Question

In: Biology

In a population of rats, the homozygous genotype BB produces black coat color, Bb produces gray...

In a population of rats, the homozygous genotype BB produces black coat color, Bb produces gray coat color, and bb produces white coat color. When the population is surveyed, you find that there are 60 black rats and 40 gray rats, and no rats with white coats.

A. What are the gene frequencies for the B and b alleles in this population?

B. If this rat population randomly mates, what are the expected ratios of black, gray, and white rats in the next generation? (Assume Hardy-Weinberg equilibrium applies.)

Expert Solution

Given the population of rats consits of Homozygous Genotype BB produces Black coat, Bb produces gray coat and bb produces white coat. So, B is Dominant or p while b = recessive or q and pq = Bb. The population is showing incomplete Dominance.

During survey of rat population, we find that there are black coat rats = 60 = BB ; gray coat rats = Bb = 40 ; no rats with white coats = bb = 0.

Ans a) gene frequencies of B and b.

Frequency of B = frequency of BB + 1/2 frequency of Bb ( as Bb is composed of half B and half b)

B = BB + 1/2*Bb

B = 60 + 1/2*40

= 60 + 20

= 80

Frequency = 80/ total population

= 80/100

= 0.80 --------------- frequency of B

Frequency of b = frequency of bb + 1/2 frequency of Bb ( composed of half b)

= bb + 1/2*Bb

= 0 + 1/2*40

= 0 + 20

= 20

= 20 / 100

= 0.20 -------------- frequency of b

Ans b) if rat population randomly mates the expected ratios of black, gray and white rats in next generation and population is in Hardy-Weinberg equilibrium.

We know the frequencies of B = 0.8 and b = 0.20 and the population is randomly mating ( any Genotype can mate with any Genotype example --- BB X Bb ; BB X BB ; Bb X Bb; and different phenotyes can be obtained )

So, Genotype frequencies in next generation after random mating are :

BB = frequency of B^2

BB = 0.8 * 0.8

BB = 0.64 ----------- p^2

bb = frequency of b^2

bb = 0.2 * 0.2

bb = 0.04 -------------- q^2

Bb = 2 * B * b

2Bb = 2 * 0.8 * 0.2

2Bb = 0.32 ----------- 2pq

Verify by using Hardy-Weinberg equation

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

0.64 + 0.32 + 0.04

= 1

Expected ratio of black : gray : white is

0.64 : 0.32 : 0.04

= 64 : 32 : 4

= 16 : 8 : 1

gladiator answered 1 year ago

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