Before revision: We construct  zig-zag processes targeting posterior distributions arising in genetics from the Kingman coalescent and two popular models of mutation.
After revision: We construct zig-zag process targeting a posterior distribution defined on a hybrid state space consisting of both discrete and continuous variables. The construction does not require any assumptions on the structure among discrete variables. We demonstrate our method on two examples in genetics based on the Kingman coalescent and two popular models of mutation.