A cladistic study of the morphology of waterfowl found that the magpie goose was an early and distinctive offshoot, diverging after screamers and before all other ducks, geese, and swans [REF].
This family is quite old, a living fossil, having apparently diverged before the Cretaceous-Paleogene extinction event - the relative Vegavis iaai lived some 68-67 million years ago.