Question

Calculate the observed frequencies of genotypes CGCG, CGCY, and CYCY at day 7. Compare these frequencies to the expected frequencies calculated in question 2. Is the seedling population in Hardy-Weinberg equilibrium at day 7, 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 7 are 0.23, 0.51, and 0.26, respectively.

Both the observed and expected genotype frequencies for each seedling are similar.

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

The seedling population is in Hardy-Weinberg equilibrium at day seven is because the observed and expected genotype frequencies for each seedling are similar. None of the genotypes is getting selected for or against evolution.

Step-by-step solution

Genotype frequency and selection

If the observed and expected genotype frequencies are similar in a population, then the population is in Hardy-Weinberg equilibrium. Selection can act and affect the genotype frequencies. In the absence of selection, the genotype frequency expected and observed remains the same.

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 7.

From the observed frequencies from day 7, it is given that:

Number of homozygous dominant or green seedlings (\({C^G}{C^G}\))= 49

Total number of seedlings= 216

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

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

\(\begin{aligned}{l}{p^2} &= \frac{{49}}{{216}}\\{p^2} &= 0.226\\{p^2} &= 0.23\end{aligned}\)

From the observed frequencies from day 7, it is given that:

Number of heterozygous genotypes or green-yellow seedlings (\({C^G}{C^Y}\))= 111

Total number of seedlings= 216

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

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

\(\begin{aligned}{l}2pq &= \frac{{111}}{{216}}\\2pq &= 0.51\end{aligned}\)

From the observed frequencies from Day 7, it is given that:

Number of homozygous dominant or yellow seedlings (\({C^Y}{C^Y}\))= 56

Total number of seedlings= 216

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

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

\(\begin{aligned}{l}{q^2} &= \frac{{56}}{{216}}\\{q^2} &= 0.259\\{q^2} &= 0.26\end{aligned}\)

Thus, the observed genotypefrequencies of the genotypes\({C^G}{C^G}\),\({C^G}{C^Y}\), and\({C^Y}{C^Y}\)are 0.23, 0.51, and 0.26, respectively.

Explanation for part (b)

To calculate: Expected frequencies of genotypes \({C^G}{C^G}\),\({C^G}{C^Y}\), and\({C^Y}{C^Y}\)at day 7 and compare them with the observed genotype frequency.

From the observed frequencies from Day 7, it is given that:

Number of homozygous dominant or green seedlings (\({C^G}{C^G}\))= 49

Total number of seedlings= 216

The allele frequency for\({C^G}\)allele (\(p\)) is:

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

\(\begin{aligned}{c}p &= \sqrt {\frac{{49}}{{216}}} \\ &= 0.476\\ \simeq 0.48\end{aligned}\)

The expected genotypic frequencyof\({C^G}{C^G}\)(\({p^2}\)) is:

\(\begin{aligned}{l}{p^2} &= 0.48 \times 0.48\\{p^2} &= 0.23\end{aligned}\)

From the observed frequencies from Day 7, it is given that:

Number of homozygous dominant or yellow seedlings (\({C^Y}{C^Y}\))= 56

Total number of seedlings= 216

The allele frequency for\({C^Y}\)allele (\(q\)) is:

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

\(\begin{aligned}{c}q &= \sqrt {\frac{{56}}{{216}}} \\ &= 0.509\\ \simeq 0.51\end{aligned}\)

The expected genotypic frequencyof\({C^Y}{C^Y}\)(\({q^2}\)) is:

\(\begin{aligned}{l}{q^2} &= 0.51 \times 0.51\\{q^2} &= 0.26\end{aligned}\)

We have:

\(p = 0.48\)and\(q = 0.51\)

The expected frequency for\({C^G}{C^Y}\)(\(2pq\)) is:

\(\begin{aligned}{l}2pq &= 2 \times 0.48 \times 0.51\\2pq &= 0.489\\2pq &= 0.49\end{aligned}\)

\(2pq = 0.5\)

Thus, the expected frequencies of the genotypes\({C^G}{C^G}\),\({C^G}{C^Y}\), and\({C^Y}{C^Y}\)are 0.23, 0.5, and 0.26, respectively.The observed genotypefrequencies of the genotypes \({C^G}{C^G}\), \({C^G}{C^Y}\), and \({C^Y}{C^Y}\)are 0.23, 0.51, and 0.26, respectively. Therefore, the seedling population is in equilibrium at day 7.

Explanation for part (c)

The seedling population is in equilibrium at day seven because each seedling's observed and expected genotype frequencies are similar. It implies that the seedling population is not undergoing evolution.

Explanation for part (d)

The observed genotype frequency meets the expected genotype frequency for each seedling. Therefore, at Day 7, there is no evolution, and there are no particular genotypes or a particular allele selected for or against.