Solution:

Given,

Total population (N) = 1300

Recessive allele frequency (q) = 0.8

Dominant allele frequency (p) = 1 - q = 1 - 0.8 = 0.2

As per the Hardy-Weinberg equilibrium,

p2 + 2pq + q2 = 1

where,

p2 = frequency of homozygous dominant individuals

2pq = frequency of heterozygous individuals

q2 = frequency of homozygous recessive individuals

Here, we need to find out the number of dominant individuals in the population.

Let's assume that there are x number of dominant alleles in the population.

Since the gene has only two alleles, the total number of alleles in the population will be 2N, i.e.,

2N = 2 x 1300 = 2600

Now, the frequency of dominant alleles (p) in the population can be calculated as,

p = x/2600

Therefore, the number of homozygous dominant individuals (p2) in the population can be calculated as,

p2 = p x p x N = (x/2600) x (x/2600) x 1300

We know that q = 0.8, so we can calculate the frequency of heterozygous individuals (2pq) as,

2pq = 2 x 0.2 x 0.8 x N = 416

Also, we know that p2 + 2pq + q2 = 1

So, q2 = 1 - p2 - 2pq = 1 - (p2 + 2pq) = 1 - 416/1300 = 0.68

Now, we can use the frequency of recessive alleles (q) to calculate the number of homozygous recessive individuals (q2) in the population, i.e.,

q2 = q x q x N = 0.8 x 0.8 x 1300 = 832

Therefore, the total number of individuals in the population can be calculated as,

N = p2 + 2pq + q2 = x/2600 + 416/1300 + 832/1300

Solving this equation, we get,

x = 832

So, the number of dominant individuals in the population is x = 832.

Therefore, the correct answer is option D.

Note: The above solution involves a lot of calculations. One can also use the shortcut formula to directly calculate the number of dominant individuals in the population, i.e.,

Number of dominant individuals = 2 x square root of (frequency of recessive alleles x total population)

= 2 x square root of (0.8 x 1300)

= 2 x 28.722 = 57.444

Rounding off to the nearest integer, we get,

Number of dominant individuals = 57

However, this formula can only be used when the gene in question has only two alleles and is in Hardy-Weinberg equilibrium.

Recessive allele frequency = q = 0.8
So , q^2 = (0.8)^2 = 0.64
p^2 + q^2 = 1
1 - q^2 = p^2
p^2 = 1 - 0.64 = 0.36
So, p = 0.6 = Dominant allele frequency
So, dominant individuals in the population = 0.36 × 1300 = 468 ...ans...


$$Hope it's help... $$