I would amend that, 'genes don't cause evolutionary changes', they measure the environment, the result is evolution. (or the environment measures them,the direction of the vector not important to me)
My little treatise there is not a truth or meant to be, it is an idea, that one must crawl into in order to present.
The environment is the wall of pressure against an allele set, we can assign that pressure to species, individuals, or the alleles themselves. We generally assign it to species.
I did not mean to in any way dismiss the environment, indeed I simply assumed it, the tapestry upon which alleles, individuals or species are measured and selected.
So yes, "If we care about variations within the allele population, then we need to think about the way populations are affected." ... but what do we mean when we say "populations" ... the members of a species? Normally that is what we do, but for life, self-replicating molecules, the distinction is somewhat arbitrary.
It is much more noticeable if we walk back to single-celled organisms, where a bug is lucky to hold a species designation for a year, before it it gest reassigned, reconsidered, and redefined. I'm not used to hearing the word "extinct" when one speaks of bacteria. Why is that?