Interesting question! I'm hardly the expert on this area, but I might have a good starting point for you. Although tropical - and even sub-tropical regions - can have land that is good for certain kinds of crops, having both access to the kinds of materials necessary for heavy shipbuilding (strong woods, metals, easily extractable salts for preserving foods).
But that alone shouldn't, and didn't stop tropical powers from becoming colonial powers; indeed, south China (included here as a 'country' not due to autonomy, though at times that was present, but simply to point out the tropical nature thereof) and the Malacca sultanate were both very successful 'colonial' powers in their region, changing the demographics of many areas to be more culturally and economically tied to their nations; a factor which would not truly change until new powers entered the region.
I think in addition to the materials for shipbuilding, food preservation et all, knowledge of long-distance sailing and mapping, the key requirement to colonial success was a government at least centralized enough to be able to intercede in the mercantile and colonial voyages their citizens partake in.
I do not think that most nations situated partly or wholly in the tropics lacked central government 'because tropics', but in a case of circumstances that were unique or semi-unique to many such powers, lacked one or more of the above traits. I would be fascinated to hear a more in-depth answer from someone who knows more in the area!
http://en.wikipedia.org/wiki/Environmental_determinism
A valid general theory, with several exceptions of course, and only explains the last 500 or so years. There were great empires that partially arose in the tropics, like several in India.
Colonial Empires as we now them are an evolution of thousands of years of amassing civilization. Even the Mongol Empire can't rival the amount of influence on a local level that even a modest stable nation can exert. Europe was emerging at the right time and were able to industrialize the acquisition of colonies.
Also no one factor decides which countries thrive and which countries wither. Europe is covered in rivers, that provide excellent transportation, with requiring little investment to navigate. Indonesia today should be similarly poised but on the other hand seafaring is expensive and those islands prevent things like a transcontinental railroad. Papua New Guinea has perhaps the highest biodiversity in the world but the many mountains and valleys, that contribute to the biodiversity and fertility, prevent communication and development.
For a long time the silk road was open to Europe to conduct trade with the East. Once Constantinople falls trade with the East is cut but the demand for goods continues. A single ship of Eastern spices could make a European merchant very wealthy and they know it. So Europeans, at first the Portuguese, begin to explore and develop ways to travel and conduct trade around Africa all the way to the East bypassing the silk road. Leading the way is a guy named Henry the Navigator who will promote and set up academies to learn the best way to travel and navigate the ocean. This dedication to innovation and education will spur a maritime revolution.
The development of the caravel gave Europeans reliable Ocean going vessels. This coincides with the brutal war known as the Reconquista. The Spanish battle to take back the Iberian peninsula. Once the Reconquista ended the Spanish were willing to carry on their fight against non believers in other parts of the world and the development of the Caravel would allow them to travel long distances. First the Iberian peninsula next the Canary islands were brutally conquered and then Colombus gives the Spanish the idea that wealth could be found west across the Atlantic. Once the Spanish set up a hugely profitable empire in the new world other European countries set out to follow their blueprint and they openly stated so.
Three things coincide to make Europe a colonizing threat to the world. The technology of long distant sailing ships, realizing investing in overseas adventures are profitable, and the desire to risk ocean travel emerged at the same time in Europe. Once the Portuguese and Spanish start making tons of money other European countries had to follow suit or be eclipsed by their neighbors.
Edit: Added sources if you are interested in the topic of colonization.
Crosby, Alfred W. “An Ecohistory of the Canary Islands” Environmental Review Autumn. 1984; 214-235.
Gibson, Charles. “Conquest, Capitulation, and Indian Treaties” The American Historical Review. Feb. 1979; 1-15.
Glas, George., et al., “Some Account of the Island of Teneriffe and It’s Inhabitants, at the Time of the Spanish Conquest” Transactions of the Ethnological Society of London. 1869; 107-114.
Katz, Stanley N, Murrin, John M, and Greenberg, Douglas. Colonial America, Essays in Politics and Social Development, Fifth Edition. New York: McGraw-Hill, 2001.
Kupperman, Karen Ordahl. Major Problems in American Colonial History, Second Edition. Boston: Houghton Mifflin Company, 2000.
Lenman, Bruce. England’s Colonial Wars 1550-1688. Singapore: Pearson Education Limited, 2001.
Merediz, Eyda M. Refracted Images, The Canary Islands Through a New World Lens. Tempe, Arizona Board of Regents, 3004.
Palmer, William. The Problem of Ireland in Tudor Foreign Policy 1485-1603. Woodbridge: The Boydell Press, 1994.
Taylor, Alan. American Colonies, The Settling of North America. New York: Penguin Books, 2002.
Kirkpatrick