Like the Moses family, nutria came to Louisiana from California. It was the 1930's and California was just a waystop from nutria's actual country of origin, Venezuela.
Even though they're sort of cute, Louisiana declared nutria personae non grata because their population exploded to the point they were causing extensive damage to the ecosystem by eating all the marsh vegetation.
The state put a bounty of $5 on every nutria tail and the population's gone down. But they still seem plenty plentiful to us.