Birth, death, and relocation
Looking at tropical diversity in terms of speciation, extinction, and migration is a bit like taking a long term view of how many people live in a particular region by keeping track of the number of births, the number of deaths, and the number of people moving in and out of the area. Regions where the birth rate is high (and the death rate is low) or where lots of people move into the area are likely to be crowded. Regions where the death rate is high (and the birth rate is low) or where lots of people move out of the area are likely to be relatively empty. The balance between these different processes is what determines the number of people living in any particular region.
Similarly, in the tropics (or any other region), diversity is ultimately the result of new species being born (speciation), species dying (extinction), and species that move in and out of the region (migration).
Check your understanding of these processes with a quick question ...