Biomaterial Database

Allometric scaling laws for water uptake by plant roots. 2008

Mario Biondini

School of Natural Resource Sciences, North Dakota State University, Fargo, ND 58105, USA. Mario.Biondini@ndsu.edu

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.

UI	MeSH Term	Description	Entries
D008954	Models, Biological	Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.	Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D001692	Biological Transport	The movement of materials (including biochemical substances and drugs) through a biological system at the cellular level. The transport can be across cell membranes and epithelial layers. It also can occur within intracellular compartments and extracellular compartments.	Transport, Biological,Biologic Transport,Transport, Biologic
D013045	Species Specificity	The restriction of a characteristic behavior, anatomical structure or physical system, such as immune response; metabolic response, or gene or gene variant to the members of one species. It refers to that property which differentiates one species from another but it is also used for phylogenetic levels higher or lower than the species.	Species Specificities,Specificities, Species,Specificity, Species
D014867	Water	A clear, odorless, tasteless liquid that is essential for most animal and plant life and is an excellent solvent for many substances. The chemical formula is hydrogen oxide (H2O). (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)	Hydrogen Oxide
D015233	Models, Statistical	Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.	Probabilistic Models,Statistical Models,Two-Parameter Models,Model, Statistical,Models, Binomial,Models, Polynomial,Statistical Model,Binomial Model,Binomial Models,Model, Binomial,Model, Polynomial,Model, Probabilistic,Model, Two-Parameter,Models, Probabilistic,Models, Two-Parameter,Polynomial Model,Polynomial Models,Probabilistic Model,Two Parameter Models,Two-Parameter Model
D017709	Fractals	Patterns (real or mathematical) which look similar at different scales, for example the network of airways in the lung which shows similar branching patterns at progressively higher magnifications. Natural fractals are self-similar across a finite range of scales while mathematical fractals are the same across an infinite range. Many natural, including biological, structures are fractal (or fractal-like). Fractals are related to "chaos" (see NONLINEAR DYNAMICS) in that chaotic processes can produce fractal structures in nature, and appropriate representations of chaotic processes usually reveal self-similarity over time.	Fractal
D018517	Plant Roots	The usually underground portions of a plant that serve as support, store food, and through which water and mineral nutrients enter the plant. (From American Heritage Dictionary, 1982; Concise Dictionary of Biology, 1990)	Plant Bulbs,Plant Root,Bulb, Plant,Bulbs, Plant,Plant Bulb,Root, Plant,Roots, Plant