If this is so, how do you explain living fossils?
Do they not mutate?
It cannot be that their environment did not change. So, if they mutate and if their environment changes, why are they the same?
Last I checked, fossils are dead.
If you have time, do some reading on "fitness peak". In this model a species becomes more adapted to a specific environment over time. The longer this occurs the more fit the species becomes. At a certain point they reach a peak where very few changes will increase their fitness. This results in a population that just doesn't change much, even if the rate of mutation is the same. In this situation, the number of deleterious mutations will be much greater than the number of beneficial mutations so selection tends to be negative.
One example is the coelacanth which has many features in common with it's distant ancestors. This fish is found in very deep waters (>200m if memory serves). These environments do not vary by more than a few degrees each year and are very, very stable. Chances are that this coelacanth species has changed very little over the last 60 million years since it moved to these deeper waters (most known fossil coelacanth species were from shallow water environments).