Evolution can occur at different rates, however, for evolution to occur, there must be?

Only the successful competitors will reproduce, mortality is very high. Four (4) conditions for natural selection. Four conditions are needed for natural selection to occur: reproduction, heredity, variation in fitness or organisms, variation in individual characters among members of the population.
A third basic principle of evolution is competition. Replicating molecules compete with one another for available resources such as chemical precursors, and the competition allows the process of evolution by natural selection to occur. Variation will produce differing populations of molecules.

This movement is also referred to as  glacial plucking