Generally speaking, there are 2 major forces that cause genetic divergence in the majority of populations and systems.
And those are;
Natural Selection
and
Mutation
Natural selection causes a divergence due to the fact that organisms with " "better", more advantageous traits dependent on their environment, survive and reproduce, while the others have the lesser chance. (This causes traits in the population to change over time.)
Mutilation/Mutations, on the other hand, is a change in the genetic material of an organism-specifically when DNA is copied incorrectly.
This changes a portion of the genetic makeup of an organism, therefore changing the organism, and changing its future generations of offspring (when made...etc)
Hope this helped, let me know if you'd like more information!
-Bumpsly