Final answer:
Allele frequencies can always be determined from the genotype frequencies regardless of whether a population is in Hardy-Weinberg equilibrium. This is because allele frequency calculations do not depend on the population meeting the equilibrium conditions, but on the known frequencies of the genotypes (AA, Aa, aa).
Step-by-step explanation:
Allele frequencies can be determined always; it does not matter whether or not the population is in Hardy-Weinberg equilibrium. When you know the frequencies of all three genotypes (AA, Aa, aa) for a gene with two alleles (A and a), you can calculate the frequency of each allele in the population. If we denote the allele frequencies as 'p' for allele A and 'q' for allele a, by definition, p + q = 1.
To calculate allele frequencies from genotype frequencies, use the following formulas derived from the Hardy-Weinberg principle: to find 'p', you would add up the frequency of individuals with AA (p² in the Hardy-Weinberg equation) plus half the frequency of individuals with Aa (since half of the alleles in Aa individuals are 'A' alleles). Similarly, to find 'q', add up the frequency of aa individuals (q² in the Hardy-Weinberg equation) plus half the frequency of Aa individuals. This is possible because each individual carried two alleles for a given trait.
The Hardy-Weinberg theorem states that allele and genotype frequencies will remain constant from generation to generation in a theoretical population that is in equilibrium, which requires no mutation, no migration, very large population size, random mating, and no natural selection. However, even if these conditions are not met, allele frequencies can still be deduced from the given genotype frequencies. The Hardy-Weinberg model provides a mathematical foundation for understanding the genetic structure of populations and for comparing actual data against a non-evolving baseline.