The lavish villas of Nordelta have for years hosted bucolic getaways for Argentina’s wealthy, protected in an enclave where industry titans and soccer stars seek escape from the torments of city life. Yet even an exclusive gated community can’t keep out the world’s biggest rodent. “The problem is that their population is out of control, and people are too scared to do anything. No one wants to look like they’re opposed to nature.” Mr. Iglesias’s lakeside garden gets a daily serving of jumbo scat ... The big rodents, which typically live in family units of as many as 40 animals,...