being selected against evolution.