looks like alternethera to me
Boca Joe

Graptophyllum. Easy to grow as long as its sunny and hot. Gets stretched out as a house plant..loves sun.

Stan - I grow several Graphtophyllum species; this is not one of them.

BocaJoe - I searched for Alternethea and found dozens in the genus. Any idea of species?

Hey Ricky
This is such a cool looking plant and I know I've seen it -- (possibly growing in your yard?) so I looked it up at glasshouseworks.com and they have several that look alot like your photo. Did you already try their site? Might give you a name you can apply....

Susie

Susie - I went to their website just now and looked at each one. If this plant is an Alternanthea, it's not one of the varieties they offer. I'll be going back to Jamaica right after Xmas and I'll see if I can find one with flowers or seeds.

Looks like Telanthera dentata'Rubiginosa' or "Wavehill Ruby" but it lacks the fuchsia variegation like the one in the pic. In the winter it produces small but showy white "straw flowers" at the end of each stem. Native to the West Indies--hence Jamaica? Recently it has been reclassified back into Alternanthera. This variegated one is much prettier than the T.d.Rubiginosa most often seen in Florida--maybe worth bringing back!
Joel

FYI: Happened to walk thru a Target garden center this week a say this very plant--with even better variegation! Home Depot is selling a similar looking species (A.herbstii) with nice variegation as well.

Thanks Joel.

By the way, are you associated with the large wholesale nursery on West Atlantic? I did business with them for years when I was in the Landscape Design trade.

yes

Joel - Then I'd like to invite you to visit our garden in Boca Raton. We've a plant swap coming up on November 4th. Check out the Florida Gardening forum for details. Here's a preview.

Beautiful garden! I'll put the "swap" on the calendar in hopes I can make it.
PS: Where did you stay in Negril? I was there in May and stayed at The Rock House.

We've been to Couples Sweptaway twice in the past year and were scheduled to go back again after Christmas to stay for New Year's but had to cancel. We're going to Couples San Souci for Memorial Day weekend, though, on the Ocho Rios side of the island.