When does a species undergoing natural selection, change more?

In the ToE the one that reproduces more IS the favoured variety. The species will change if a new variety has an advantage in terms of offspring. If the existing variety has the advantage then the new variety will tend to be eliminated producing stasis.In many cases selection does not favour either allele strongly enough for long enough to fix one of them, but when it does one of the alleles will be eliminated. So you are right that natural selection will tend to eliminate some alleles, narrowing the variation of the species.This is why the modern version of the ToE proposes mutation as the mechanism by which new alleles are introduced into the species.