Hi, I really need help in how to approach this question:
A species of tiny antelope, known as the zephyr, has an XY system of sex determination, similar to mammals. Zephyr males have small antlers and females do not. The antlers can be two pronged (2-pr) or three pronged (3-pr) and this is determined by a single gene which is found on the X chromosome (there is no allele for 2-3 pronged on the Y chromosome). In a large population, 74% of the adult males have two-pronged antlers and the rest of the adult males have three pronged antlers.
a) What is the frequency of the three pronged allele in the adult male population?
Is it 0.26??
b) Assuming that the allele frequency is the same in the females, what are the expected genotypic frequencies in the females.
Any help would be very much appreciated. Thanks.
I think a) is 0.26.
b) if you take the 2-pr allele to be 'p' and the 3-pr allele to be 'q' then genotypic frequencies are p^2 for Xp2Xp2, 3^2 for Xp3Xp3 and 2(p)(q) for Xp2Xp3.
so Xp2Xp2 = 0.55
Xp3Xp3 = 0.07
Xp2Xp3 = 0.19
To approach this question, we need to use the principles of population genetics and the Hardy-Weinberg equilibrium. The Hardy-Weinberg equilibrium states that if certain conditions are met, the frequencies of alleles and genotypes in a population will remain constant from one generation to the next.
Let's address each part of the question:
a) To determine the frequency of the three-pronged allele in the adult male population, we can use the Hardy-Weinberg equation:
p^2 + 2pq + q^2 = 1
Where:
- p^2 represents the frequency of homozygous two-pronged individuals (2-pr/2-pr)
- 2pq represents the frequency of heterozygous individuals (2-pr/3-pr)
- q^2 represents the frequency of homozygous three-pronged individuals (3-pr/3-pr)
- p represents the frequency of the two-pronged allele
- q represents the frequency of the three-pronged allele
Given that 74% of the adult males have two-pronged antlers, we can state that p^2 (the frequency of two-pronged homozygotes) is equal to 0.74.
Therefore, we can calculate the frequency of the two-pronged allele (p) as the square root of 0.74:
p = sqrt(0.74) ≈ 0.861
Since there are only two alleles (two-pronged and three-pronged), the frequency of the three-pronged allele (q) is equal to 1 - p:
q = 1 - p ≈ 1 - 0.861 = 0.139
So, the frequency of the three-pronged allele in the adult male population is approximately 0.139.
b) Assuming that the allele frequency is the same in females as in males, we can still use the Hardy-Weinberg equation to determine the expected genotypic frequencies in females. Since the allele frequency remains the same, the calculations for p and q would also remain the same as in part a.
In females, we have two X chromosomes. Therefore, we can consider the genotypic frequencies in females as follows:
- Frequency of two-pronged homozygous females (2-pr/2-pr): p^2
- Frequency of heterozygous females (2-pr/3-pr): 2pq
- Frequency of three-pronged homozygous females (3-pr/3-pr): q^2
Substituting the values we obtained in part a:
p^2 ≈ (0.861)^2 ≈ 0.742
2pq ≈ 2 * 0.861 * 0.139 ≈ 0.240
q^2 ≈ (0.139)^2 ≈ 0.019
Therefore, the expected genotypic frequencies in females are approximately:
- Two-pronged homozygous females: 0.742 (74.2%)
- Heterozygous females: 0.240 (24.0%)
- Three-pronged homozygous females: 0.019 (1.9%)
So, the expected genotypic frequencies in females are approximately 74.2%, 24.0%, and 1.9% for two-pronged homozygotes, heterozygotes, and three-pronged homozygotes, respectively.
Note: Keep in mind that these calculations assume no selection, mutation, migration, or other evolutionary factors at play. They provide the expected frequencies under the assumption of a stable population and random mating.