Under what conditions would you expect allele frequencies to stay the same

When the population is in Hardy-Weinberg equilibrium

Explanation:

When a population is in Hardy-Weinberg equilibrium for a gene then the allele frequencies with in a population remains the same across generation.

A population is considered to be in Hardy-Weinberg equilibrium under the following assumptions -

a) When there is no mutation

b) When there occurs no random mating

c) When there is no gene flow

d) When the population size is finite or no genetic drift is  happening

e) When there is no natural selection.

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