21% of a population is homozygous dominant, 49% are heterozygous and 29% are homozygous recessive. if the Hardy-Weinberg Law applies, what percentage of the next generation is predicted to be homozygous recessive?
29%
To predict the percentage of the next generation that is homozygous recessive, we can use the Hardy-Weinberg equilibrium equation. The equation is given by:
p^2 + 2pq + q^2 = 1,
where:
- p represents the frequency of the dominant allele in the population.
- q represents the frequency of the recessive allele in the population.
- p^2 represents the frequency of homozygous dominant individuals.
- 2pq represents the frequency of heterozygous individuals.
- q^2 represents the frequency of homozygous recessive individuals.
Given the information provided, we can calculate the values of p and q using the following steps:
Step 1: Calculate the frequency of the dominant allele (p):
From the information given, we know that the sum of homozygous dominant individuals and heterozygous individuals is 21% + 49% = 70%. So, the frequency of the dominant allele (p) can be estimated as the square root of 70% (0.70). Therefore, p = √0.70 ≈ 0.84.
Step 2: Calculate the frequency of the recessive allele (q):
Since the sum of the allelic frequencies must equal 1, we can subtract the frequency of the dominant allele (p) from 1 to find the frequency of the recessive allele (q). Therefore, q = 1 - p = 1 - 0.84 = 0.16.
Step 3: Calculate the predicted frequency of homozygous recessive individuals (q^2):
Using the value of q, we can calculate the square of q to find the frequency of homozygous recessive individuals. Hence, q^2 = 0.16^2 = 0.0256.
Finally, multiply the value of q^2 by 100 to convert it to a percentage. Therefore, the predicted percentage of the next generation that is homozygous recessive is approximately 2.56%.