Although he got the idea from Buffon,
GEORGE CUVIER, actually developed the concept of a "species extinction" from studying fossil reptiles and brachiopods. He made a discovery that , today wed just say duuhhh, whats so difficult , but in Cuviers time we must remember that the foundations in evidence were just not there until someone like he, began peering into rock layers to examine the critters therein.
Cuvier convinced his colleagues that, the earth wasnt populated by everything in its"kind", and all at once but was somehow sequentially populated by beings that show up in successive layers of the fossil record, and these beings are different, and often more complex, with ascending layers of the strata.
This seems like such a simple minded concept to us but back then it was huge. In fact, it was the idea of extinction that gave Darwin his own ideass for the mechanisms of natural selection, namely competition for resources through time.
As Dobzhansky said that"Nothing in biology makes sense except in the light of evolutionary theory", nothing in evolutionary theory can be clerly demonstrated except in the light of extinction .