Final answer:
The frequency of a new mutant allele that does not affect an organism's fitness will primarily be governed by genetic drift, although other factors like mutation, gene flow, and nonrandom mating can also play a role.
Step-by-step explanation:
If a new mutant allele is so similar to other alleles that fitness does not change, then its frequency will be governed by genetic drift, mutation, gene flow (or migration), and nonrandom mating. These are the factors that can affect allele frequencies according to the Hardy-Weinberg principle. However, if the mutant allele does not confer any advantage or disadvantage in terms of fitness, natural selection will not act on it, and its frequency in the population will fluctuate due to the other evolutionary forces, primarily genetic drift, which causes random fluctuations in allele frequencies especially in small populations. This principle is critical in population genetics, which studies changes in allele frequencies to understand the evolutionary forces at play within a population.