believed that just as the struggle for survival in the natural world depended on "the survival of the fittest," human society would evolve through natural selection

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Yes ... ?

This is kind of obviously portrayed in out history and evolution through the many many years that humans have existed on this planet.

"Natural selection" is the process whereby organisms better adapted to their environment tend to survive and produce more offspring.

The theory of its action was first fully expounded by Charles Darwin and is now believed to be the main process that brings about evolution.