Question

after graduation, you and 19 friends build a raft, sail to a deserted island, and start a new population, totally isolated from the world. two of your friends carry (that is, are heterozygous for) the recessive cf allele, which in homozygotes causes cystic fibrosis. a) assuming that the frequency of this allele does not change as the population grows, what will be the instance of cystic fibrosis on your island? b) cystic fibrous births on the island is how many times greater than the original mainland? the frequency of births on the mainland is 0.059%.

Answer 1

cystic fibrosis births on the island would be approximately 16.95 times greater than on the original mainland.

Step-by-step explanation:

To calculate the incidence of cystic fibrosis on the island, we need to consider the Hardy-Weinberg principle. According to the principle, in a population where the allele frequencies do not change, the genotype frequencies can be predicted using the following equations:

p^2 + 2pq + q^2 = 1

where:

p^2 represents the frequency of homozygous dominant individuals (AA)

2pq represents the frequency of heterozygous individuals (Aa)

q^2 represents the frequency of homozygous recessive individuals (aa)

In this scenario, two out of the 20 friends (or 2/20 = 0.1) carry the recessive cf allele. This corresponds to the frequency of the recessive allele (q) in the population. Therefore, q = 0.1.

To find the frequency of the dominant allele (p), we subtract the recessive allele frequency from 1: p = 1 - q = 1 - 0.1 = 0.9.

Now we can calculate the incidence of cystic fibrosis (q^2) on the island:

q^2 = (0.1)^2 = 0.01

Therefore, the incidence of cystic fibrosis on the island would be 0.01 or 1%.

To determine the comparison with the original mainland, we need to calculate the frequency of cystic fibrosis births on the mainland. Given that the frequency of births with cystic fibrosis on the mainland is 0.059%, we can compare this with the incidence on the island:

Cystic fibrosis births on the island / Cystic fibrosis births on the mainland = 0.01 / 0.00059

This calculation shows that cystic fibrosis births on the island would be approximately 16.95 times greater than on the original mainland.