The idea that evolution proceeds slowly and steadily is called gradualism. In evolutionary biology, gradualism describes profound change as the cumulative result of many small changes over long periods rather than sudden, large transformations.
The concept has roots in geology. James Hutton argued in 1795 that Earth's features were shaped by slow processes still observable in the present. Charles Lyell later developed related uniformitarian ideas, which strongly influenced Charles Darwin's thinking about evolution. Darwin proposed that small heritable variations, preserved by natural selection, could accumulate across generations.
Gradualism is often contrasted with catastrophism, which emphasizes sudden large-scale changes, and with punctuated equilibrium. Punctuated equilibrium proposes that species may remain stable for long periods, with relatively rapid evolutionary change concentrated around speciation events. The distinction concerns evolutionary tempo, not whether evolution occurs.
A useful refinement is phyletic gradualism: the more specific model that an entire lineage changes steadily into a descendant species. Modern evolutionary biology recognizes that rates vary, so “gradualism” should not be taken to mean that every trait changes at a perfectly constant speed.