Hardy Weinberg Equilibrium

Question

You identify a population of rats on an island. Their coat color is controlled by a single gene: BB rats are black, Bb rats are gray, and bb rats are white. You take a census of the population and record the following numbers of rats 

 

Black 150

Gray 120

White 30

a) What are the frequencies of the two alleles?

b) What are the Hardy-Weinberg equilibrium frequencies for these three phenotypes?

c) A heat wave hits the island. All 150 rats with black fur die from heat stroke, but the other rats survive. What are the new allele frequencies for the population?

d) If the population suffers no further cataclysms after the heat wave, and the surviving animals mate randomly, what will be the frequency of rats with black fur in the next generation?

For I did my work for 1-c but I am stuck on d. Here's my work so far

a). p= black

q= white

 

White: 30/300= .1= q^2

√(𝑞²) = √(0.1)= .316

 

p + q=1 

 

p+.316=1

p= .684

Black:  p^2= .465

 

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

 

2pq= 2(.316)(.684)= .432

 

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

.465+ 2(.684)(.316)+.316= 1.213

b). Black: .465

1. White: .316
2. Gray: 2pq= 2(.316)(.684)= .432

c). 120+ 30= 150

 

Gray: 120/150= .80

 

 

 

White: 30/150= .20= q^2

 

√(𝑞²) = √(0.20)= .447

 

P + q =1

P+ .447=1

p= .553

 

Answer 1

You did a great job so far!

Part D involves the concept that each gamete will only have one allele. Additionally, because mating is random, we can think of these diploid individuals as simply mixing their gametes. We do not need to consider the parental origin of a given gamete (i.e. if it comes from a heterozygous or homozygous parent), but simply the proportion of alleles in the population

Let's think of this problem as the probability of an allele randomly interacting with any other allele. This means the probability of a gamete P meeting a gamete P is 0.553*0.553 = 0.306. The probability of a gamete P meeting a gamete Q is 0.553*0.447 = 0.404. The probability of a gamete Q meeting a gamete Q is 0.447*0.447 = 0.200.

Therefore in the following generation, we would expect to have the following proportion of genotypes:

PP = 0.306

PQ = 0.404

QQ = 0.200

Where rats with black fur would be a 0.306 proportion of the population.