Final answer:
Allelic frequencies of a and a represented as p and q will stay constant from generation to generation if no evolutionary pressures such as selection, mutation, migration affect them, and the population is large with random mating, as depicted in the Hardy-Weinberg equilibrium.
Step-by-step explanation:
Demonstrating the Stability of Allele and Zygotic Frequencies
In a gene pool, the alleles a and a have initial frequencies of p and q, respectively. We can show that the allelic frequencies and zygotic frequencies remain unchanged under certain conditions, which are essentially the five principles of the Hardy-Weinberg equilibrium. These conditions include no selection, no mutation, no migration, a large population size, and random mating. When these conditions are met, the allele frequencies (p and q) will remain constant, as will the zygotic frequencies of the three possible genotypes (pp, pq, and qq).
The Hardy-Weinberg equilibrium describes a state of genetic stability within a population where the allele frequencies are stable and do not change from generation to generation. This stability can be represented mathematically since the sum of the allele frequencies for a gene locus must be equal to 1 (p + q = 1), and similarly, the sum of the genotype frequencies must also be equal to 1 (p² + 2pq + q² = 1). Therefore, if p and q represent the frequencies of two alleles in a population, and there is no evolutionary pressure, the expected frequencies of homozygous dominant (pp), heterozygous (pq), and homozygous recessive (qq) genotypes can be easily calculated and will be consistent across generations.
Should a phenotype be favoured by natural selection, allele frequencies can shift, and if random events cause allele frequencies to change, this is referred to as genetic drift. An extreme example of genetic drift is the founder effect, where a new population that is not genetically representative of the original population is established, leading to a different set of allele frequencies. However, under Hardy-Weinberg conditions, these shifts do not occur, and the genetic structure of the population remains unchanged.