What will most likely happen if the gene frequencies in a given population remain constant?

When gene frequencies stay relatively constant, Hardy-Weinberg equilibrium occurs. HW equilibrium occurs in large populations with random mating, with no migration, mutation, or natural selection. In this case, the proportion of dominant homozygous equals the square of the frequency of the dominant allele (p2), the proportion of recessive homozygous equals the square of the frequency of the recessive allele (q2) and the proportion of heterozygotes equals 2pq.