Communism is based on the Communist Manifesto, which makes no mention of biology or evolution whatsoever- it's essentially a treatise on economics.
Nazism is based on primitive notions of race and genetic superiority which arose from the ramblings of a quasi-educated frustrated Austrian artist.
If you want to make a statement like that, please back it up. It would be akin to me saying "Christian fundamentalism is based on Nazism"- a statement not based on any facts.
Almost all of Marx's work was published before Darwin published anything about evolution. So Marx was a full-blown commie totally independent of evolution. His final work, Das Capital, was published later, but made no mention of Darwin or his work. He tried to snatch a bit of Darwin's fame by attempting to dedicate the book to Darwin, but Darwin refused the "honor," saying that he didn't understand Marx's work. That brief exchange was the only contact the two men ever had.
Hitler ... ah, where was the biology training in his background? He wanted to be an artist, or an architect. He knew nothing of Darwin's work. In the field of economics, the closest thing to "survival of the fittest" is the free enterprise system, which Hitler opposed. Stalin too (and Stalin had studied for the priesthood. No biology exposure there).
There are over 9,000 biology teachers in the US. All of them exposed to the allegedly destructive teachings of Darwin. How many of them are mass murderers? Tyrants? Nazis? Probably not one.
Finally, communism has been around long before Darwin. Read William Bradford's diary, "Of Plymouth Plantation." The Mayflower pilgrims initially established a commune system, based on their reading of scripture. Had to give it up or they would have all starved to death.