Knowing that some individuals from Island 1 colonized Island 2, biologists sample the Mainland and two Island populations fifty years after the colonization events. They determine that allele frequencies are similar on both islands, but they are significantly different than the frequencies of the mainland population. Which of the evolutionary mechanisms could be used to explain these observed

The evolutionary mechanism that could be influencing the allele frequencies between both islands and the mainland population might be Founder Effect.

Explanation:

Genetic drift is the random change that occurs in the allelic frequency of a population through generations. The magnitude of this change is inversely related to the size of the original population. These changes produced by genetic drift accumulate in time and eventually, some alleles get lost, while some others might set. Genetic drift affects a population and reduces its size dramatically due to a disaster -bottleneck effect- or because of a population split -founder effect-. In founder effect, a new population originates when a few individuals who are coming from a bigger population carrying its genes, settle down in a new area and reproduce. This small population might or might not be genetically representative of the original one. Some rare alleles might be exceeded or might be completely lost. Consequently, when the small population increases in size, it will have a genetically different composition from the original one. In these situations, genetic variability is reduced and there exists the possibility of developing a peculiar allelic composition. If the number of individuals that originated the new population is low, the founder effect will be very extreme, because the effects of the genetic drift are inversely proportional to the original number of individuals.  

In the exposed situation, the evolutionary mechanism that could be influencing the allele frequencies between both islands and the mainland population might be Founder Effect. The fact that both islands are similar in their frequencies might be due to little genetic variation on island 1, or because dispersion to island 2 is a recent event on time.