The two processes I've found in my old notes are the Bottleneck effect (when catastrophic events occur that result in a smaller population) and the Founder effect (when one specific animal from a species founds a new area, where only their alleles will be present, no matter how common or rare they were in their old home). The smaller the population, the less likely that the family gene pool will be represented in the next generation, eventually resulting in different genetics and eventually species.
I hope this helps!
