Plant and Soil 247: 123–130, 2002.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
Use of modelling to understand nutrient acquisition by plants
G. J. D. Kirk
International Rice Research Institute, MCPO Box 3127, 1271 Makati City, Philippines. Present address:
Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EA, UK
Received 11 October 2001. Accepted in revised form 20 August 2002
Key words: modelling, nutrient acquisition, rhizosphere, rice
The deﬁnition, testing and uses of explanatory models in plant nutrition are discussed and contrasted with descript-
ive, predictive models. Two examples are given. First a model of phosphorus acquisition by rice plants growing in
soils that undergo ﬂooding and drainage, in which changes in the soil induced by roots are important. The changes
are, in ﬂooded anaerobic soil, oxidation of mobile reductants and consequent production of H
ions in the soil as
well as direct release of H
ions from the roots to balance excess intake of cations over anions; and in non-ﬂooded
aerobic soil, release of organic anions from the roots. The model’s predictions are tested against experimental data.
Second a model of N acquisition by rice plants in ﬂooded anaerobic soil, in which the uptake properties of the roots
are important. The contribution to N uptake of NO
formed in the rhizosphere of rice in ﬂooded soil is compared
with that of NH
from the bulk soil using a model and absorption properties of rice roots measured in nutrient
culture. The models’ uses and limitations are discussed.
Models can be used to understand complex systems, to
study experimentally inaccessible systems, as a frame-
work for discussion, especially across disciplines, and
to identify gaps in knowledge or understanding. In this
paper, I discuss the characteristics of explanatory mod-
els aimed at such uses – as distinct from descriptive,
predictive models with a practical aim – and illustrate
their use in understanding complex problems in plant
Explanatory models are distinguished from pre-
dictive models by their different structure and content
and by the requirements for their testing (Nye, 1992).
All models contain:
1. Facts. For example, in models of nutrient trans-
fer through soil into roots, the initial concentration
of the nutrient in the soil and the soil moisture
2. Mechanistic relations, derived from ﬁrst principles
and the laws of physics and chemistry. For ex-
FAX No: +44-122-333-3953.
ample, equations for the transport of a nutrient
through soil by mass ﬂow and diffusion.
3. Empirical relations. For example, Michaelis-
Menten equations for the relation between the
inﬂux of a nutrient into a root and its concentration
in solution at the root surface, or for the dynam-
ics of microbial populations in the rhizosphere.
These are necessary because it is not possible
to describe biological systems in purely mechan-
istic terms. Preferably, any empirical relations are
derived from lower order, mechanistic models.
In explanatory models mechanistic relations dominate,
and it is important that any empirical inputs are derived
as far as possible independent of the model’s output.
Otherwise the whole exercise becomes an elaborate
form of curve ﬁtting. As such the model may be a use-
ful summary of empirical knowledge, but it cannot be
used to judge the truth of any supposed mechanisms.
Nye (1992) discusses the different requirements for
testing predictive and explanatory models and deﬁnes
separate terms to distinguish them: predictive mod-
els are merely veriﬁed by comparing their output with
available empirical data, whereas explanatory models