My question is related to one of the oldest question in ecology: "What determines global patterns of species richness?". However, I want to focus on one particular part of this question, which has been bothering me for a long time.
Background information
One of the most widely recognized ecological patters on Earth, which is found at most scales and in most biological taxa, is the latitudinal diversity gradient (LDG) -- there are more species in the tropics than in the temperate regions, and the further away you move from the tropics, the fewer species you encounter. Furthermore, such pattern exists not only along the latitudinal gradient, but species richness also covaries with altitude in terrestrial environments and depth in marine environments, showing the same diversity gradient!
It seems to be fair to suggest that energy should somehow underline all these diversity gradients and create some sort of universal mechanism that would ultimately affect all species richness patterns on Earth. Unfortunately, there is no consensus on questions as grand as this one, but I'm looking for hypothesis that would specifically attempt to explain all three gradients together.
Question
Is there a hypothesis that attempts to explain patterns of species richness along all three energy-related environmental gradients together: latitude, altitude and depth? If there is, what it's weakness? If there's no such hypothesis, do we have reasons to believe that such a broad link across the three gradients can exist?
Please note how I'm trying to emphasize that I don't want you to list all the hypotheses that describe LDG only, but rather the three gradients together.