Species richness and the analytic geometry of latitudinal and altitudinal gradients

Extensive empirical work has shown that species richness decreases roughly exponentially or quadratically with latitude. What appears to be a latitudinal gradient in fact may simply be a negative correlation of latitude with area at that latitude, due to convergence of lines of meridian at the poles. There is simply less area at high latitudes, which means fewer niches and fewer opportunities for speciation, hence diminished biodiversity at high latitudes. Similarly, analytic geometry of a cone shows that species number should decrease linearly with altitude on a conical mountain. Here, I provide an explicit mathematical model of the area hypothesis of species richness along latitude and altitude gradients. I re-analyze a previously published latitudinal gradient dataset and show that species number is a linear function of the predicted area and that species number is more fully explained by predicted area than by a quadratic function of latitude. However, analytic geometry is not needed if precise measures of area are known.