Use Darwinian to describe something that relates to the scientist Charles Darwin or his "survival of the fittest" theory of evolution.
A naturalist who studies evolution and natural selection — scientific theories that were first developed in the 1800's by Charles Darwin — might call herself a Darwinian. The work and writing of Darwin himself are also called Darwinian, particularly evolution. Likewise, anything that resembles the process of natural selection or "survival of the fittest" itself, like a competition in which only the strongest athletes make it to the finish line, is commonly described as Darwinian.