One important thing to remember is that both models are likely correct. If Natural Selection is right, we should see some things that show almost no change over time, some things that gradually change over time and others where there is a rapid change.
And that is pretty much what is seen. It's not one or the other, it is what happened within the population or period that you are examining.
We know that the outside forces and conditions have varied. There have been periods of major local change, major global change, minor change, long periods of stability and even environments that have remained almost identical over most of history.
Why should the record found in fossils be any different?
Aslan is not a Tame Lion
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