According to the online Santiago Times, quoting from the dailies El Mercurio and La Tercera, there remain only 24 surviving individuals of the flightless ostrich-like lesser rhea or ñandú in Torres del Paine National Park. Conaf, Chile's national park service, attributes an apparent decline to predation (from pumas and foxes), poaching (which seems improbable within the park), and road kill (unsurprising, as improved roads to, from, and in the park now permit higher speeds).
While I can't quarrel with statistics that must be the result of a local census, they did surprise me to some degree. I visit the park almost every year, and I often see at least that many birds en route from Puerto Natales and additional individuals within. It's anecdotal, but when I drove Argentina's Ruta 40 from El Calafate to Bajo Caracoles in December, I think I saw more rheas than ever before, even as they're apparently declining within Paine.
I'm only speculating, but a reduced rhea population within Paine could have to do with conservation measures there--outside the park, sheep ranchers often shoot foxes (which eat rhea eggs) and pumas (which can attack adult rheas), both of which are protected within. The number of foxes within the park is greater than I've ever seen and their boldness is remarkable, but again this is an anecdotal observation.
Another biogeographical issue related to the rhea has also aroused my interest. The guanaco, a relative of the domestic llama, is common in the Patagonian steppe, where it often shares habitat with the rhea, but the rhea appears to be absent from similar habitats on the island of Tierra del Fuego (where the guanaco is common). I would speculate that the guanaco was present in Patagonia well before the rhea, and that when continental drift created the Strait of Magellan, it survived on both sides of the Strait. The rhea, then, would have evolved or immigrated after the Strait came into existence, and could not cross the water.
According to the IUCN (see the link for the lesser rhea above), there is an introduced population on the northern part of Tierra del Fuego, but I've never seen it despite many trips through the area. If anyone knows anything more about this, I'd be most interested to hear.