Some hundreds of years ago, all humanity was removed from the Americas. In fact, most humans are gone from the world altogether. In the intervening time, nature has overrun the formerly human dominated landscapes of the former United States.
The area referred to in the title is the lands formerly around New Orleans. Much of it is underwater after a millenium of global warming and sea level rise; but what remains is cypress and tupelo swamp, live oak thickets, and grassy fire-dominated pine savanna. It is hot and humid in the summer, wet all year round, and rarely freezes in the winter.
In short, this is the perfect environment for the capybara. 1000 years was enough time for many Central American animals to migrate up to the swamps and savanna of former Louisiana. Jaguars are here, along with peccaries and brocket deer. In addition, many escaped domestic animals--horses, cattle, chickens--roam the savannah. But the problem with the capybara is that it is starting pretty far away in the Orinoco Delta of Venezuela.
There are two ways the capybara could get from Venezuela to New Orleans. It could walk along the Mexican coast; or it could island hop, spreading across the many capybara-friendly islands of the Caribbean. Can capybaras spread to Louisiana from Venezuela and populate it in less than 1000 years?