Since you are both better qualified than I am to discuss this, I won't say much. But it is important to realise that using concepts like 'differential rates of survival' is only meaningful when the populations are moderately large. But *every* mutation starts off as the only instance of that mutation in the entire population, so whether and how long that individual survives is absolutely crucial to the potential spread of that mutation more widely. This is a completely different situation to that in which the population size is sufficiently large that the proportion of individuals with the mutation can be approximated by continuous variable, rather than a discrete one.

Now, working with continuous mathematics is a damn sight easier, so it is no surprise that the relatively few papers I've read on the subject assume it. But be aware that it not valid for small populations and in particular for the early spread of a mutation.