Question

In an isolated lagoon in the caribbean, a population queen conch is in hardy-weinberg equilibrium. Of the 350 individuals in the lagoon, 70 have a pink coloration on the inside of their shell (genotypes pp and pc). The other 280 have a cream coloration on the inside of their shell (genotype cc). This year, these snails produce 300 offspring. How many of those offspring do you expect will have pink shell coloration?

Answer 1

Given:

Genotypes pp and pc, give pink coloration in 70 out of 350 conches.

Genotype cc, gives cream coloration in 280 out of 350 conches.

To find: the number of offspring in a population of 300 snails with pink coloration.

Method: Using punnett square and hardy wineberg equation to solve the problem.

Solution:

The Punnett square for the given data is shown in the image. Based on the given data, one can infer that the presence of 'p' allele hinders the expression of 'c' allele inspite of 'c' being the dominant allele. Thus we'll use the homogenous dominant 'cc' conches to find the frequency of the 'c' allele.

No. of conches with 'cc' genotype = 280

Frequency of 'cc' allele = $\frac{280}{350} = 0.8$

∴ c² = 0.8

c = √0.8 = 0.89

Since 'c' and 'p' alleles are in equilibrium,

p + c = 1

p = 1 - c = 1 - 0.89 = 0.11

∴ c = 0.89 and p = 0.11

Now, the number of heterogenous carriers will be,

$2pc = 2\times 0.89\times 0.11 = 0.2$

Hence, no.of heterogenous carriers (pc),given by 2pc = 0.2

Now, the number of pink colored snails will be, p² + 2pc = 0.0121 + 0.2 = 0.21

Hence, any population size will have 21% of the snails in pink coloration.

The, 21% of a 300 sized population will be, $\frac{300\times 21}{100}$ = 63.

Hence, 63 snail offspring will be pink colored.