To maintain genetic equilibrium within a population, five conditions must be met:

1. Large Population Size: The population must be large enough to minimize random fluctuations in allele frequencies due to chance events like genetic drift. In smaller populations, chance occurrences can have a more significant impact on gene frequencies, leading to deviations from equilibrium.

2. Random Mating: Individuals must mate randomly within the population, meaning that there should be no selective mating based on traits like phenotype or genetic relatedness. Non-random mating, such as assortative mating (where individuals choose mates with similar traits), can alter genotype frequencies and disrupt genetic equilibrium.

3. No Mutations: The genetic makeup of the population should remain stable in terms of allele frequencies over time. New mutations can introduce novel alleles into the gene pool, potentially changing allele frequencies and disrupting equilibrium.

4. No Gene Flow: There should be no migration of individuals into or out of the population. Gene flow, or the movement of alleles between populations, can introduce new alleles or remove existing ones, altering the genetic composition and preventing equilibrium.

5. No Natural Selection: Natural selection should not favor specific genotypes over others. Differential survival and reproduction based on genotype can lead to changes in allele frequencies, as certain alleles become more or less common in the population. Without natural selection, allele frequencies remain stable over generations, maintaining genetic equilibrium.

When these conditions are met, allele frequencies in a population remain constant from one generation to the next, and the population is said to be in genetic equilibrium under the Hardy-Weinberg principle. Any deviation from these conditions can result in evolutionary change, such as genetic drift, gene flow, mutation, or natural selection, leading to shifts in allele frequencies and changes in the genetic makeup of populations over time.