Question

Use the observed genotype frequencies from the day 7 data to calculate the frequencies of the CG allele (p) and the CY allele (q).

Short answer

The frequencies of the \({C^G}\) allele (\(p\)) and the \({C^Y}\)allele (\(q\)) calculated from the day 7 data are 0.48 and 0.51, respectively.

Step-by-step solution

Hardy-Weinberg equilibrium

Hardy-Weinberg equilibrium assumes that a population stays constant if not driven by natural selection, mutation, and migration. Both genotypic and allelic frequencies are related. It also explains the maintenance of variation in a population and how it lacks variation without disturbing factors.

The mathematical equation for Hardy-Weinberg equilibrium is:

\({p^2} + 2pq + {q^2} = 1\)

And, \(p + q = 1\)

Genotypic frequency

Genotype frequency is calculated as the number of individuals with a particular genotype upon the total number of individuals in the population. It provides an idea of how often a specific genotype is present in the population.

The genotypic frequency is always greater than zero but less than one. Genotype frequency, along with allelic frequency, is used to determine the variation in a population.

CG allele (p) and CY allele (q)

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:

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

\({p^2} = \frac{{49}}{{216}}\)

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

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

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:

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

\({q^2} = \frac{{56}}{{216}}\)

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

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

Thus, the frequencies of the \({C^G}\) allele (\(p\)) and the \({C^Y}\)allele (\(q\)) are 0.48 and 0.51, respectively.