On the island of Bilago, on the Planet Ceti Alpha 6, there lives a population of

Question

On the island of Bilago, on the Planet Ceti Alpha 6, there lives a population of armadiles (cross between an armadillo and a crocodile). A portion of these armadiles have small teeth; as a result, they are vegetarian. About 15% of vegetarians on the planet are amradiles. Tooth size is determined by a single autosomal locus with two alleles: T (trait allele) and t (wild type allele). In a recent study, researchers collected the values in the following table:

The T allele frequency in this population is 0.45, and the genotypes are in Hardy-Weinberg proportions at the locus. In a mating of Tt (heterozygous) armadiles, what is the expected proportion of offspring that will have small teeth?

A. 0.067. B. 0.250. C. 0.870. D. 0.342. E. 0.667.

Table 1. Counts of armadile tooth sizes by genotype Phenotype Genotype Small teeth Standard size (wild type) teeth TT 100 15 Tt 65 10 tt 10 150

Explanation / Answer

Under the assumption of random mating, the probability of producing a zygote that is homozygous for the allele T is simply p*p = p2. This is because p is the frequency of the alleleT in both the gametes.

Likewise, the probability of producing a tt homozygote is q*q = q2.

For the Tt heterozygote, two possibilities exist with a probability of p*q, the total probability of forming heterozygote is 2pq.

p + q = 1

p2 + q2 + 2pq = 1

According to the data provided, the allele frequency of T (p) is 0.45.

Thus, allele frequency of t (q) =1-0.45 = 0.55

Now, the frquencies of homozygote and heterozygote offsprings would be

TT = p2 = (0.45)2 = 0.2025

tt = q2 = (0.55)2 = 0.3025

Tt = 2pq = 2*0.45*0.55 = 0.4950

According to the phenotype in the number of offsprings based on the genotype as provided in the table above, TT ad Tt are responsible imparting small teeth.

Thus, the expected proportion of offsprings with small teeth = p2 + 2pq = 0.2025 + 0.4950 = 0.6975.

Hence, option E is the correct answer.

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