What is the meaning of a selection regime in this context?
I'm an evolutionary biologist. When someone says "selection regime" they simply mean the general conditions (environmental, ecological, etc.) that could have produced a particular evolutionary outcome. For instance, in the example that you mention, they seem to imply that they are interested in knowing if these condtions (i.e. the "selection regime") in the branch that lead to the evolution of humans were somehow different than these of other primates. So, it is a hypothesis, in this case. Unless they state elsewhere in the paper what exactly is this "selection regime", they are simply referring to this idea.