Question

15. Two Siamese and three Persian cats survive a shipwreck and are carried on driftwood to a previously uninhabited tropical island. All five cats have normal ears, but one carries the recessive allele for folded ears (his genotype is Ff). Calculate the frequencies of alleles F and f in the cat population of this island. If you assume Hardy-Weinberg equilibrium for these alleles (admittedly very improbable), about how many cats would you expect to have folded ears when the island population reaches 16,000?

Answer 1

To calculate the frequencies of the F and f alleles, we can use the allele frequency equation:

p + q = 1

where p is the frequency of the F allele and q is the frequency of the f allele. Since the population is small and we know the genotype of one of the cats, we can calculate the frequency of the f allele directly:

f = sqrt(q^2) = sqrt(1/5) = 0.447

Since the f allele is recessive, we can use the Hardy-Weinberg equation to calculate the frequency of the FF genotype (normal ears) as:

p^2 = 1 - 2pq - q^2 = 1 - 2(0.553)(0.447) - (0.447)^2 = 0.307

The frequency of the Ff genotype (normal ears) is given by:

2pq = 2(0.553)(0.447) = 0.494

The frequency of the ff genotype (folded ears) is:

q^2 = (0.447)^2 = 0.200

To estimate how many cats would have folded ears when the island population reaches 16,000, we can use the Hardy-Weinberg equation and assume that the population is in equilibrium:

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

The total number of cats with folded ears (ff genotype) would be expected to be:

ff = q^2 x 16,000 = 0.200 x 16,000 = 3,200

Therefore, we would expect about 3,200 cats to have folded ears in the island population when it reaches 16,000, assuming Hardy-Weinberg equilibrium. However, it is important to note that this assumption is unlikely to hold true in reality, as the small population size and genetic drift could lead to deviations from the expected frequencies.