No, Natural Selection means that the most adapted species will survive and thrive. It is the least adapted species that dies off.
Further, if you are using Occam's Razor to question two theories, then all prerequisites for both theories must be listed as unproven degrees of freedom.
This is a different way of saying the same thing as it applies to biology. "Natural selection" is actually about reproductive success and the termination of reproductive capability, which usually (though not always) means death in living organisms. "Death" may have been a poor bit of shorthand, but when I thought about it, what you wrote wasn't right either. I don't think anyone questions that there is variation in the level of reproductive success of individual organisms in a population.