Question

Within a population of butterflies, the color brown (B) is dominant over the color white (b). And, 40% of all butterflies are white.

Given this information, calculate the following:
a) The percentage of butterflies in the population that are heterozygous.
b) The frequency of homozygous dominant individuals.

Answer 1

The find the percentage of heterozygous and homozygous dominant butterflies in a population where brown is dominant over white and 40% are white, use p + q = 1 and q² = 0.4, resulting in approximately 46.5% heterozygous and 13.5% homozygous dominant butterflies. So, the correct optyion is a) The percentage of butterflies in the population that are heterozygous.

Step-by-step explanation:

Calculating Genotypic Frequencies in a Butterfly Population

Within a butterfly population where color brown (B) is dominant over white (b) and 40% of all butterflies are white (bb), we can determine the percentage of heterozygous individuals and the frequency of homozygous dominant individuals using the Hardy-Weinberg principle.

To solve for heterozygosity, first, we note that white butterflies (bb) represent the homozygous recessive (rr) frequency, which is 40% (or 0.4 when used in calculations).

Using Hardy-Weinberg equilibrium, we can determine that p² + 2pq + q² = 1, where p² is the frequency of BB, 2pq is the frequency of Bb, and q² is the frequency of bb (0.4). Since q² (bb) is known, q = √0.4 ≈ 0.632. Accordingly, p (B) = 1 - q ≈ 1 - 0.632 = 0.368.

The percentage of heterozygous butterflies, 2pq, is then 2 * 0.368 * 0.632 ≈ 0.465 or 46.5%. The frequency of homozygous dominant butterflies, p², is 0.368² ≈ 0.135 or 13.5%.

In summary:

Heterozygous (Bb) butterflies: ~46.5%

Homozygous dominant (BB) butterflies: ~13.5%

Applying this knowledge to plants with purple (V) and white (v) flowers where p = 0.8 and q = 0.2 in a population of 500, we expect:

Homozygous dominant (VV): p² * population = 0.8² * 500 = 320

Heterozygous (Vv): 2pq * population = 2 * 0.8 * 0.2 * 500 = 160

Homozygous recessive (vv): q² * population = 0.2² * 500 = 20

Therefore, 320 + 160 = 480 plants would have violet flowers, and 20 plants would have white flowers.

So, the correct optyion is a) The percentage of butterflies in the population that are heterozygous.

Answer 2

For the population of butterflies:

• (a) Percentage of heterozygous butterflies: 72%
• (b) Frequency of homozygous dominant individuals: 36%

How to find percentage and frequency?

To calculate the percentage of heterozygous butterflies and the frequency of homozygous dominant individuals in the population:

a) Since 40% of the butterflies are white, and white is recessive (represented by b), the frequency of the recessive allele (q) is:

q = √(40/100)

= √(0.4)

= 0.6

The sum of the squares of the allele frequencies must equal 1:

p² + q² = 1

p² + 0.6² = 1

p² = 0.36

p = √(0.36)

= 0.6

Heterozygous individuals carry one dominant allele (B) and one recessive allele (b). Their frequency is:

2pq = 2 × 0.6 × 0.6

= 0.72

Therefore, 72% of the butterflies in the population are heterozygous.

b) Homozygous dominant individuals carry two dominant alleles (BB). Their frequency is:

p² = 0.6²

= 0.36

Therefore, 36% of the butterflies in the population are homozygous dominant.