Gradualism

Gradualism is a process of change by gradual, slow stages. In politics, it is the opposite of revolutions and rapid change. "Gradualism is... sometimes associated with social democracy".
In geology it is in tune with uniformitarianism, and against catastrophism. In biology it is in tune with Darwinian ideas of slowly changing species as opposed to big, rapid changes
Politics and society.
Gradualism is one of the defining features of political liberalism and reformism. It is against abrupt strokes such as revolutions or uprisings. Instead, change ought to be brought about in small, discrete steps.
Martin Luther King, Jr. was opposed to the idea of gradualism as a method of eliminating segregation. The government wanted to try to integrate African-Americans and European-Americans slowly into the same society, but many believed it was a way for the government to put off actually doing anything about racial segregation:
This is no time to engage in the luxury of cooling off or to take the tranquilizing drug of gradualism. Now is the time to make real the promises of democracy.— Martin Luther King Jr.'s "I Have a Dream" speech, delivered August 28, 1963 at the Lincoln Memorial in Washington DC
Charles Lindblom was an influential professor and author who believed in muddling through ("incrementalism") as the right way to go. He pointed out the connexions between the political system, the market-place and democratic freedom.
Geology and biology.
In the natural sciences, gradualism is a theory that profound change is the product of slow but continuous processes. It is often contrasted with catastrophism. Gradualism was proposed in 1795 by James Hutton to explain geology, and was later was the basis for Charles Lyell's "Principles of Geology". William Whewell called the idea 'uniformitarianism'. It formed the basis of early evolutionary theory.
Charles Darwin was influenced by Lyell's "Principles of Geology". Everything we see from the past is explained by processes we can see going on today. The present is key to the past. So Darwin thought evolutionary must occur gradually, not in jumps ('saltations'), since we do not see big changes going on today. Extreme and rapid changes in an organism would be most likely to be fatal. It is almost universally agreed that complex organs such as the eye must have evolved by many small steps rather than by one or two mutations.
"Phyletic gradualism" is a term coined by Stephen Jay Gould and Niles Eldredge to contrast with their model of punctuated equilibrium. They proposed that most evolution is marked by long periods of evolutionary stability or stasis, punctuated by rare instances of branching evolution. Their idea is less accepted today.