This is a reference to Charles Darwin's theory of evolution, which he first put forward in in 1859 book On the Origin of Species.
Tolstoy didn't accept the theory of evolution. Shortly before his death he wrote to two of his children that "the views you have acquired about Darwinism, evolution, and the struggle for existence won’t explain to you the meaning of your life and won’t give you guidance in your actions, and a life without an explanation of its meaning and importance, and without the unfailing guidance that stems from it is a pitiful existence."
As this shows, his refusal to accept the theory stemmed less from faults he perceived in the theory itself than from its implications for his religious beliefs. He felt that Darwinism threatened to undermine morality.