Final answer:
It is easiest for a mutation to quickly increase in frequency when there are many mutagens present, when the mutation is advantageous and favored by selection, and in small or isolated populations where genetic drift can play a significant role in allele frequency changes.
Step-by-step explanation:
A mutation is more likely to quickly increase in frequency within a population when there are certain factors at play. These factors include a high number of mutagens such as UV radiation, which increase the rate of mutations; a situation where a mutation results in a favorable adaptation that gives an advantage under natural or sexual selection pressures; and genetic drift in small or isolated populations where even neutral or deleterious mutations can become common more quickly due to random chance.
In the context of allopatric speciation, the rate of mutation is a crucial factor. Given a large enough population and time, beneficial mutations can spread, albeit slowly, unless they are particularly advantageous in a changing environment. Sudden changes, such as an increase in average temperature leading to less fruit production, can shift allele frequencies substantially in small populations as they may be more affected by genetic drift and the specific selective pressures of the environment.