The National Geographic program was designed to sensationalize, scare, and disgust the viewers. Their characterization of nutria was not realistic. Nutria are vegetarians. They eat the same food as rabbits and cows. Nutria do not eat garbage, and avoid humans. They do not taste like chicken. They taste more like rabbit. Anyone that is not disgusted by the appearance of catfish should be able to eat nutria without blinking.
If nutria should infest my pond, I'll be a little upset about the burrows, but I'll eat well.
