MARAJÓ ISLAND, Brazil — Legends flourish about how the first Asian water buffaloes made it to this colossal island in the Amazon River Delta.

One tale holds that they originally came from the steamy rice fields of French Indochina, but washed up here after the wreck of a ship bound for French Guiana. Another yarn contends that inmates escaping from a penal colony in French Guiana used the adroitly swimming buffaloes to help guide their makeshift barges all the way to freedom in Marajó’s mangroves.

However they arrived, the invasive species multiplied on Marajó, and now numbers about 450,000 on an island the size of Switzerland. So much of daily life here revolves around the water buffaloes that islanders haul garbage with them, race them during festivals and regularly savor fillets of buffalo steak smothered in cheese made from, yes, buffalo milk.

“The importance of the buffalo in Marajó got us thinking,” said Maj. Francisco Nóbrega, 41, an official with the 8th Battalion of the military police of Pará, the vast state in Brazil’s Amazon that encompasses Marajó. “Why not patrol on buffalo as well?”