As I have suggested before, the way I see it is that the 'process' of drift has far too many variables for us to model approriately.
Well, I would disagree. Too many to model as a deterministic process, perhaps, but I would question if that was appropriate even if it was possible. And that doesn't explain why you excluded the environment from your drift function, while including it in your natural selection function when, under your definition it affects both. It looks very much as if you are using a more normal definition of environment.
So do you accept or reject 'universal determinism'? i.e. that what we see as random is actually the result of interactions too complex for us to comprehend.
Universal determinism is irrelevant to the questions before us. If natural selection is "deterministic" solely because of universal determinism then it is deterministic only in a trivial sense which tells us nothing useful about it. Regardless of determinism the outcome of evolution is influenced by many factors which might as well be random and therefore treating them as random gives us a clearer view of natural selection, whether they are random or fully deterministic.
No k is the current generation, the gene distribution of which is a function of past changes and current changes due to survivability.
I see your mistake now. You assume that natural selection is primarily about survival. It isn't. It's all about reproductive success, and the survival of individuals is only relevant insofar as it contributes to reproduction.
Therefore, the generation you need to look at is the previous generation, the parents.
But the distribution of genes in the current generation is about which 'genes' survive ... isn't it?
That is very unclear. However, I think I can say that whatever it means exactly, it is wrong. For instance a living individual that is sterile due to a genetic defect is in the current population, but does not contribute genetic material to the next. If you exclude dead individuals, then a dead individual that has already bred successfully has contributed to the next generation, despite being excluded from the current one.
It is breeding that is important, not simple survival.
At any point in time, k, the genetic makeup of the population is an acculation of the results from the past .... which will include deceased individuals. So maybe I changed tack a bit there, but it's been a while since I even looked at what I was saying here.
'Behaviour' is part of my environment ....
The deceased are no longer part of the population at time k, but were at some point from k-1 .... k-n.