Critical path analysis (CPA) is suited to calculating the hydraulic conductivity, K, of heterogeneous porous media by quantifying the paths of least resistance. Whenever CPA can be used to calculate K, advective transport scaling relationships from percolation theory should describe solute transport. Two solute transport relationships were applied to predict soil development and edaphic constraints on natural vegetation growth. These results used known exponents from percolation theory and known subsurface flow velocities. The typical flow velocity itself constrains the optimal growth rates of cultivars. The percolation scaling relationship constraining vegetation growth was shown to be in accord with data across time scales from hours to 100,000 yr, including more than a dozen studies (and two models) of tree growth. The scaling function for soil development explains time scales for the formation of soils from years to hundreds of millions of years. Data on soil development came from 23 different studies. The key unification is the common origin of the time and space coordinates for all three relationships in the transport time through a single pore of roughly micrometer size at a typical subsurface pore-scale flow velocity. The distinction in evolving time scales is primarily a result of the hierarchical nature of vascular plant root systems, which speed up nutrient access relative to physical transport rates in the soil. The results help explain reductions in forest productivity with age, diminishing soil production with time, and the temporal distinction between chemical and biological processes in soils and their relevance to the global C cycle.

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