Final answer:
Small population size, long periods of geographic isolation, and the effects of genetic drift are significant factors that increase the likelihood of allopatric speciation occurring more quickly. High gene flow would actually hinder this process by maintaining genetic similarity.
Step-by-step explanation:
Among the variables mentioned, small population size, long periods of geographic isolation, and genetic drift are factors that can increase the likelihood of allopatric speciation occurring more quickly. High gene flow would decrease the likelihood as it maintains genetic homogeneity between populations. Random mating does not necessarily hasten allopatric speciation. Instead, a small population size allows for more pronounced effects of genetic drift, as allele frequencies can change more drastically from generation to generation due to chance events. Long periods of geographic isolation ensure that separated populations have sufficient time to diverge genetically, developing distinct adaptations and reproductive barriers. Thus, the conditions that lead to the violation of the Hardy-Weinberg Equilibrium and facilitate allopatric speciation involve limited gene flow due to geographic barriers and the pronounced effects of genetic drift in small, isolated populations.