At the end of the term, the professor locks the students in the classroom with plenty of food and water and leaves them there for 200 years, during which time they undergo 10 rounds of random mating with no selection, mutation or genetic drift. 31a. What is the frequency of the Aallele in the population at the end of the 200 years? b. What is the frequency of the aallele at the end of the 200 years? c. Is the population at Hardy-Weinberg equilibrium at the end of the 200 years? d. At the end of the 200 years, the professorʼs granddaughter examines the genotype of the 1000 people drawn at random from the population. How many sleepyheads should she find, on average (your answer should be a number between 0 and 1000) ?

a. 0.7

b. 0.3

c. Yes

d. 90

Explanation:

As the random mating population was escaped from external evolutionary forces such as mutation, natural selection, and migration, the gene frequency will not change over time. The population will be at Hardy-Weinberg equilibrium throughout the time.

As the number of sleepyheads (recessive trait) was 90 out of class of 1000 students at the start of course.

q²=0.09 ∵ fraction of sleepyheads = 90/1000 = 0.09 denoted by q²

q that is the recessive gene frequency will be equal to 0.3 (by taking square root of P²

Hence, allele frequency of a allele is 0.3

As, frequency of dominant allele A is denoted by letter p and p+q=1

∴ p=0.7 As p=1-0.3

Hence, allele frequency of A allele is 0.7

Counting the probability of aa alleles (sleepyheads);

As a = 0.3

∴ aa = 0.3*0.3 = 0.09 (In terms of percentage, it is 9%)

To 0.09*1000 = 90 or 9% of 1000 = 90

Hence, 90 students should be sleepyheads.