The broadcaster, 87, said that he was not optimistic about the future and "things are going to get worse".
He said he did not believe humans will become extinct but told the Radio Times: "I think that we've stopped evolving. Because if natural selection, as proposed by Darwin, is the main mechanism of evolution - there may be other things, but it does look as though that's the case - then we've stopped natural selection. We stopped natural selection as soon as we started being able to rear 95-99% of our babies that are born. We are the only species to have put a halt to natural selection, of its own free will, as it were."
Sir David said human beings were still evolving in the cultural sphere.
"Stopping natural selection is not as important, or as depressing, as it might sound, because our evolutionary process is now cultural," he said.
"Humans have a great cultural inheritance as well as a physical, genetic inheritance. We can inherit a knowledge of computers or television, electronics, aeroplanes and so on.
"Each generation has got all these books that tell them these things, so our cultural evolution is proceeding with extraordinary swiftness."
The broadcaster said of the future: "We're very clever and we will find ways of preserving ourselves. But whether our lives will be as rich as they are now is another question."