A population of animals has a dominant allele for dark-colored fur and a recessive allele for light-colored fur. If the population of animals is 100 and 12 members of the population have the light-colored fur, about what percentage of the population is heterozygous? What percentage of the population is homozygous dominant? Use the Hardy-Weinberg Principle to solve.
To solve this problem using the Hardy-Weinberg Principle, we need to know the allele frequencies in the population.
Let's denote the dominant allele for dark-colored fur as "D" and the recessive allele for light-colored fur as "d".
According to the Hardy-Weinberg Principle, the frequencies of alleles in a population will remain constant over multiple generations if certain assumptions are met. These assumptions include no mutation, no migration, random mating, no natural selection, and a large population size.
Let's use the formula to calculate allele frequencies:
The frequency of the dominant allele (D) is calculated as follows:
p = (2 * number of homozygous dominant individuals + number of heterozygous individuals) / (2 * total population)
In this case, we have the following information:
- Total population (N) = 100 individuals
- Number of individuals with light-colored fur (dd genotype) = 12
The frequency of the recessive allele (d) can be found using the equation:
q = (2 * number of homozygous recessive individuals + number of heterozygous individuals) / (2 * total population)
Again, in this case, we have the following information:
- Total population (N) = 100 individuals
- Number of individuals with light-colored fur (dd genotype) = 12
Using these formulas, we can calculate the allele frequencies:
Frequency of allele D (p) = (2 * (100 - 12) + 12) / (2 * 100) = 0.88
Frequency of allele d (q) = (2 * 12 + 12) / (2 * 100) = 0.12
Now, we can use these allele frequencies to calculate the expected genotype frequencies:
The expected frequency of homozygous dominant individuals (DD genotype) is p^2:
Frequency of DD genotype = (0.88)^2 = 0.7744
The expected frequency of heterozygous individuals (Dd genotype) is 2 * p * q:
Frequency of Dd genotype = 2 * 0.88 * 0.12 = 0.2112
The expected frequency of homozygous recessive individuals (dd genotype) is q^2:
Frequency of dd genotype = (0.12)^2 = 0.0144
To calculate the percentage of the population with each genotype, we need to multiply the frequencies by 100:
Percentage of the population that is heterozygous (Dd genotype) = Frequency of Dd genotype * 100 = 0.2112 * 100 ≈ 21.12%
Percentage of the population that is homozygous dominant (DD genotype) = Frequency of DD genotype * 100 = 0.7744 * 100 ≈ 77.44%
So, about 21.12% of the population is heterozygous (Dd genotype), and about 77.44% of the population is homozygous dominant (DD genotype) based on the given information and the assumptions of the Hardy-Weinberg Principle.