The fall 2015 cover of Modern Farmer features a svelte model with the hair of Lyle Lovett and the eyes of a seal pup. Her neck is long, her lashes are full, and skin looks like a fine sweater. She is an alpaca, and according to the cover, her time has come.

Alas, Modern Farmer is a little late to the game on this one. After a surge in alpaca popularity gave breeders hope of cashing in and retiring to the islands, the fuzzy guys are on their way out … and they’re taking some humans down with them. Harvest Public Media’s Luke Runyon reports:

Ever since imports of the animals began, alpacas have proliferated across the country, boosted by aggressive breeding programs. Back in the 1980s you’d really only find them in zoos. Now there’s close to 150,000 in the U.S.

Rarely slaughtered for meat in the U.S., the alpaca’s only real marketable product is wool. And the alpaca fiber market never took off the way many breeders were hoping it would. There’s little infrastructure devoted to large-scale processing of alpaca fiber. Today it’s mostly used in high-end, niche clothing, failing to significant inroads into the mainstream garment industry.