That's a foolishly simplistic view.

From simple models -- e.g. foxes and rabbits: https://niko.roorda.nu/computer-programs/fox-rabbit-theoreti... -- to more complex web models -- http://journals.plos.org/ploscompbiol/article?id=10.1371/jou....

In any such models, sometimes, with extreme population growth of any one member species, the result can be collapse so severe that that species goes totally extinct.

We're not looking at a simple redistribution. We're looking at exponential explosions, and they tend to be followed by a total collapse.