How can poor tropical soils be enriched by biological means?
There are two main problems that "wear out" soil, and people working on this deal with both of them.

A soil might be low in organic matter and nitrogen, perhaps because all the crops were sold away and the topsoil eroded off. This would also happen on a new sandbank, or where a landslide had revealed a lot of subsoil. Naturally what happens is that the site is colonized by "primary succession" plants that are good at surviving there. These plants photosynthesize carbon compounds, and have bacteriological associates that fix nitrogen out of the atmosphere. The plants and bacteria live and die and leave detritus that slowly turns into richer soil, and somewhat more complex "secondary succession" plants move in. Reclamation agriculture or reforestry helps this along, and agroforestry tries to forestall soil loss by growing trees instead of arable crops. 

But C and N are not all that plants and bacteria are made of -- just about everything else, eg P and K and Mg and Ca, comes from the geological parent material of the soil. When as anions and cations these elements are being traded and fought over by plants and microbes, they are soluble, and over time they will weather out of the soil. Over geological time they weather out of the underlying rock, which is the problem in the oldest parts of the Earth, and then it's difficult for even primary succession plants to grow. 

Hawaii is a beautiful natural laboratory for this, as the islands are made of the same lava but are of very different ages. The classic work on this is by Vitousek; here's an open access paper following up on it: Primary Succession on a Hawaiian Dryland Chronosequence. 

There's a ecology-economy group trying to fix this problem in Haiti. Haiti has exported so much, for historical reasons, that their soil is terrible and they have to import a lot of food although they were recently a very NPP-productive place. SOIL works on designing and introducing composting toilets so that the elements imported as food are incorporated into agricultural soil instead of running off (causing public health and fisheries problems as they go!). It's a very nice virtuous-circle, though it takes a lot of work to keep it going.