The following conditions would be sufficient for the Hardy-Weinberg equation to accurately predict genotype frequencies from allele frequencies:
1. Random mating: Individuals must mate randomly, with no preference for specific genotypes or phenotypes.
2. Large population: The population must be large enough so that chance events, such as genetic drift, do not significantly affect allele frequencies.
3. No mutations: The alleles in the population must not be changing due to mutations.
4. No migration: There can be no migration of individuals or alleles into or out of the population.
5. No selection: Natural selection cannot be acting on the traits controlled by the alleles in question.