Wiktionary
outcompete
vb. To be more successful than a competitor; especially to thrive in the presence of an organism that is competing for resources
Usage examples of "outcompete".
No signs of slaughter have ever been found, so most authorities believe the newer hominids simply outcompeted the older ones, though other factors may also have contributed.
That was why most of the big animals had quickly disappeared, outcompeted by their smaller cousins.