Allometric scaling laws for water uptake by plant roots

Abstract

This paper develops scaling laws for plant roots of any arbitrary volume and branching configuration that maximize water uptake. Water uptake can occur along any part of the root network, and thus there is no branch-to-branch fluid conservation. Maximizing water uptake, therefore, involves balancing two flows that are inversely related: axial and radial conductivity. The scaling laws are tested against the root data of 1759 plants from 77 herbaceous species, and compared with those from the WBE model. I further discuss whether the scaling laws are invariant to soil water distribution. A summary of some of the results follows. (1) The optimal radius for a single root (no branches) scales with volume as r approximately volume(2/(8+a))(0<a< or =1). (2) The basic allometric scaling for root radius branches (r(i+1)=beta*r(i)) is of the form beta=f(N)((2*epsilon(N))/(8+a)), where f(N)=A(N)/(n(b)*(1+A(N))), n(b) is the number of branches, and A(N) and epsilon(N) are functions of the number of root diameter classes (not constants as in the WBE model). (3) For large N, beta converges to the beta from the WBE model. For small N, the beta's for the two models diverge, but are highly correlated. (4) The fractal assumption of volume filling of the WBE model are also met in the root model even though they are not explicitly incorporated into it. (5) The WBE model for rigid tubes is an asymptotic solution for large root systems (large N and biomass). (6) The optimal scaling solutions for the root network appears to be independent of soil water distribution or water demand. The data set used for testing is included in the electronic supplementary archive of the journal.