Percentage will be one because there only one genotype with AABBCC which is responsible for darkest colour

Explanation:

To determine the percentage of the darkest individual in the F2 generation, we need to understand the principles of inheritance and the concept of polygenic traits.

Principles of Inheritance:
Inheritance is the process by which traits or characteristics are passed from parents to offspring. It follows certain principles, including the Law of Segregation, the Law of Independent Assortment, and the concept of dominance and recessiveness.

Polygenic Traits:
Polygenic traits are controlled by multiple genes. Each gene contributes to the phenotype, and the cumulative effect of all the genes determines the trait's expression. The expression of polygenic traits can range from a continuous variation to discrete categories.

Crossing Darkest and Lightest Individuals:
In this scenario, the darkest and lightest individuals are taken as parents. Let's assume that the darkest individual is homozygous for the dominant trait (DD) and the lightest individual is homozygous for the recessive trait (dd).

Generation F1:
When these individuals are crossed, the F1 generation will be heterozygous for the trait (Dd). The F1 generation will exhibit an intermediate phenotype, which will be darker than the lightest individual but lighter than the darkest individual.

Generation F2:
When the F1 individuals are crossed among themselves, the F2 generation will show a range of phenotypes due to the polygenic nature of the trait. The distribution of phenotypes in the F2 generation follows a bell-shaped curve known as a normal distribution or Gaussian distribution.

Percentage of Darkest Individuals:
To determine the percentage of the darkest individuals in the F2 generation, we need to consider the number of genes controlling the trait. Since the trait is controlled by three polygenes, it means there are three sets of genes involved.

The expression of each gene follows the principles of dominance and recessiveness. Assuming that each gene follows complete dominance, the darkest phenotype would require all three genes to be homozygous dominant (DDD). This combination will occur less frequently compared to other genotypes.

The percentage of individuals with the darkest phenotype can be estimated by using the binomial expansion formula: P(k) = (nCk) * (p^k) * (q^(n-k))

Here, n is the number of genes controlling the trait (3 in this case), k is the number of dominant alleles required for the darkest phenotype (3 in this case), p is the probability of obtaining a dominant allele (0.5 assuming complete dominance), and q is the probability of obtaining a recessive allele (0.5).

P(3) = (3C3) * (0.5^3) * (0.5^(3-3))
P(3) = 1 * 0.125 * 1
P(3) = 0.125 or 12.5%

Therefore, the percentage of individuals with the darkest phenotype in the F2 generation would be approximately 12.5%.