Question

A population of water snakes is found on an island in lake Erie. Some of the snakes are banded and some are unbanded; banding is caused by an autosomal allele that is recessive to an allele for no bands. The frequency of banded snakes on the island is 0.16; whereas the frequency of the banded snakes in the mainland is 0.25. One summer, a large number of snakes migrate from the mainland to the island. After this migration, 20% of the island consists of snakes that came from the mainland. A. If both the mainland and the island populations are assumed to be in Hardy-Weinberg equilibrium for the alleles that affect banding, what is the frequency of the allele for bands on the island and on the mainland before migration? B. After one generation of migration has taken place, what is the frequency of the banded allele on the island?
Can someone explain how to solve this in detail?

Answer 1

Solution for question A:-

Island - Frequncy of banded snakes = 0.16 ie; genotype frequency of banded snakes (q²) = 0.16.

(given-banding is caused by recessive allele)

Therefore q = Squareroot of 0.16

q = 0.4

Mainland - Frequncy of banded snakes = 0.25 ie; genotype frequency of banded snakes (q²) = 0.25.

(given-banding is caused by recessive allele)

Therefore q = Squareroot of 0.25

q = 0.5

Thus frequency for alleles for bands on island and on mainland before migration is 0.4 and 0.5 respectively.

Solution for question B:-

Given Migration rate as 20% ie; 0.2

Now,

Change in recessive allele frequency (q_change)= migration rate * [recessive allele frequency of the migrants (Mainland) - recessive allele frequency of the host (island)]

Therefore q_change = 0.2 * (0.5 - 0.4)

q_change = 0.02.

Now,

Post migration frequency (recessive allele) at island q_new = pre migration frequency (recessive allele) at island + q_change

Therefore, q_new =0.4 + 0.02 = 0.42.

Post migration recessive allele frequency (banding allele) = 0.42