Plants on Sanibel

Does anyone know what this is?  It's a plant, a large shrub or small tree, found all over Sanibel.  The leaf is thick, round, and 4 to 5 inches across.

The plants here are very tropical - lots of palm trees of all kinds, plants with large fronds similar to banana plants and lokelani plants, banyan trees, and so on.  It does remind me of Maui.  Lee and I went to a small shopping center today, which was beautifully landscaped.  We had ice cream, and enjoyed the scenery and the breeze.

We then took our daily walk on the beach - great exercise, restorative. 

Generally, a quiet day.