Thanks for that info. I had thought a hot pepper since Jamaica is known for it’s hot spicy food. Wonder why they called it a pepper though.
Ah Ha, I think I found out why
http://greekfood.about.com/od/herbsspices/p/allspice.htm
((Allspice (Pimenta dioica) was discovered by Christopher Columbus on the island of Jamaica during his second voyage to the New World, and named by Dr. Diego Chanca. It was introduced into European and Mediterranean cuisines in the 1500s.
The “Jamaica pepper” - another name for allspice - continues to be grown primarily in Jamaica, though a few other Central American countries produce allspice in comparatively small quantities....))
Probably called it ‘pepper’ because they look like peppercorns.

There is a Jamaican hot pepper.
http://home.acceleration.net/2000/HotPeppers/peppers.htm
Scroll down
If you haven't tried grains of paradise (gotta love the acronym) do yourself a favor.