I'd think of two factors acting simultaneously.
One is natural selection not for odd things by human, but against such things as four-legged birds. Other one is that chicken and ducks are grown in population dozens of times greater than natural pops.
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Roberto Takata
<<My favorite story dates back to the 1980's in which a four-legged duck died while trying to lay a three-yolked egg! Its funny how these four-legged birds are domestic birds not wild birds.>>
I'd imagine natural selection would be likely to frown upon them, Ian, whereas strange primates find them somehow fascinating and tend to attempt to preserve them.