Lyell's theory that geological processes occurred over time led Darwin to formulate what concepts?

Darwin was greatly influenced by Lyell's theory of slow uniform processes. Darwin observing the giant canyons in South America speculated about how many millions of year cutting the canyon would take at the present rate of erosion.

Darwin also found fossils of giant animals similar to present animals. He speculated that over vast periods of time these animals could have changed ( evolved ) into the present animals.

Lyell's theory that the present was the key to the past led Darwin to look at present day processes that could explain the changes in animals. Darwin observed that animals produced more offspring that could survive and that there seemed to be an infinite variety of possible off spring. Darwin theorized that natural selection would preserve the off spring best adapted to survive thereby changing the species. Darwin then extrapolated the observations of changes in present day species to changes in the past.

Darwin's theory of Evolution of all species having a common ancestor is based on Lyell's theory of slow uniform changes.

Theories of sudden changes have been rejected or resisted because of the acceptance of Lyell's theories, which would threaten Darwin's theory of Evolution. Examples would be Continental Drift. The Missoula Flood, Rapid formation of the Grand Canyon.

Also present day understanding of DNA and information theory challenge the idea of infinite possibilities of variation in off spring.

Lyell's theory of geological processes occurring over time influenced Darwin to formulate the concepts of gradualism and uniformitarianism.