Diversity is higher in the tropics (not just tropical rainforests) primarily because there are fewer ecological obstacles to higher biodiversity. Like the previous answer said, the climate is wet and warm, and has experienced fewer ice age type events where glaciers have covered the land. read more
If you compare for example one square meter of rain-forest to one square meter of desert, you would find on average more different birds, reptiles, mammals, insects, micro organisms, plants, etc in one square meter of rainforest that you would in one square meter of desert. read more
High mean annual temperature, primary productivity, and evapotranspiration rates are probably all involved, but we do not know whether or not the higher energy levels found in rainforests are causal factors in the generation of biodiversity. read more