Organism X requires seven parents to breed. Let the dominant and recessive alleles of a certain trait (fur color) be represented by Y and y.
In a certain population of X, $99.2\%$ of the population has the Y phenotype.
a. Compute the frequency of the Y gene in the population.
b. The phenotypes show incomplete dominance. The more Y genes present, the colors of organism X traverse down the rainbow, from white-pink-scarlet-yellow-turquoise-indigo-brown-black
i. Compute the frequency of scarlet fur in the population.
ii. What is the most common color fur in the population?
I can't really verify the validity of my answers, so here they are.
a. We know that $7$ recessive alleles will result in the y phenotype, so $100-99.2$= $0.8\%=0.008 =>\sqrt[7]{0.008}=0.5017=50.17 ==>$ The Y frequency is the complement = $\boxed{49.83\%}$.
Let the frequency of the Y gene be Y' and the y gene be y'.
b.
i. Scarlet fur requires $2$ Y genes and $5$ y genes.
$\displaystyle\binom{7}{2}(49.83\%)^2(50.17\%)^5=\boxed{16.57\%}$
ii. Function $p(Y)=\displaystyle \binom{7}{Y}(Y')^n(y')^{7-n}$ has a maximum at $Y=3.486$ and $Y(3)>Y(4)$, so by very little, the most common fur color in the population is $\boxed{\text{yellow}}$.
Could someone verify my calculations? Our teacher didn't explain the math for heredity.
Alright Saketh, it's cool to see a mix of math and biology =)
The math looks good, this is a quite good exercise about the binomial law for a discrete random variable.
My understanding of the "math for heredity" here is that each organism X got 7 different copy of each chromosome.
If I missed something please feel free to ask, I didn't do the calculations so I can't check your numbers but the reasoning is good =)