Final answer:
Genetic divergence that leads to speciation can occur through allopatric speciation, due to geographic isolation, and sympatric speciation, without geographical barriers, where small genetic changes and reproductive isolation eventually result in the formation of new species.
Step-by-step explanation:
Genetic divergence that can result in speciation occurs when there is a build-up of small genetic changes within a population. This can lead to the formation of new species through mechanisms such as allopatric speciation and sympatric speciation.
In the case of allopatric speciation, geographic isolation, such as a river forming a new branch or the formation of a new valley due to erosion, prevents gene flow between populations, allowing them to evolve independently. Over time, due to different environmental pressures and changes, such as variations in prey choices or climate, these populations may diverge significantly at the genetic level and become reproductively isolated. This has been observed in species like Darwin's finches and Mexican spotted owls.
Sympatric speciation, on the other hand, occurs without geographic separation. Populations evolve within the same physical space, potentially due to reproductive barriers such as differences in mating seasons or courtship behaviors, or ecological niches that result in reproductive isolation. Examples include the divergence of cichlid fish species in the same lake.