Predicting Ecosystem Net Primary Productivity by Percolation Theory and Optimality Principle

Abstract

The basic partitioning of precipitation P into evapotranspiration ET and run-off Q is known as the “central problem of hydrology.” ET depends primarily on precipitation, P, and potential evapotranspiration, PET, which are connected by the biological process of photosynthesis. Photosynthesis is the fundamental step underlying the productivity of plant ecosystems. An important measure of plant productivity is the creation of plant biomass, which is quantified by net primary productivity, NPP. NPP is most parsimoniously related simply to the evapotranspiration, ET. The dependence of NPP (ET) appears to be in the form of a power law with an upper limit derived from the maximum plant-available solar energy accessible on Earth. However, theoretical, rather than phenomenological, treatments relating ET and its complementary variable, run-off (P − ET ≡ Q) to climate variables that measure the available energy (PET) and available water (P) (known as the water balance) are, at best, scarce, and their continued application to predicting NPP (P, PET) even more so. One theory developed recently to predict the water balance is based on determining how to divide P into Q and ET in such a way as to maximize NPP. Substitution of the resulting optimized ET (P, PET) into the function NPP (ET) then yields NPP (P, PET). We investigate the possibility that this new theoretical framework, which yields ET(P, PET) based on ecological optimality and percolation theory, can predict the dependence of NPP (P, PET). If the prediction of NPP (P, PET) is verified, this result may lead to significant progress in other areas, including the problem of the chief causes of geographical variability of species richness.