A density-based approach for the modelling of root architecture: application to Maritime pine (Pinus pinaster Ait.) root systems

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Abstract

Root morphology influences strongly plant/soil interactions. However, the complexity of root architecture is a major barrier when analysing many phenomena, e.g. anchorage, water or nutrient uptake. Therefore, we have developed a new approach for the representation and modelling of root architecture based on branching density. A general root branching density in a space of finite dimension was used and enabled us to consider various morphological properties. A root system model was then constructed which minimizes the difference between measured and simulated root systems, expressed with functions which map root density in the soil. The model was tested in 2D using data from Maritime pine Pinus pinaster Ait. structural roots as input. We showed that simulated and real root systems had similar root distributions in terms of radial distance, depth, branching angle and branching order. These results indicate that general density functions are not only a powerful basis for constructing models of architecture, but can also be used to represent such structures when considering root/soil interaction. These models are particularly useful in that they provide a local morphological characterization which is aggregated in a given unit of soil volume.

Introduction

Plant anchorage, water and nutrient uptake depend largely on root growth and architecture. A description of spatial distribution and root morphology is usually needed to represent such phenomena (Fitter et al., 1991). It is hence of great interest to develop suitable methods for the representation, analysis and modelling of root growth.

Traditionally, the study of root architecture has focused on the understanding of growth processes from a physiological point of view (Coutts, 1989; Puhe, 2003). As a consequence, previous mathematical descriptions have all been based on the functioning of apices, in terms of branching and orientation in space (Henderson et al., 1983; Diggle, 1988; Pagès et al., 1989; Fitter et al., 1991; Jourdan and Rey, 1997). It is possible to reconstruct entire root systems from these models by using simulation programs. However, the complexity of root growth through time makes it difficult to parameterize such models in relation to nutrient uptake, soil mechanical impedance or plant physiology. In addition, the collection of appropriate root data generally requires excavation of the complete root system through the use of time-consuming and difficult techniques, e.g. air spade excavation (Rizzo and Gross, 2000) or digitizing (Danjon et al., 1999). As a consequence, there has been an increasing interest in the development of new concepts for the analysis of root architecture using global properties, e.g. fractal geometry (Oppelt et al., 2001; Berntson, 2002) and fractal branching analysis (van Noordwijk et al., 2000). Geostatistical methods have also been found to give good results for descriptions of root distribution in soil (Bengough et al., 2000). Nevertheless, none of these approaches are general enough to consider any given root morphological property in an aggregated way. The use of different types of density, e.g. biomass, volume, length or branching density, can be employed to describe locally the distribution of roots in soil (Danjon et al., 1999). When using different kinds of morphological variables in the calculation of density (other than spatial coordinates), it is possible to consider various properties exhibited by real root systems. Such representations are very promising, as they can exploit fast sampling methods (Pierret et al., 2000) and would be well adapted to problems concerning root/soil interactions (Persson and Jansson, 1989; Wu et al., 1988; Dupuy et al., 2005).

In this paper, we have developed a new modelling approach using general density functions. This approach is based on the mathematical representation of the distribution of root properties in soil, e.g. number, angle or diameter. The method was tested on 50 year old Maritime pine Pinus pinaster Ait root systems data. The structural components of these root system had been measured previously. This study case aimed at demonstrating the ability of density functions to represent real root system complexity using a limited number of morphological variables.

Section snippets

Definition of the root system

In order to use density functions for root architecture modelling, we need to mathematically define root systems as well as single roots and root topology.

We aim to represent a root system S at target time T, as a set of single roots Rk connected together according to a set of relationships τ, called topology, that are inherent to the root architecture. The final root system results from a construction process through time and S(t) defines the root system at each time t of its development (t[0,

Results

The calculation time required to perform the 50 increments during the simulation of a given root system was less than 1 min using a personal computer of 1.2 GHz CPU and 500 Mb RAM. During the construction, the error between probability densities decreased exponentially, with only few occasional increase being observed (Fig. 5).

Computing of root systems using the different bootstrap samples produced a range of simplified root architectures. The discretization of variables had a coarse simplifying

Models of Maritime pine root systems

The method we developed for the modelling of root systems using density functions of root branching points is relatively simple and could be developed further. The simplified simulations carried out on Maritime pine root systems showed that the method produces realistic results and takes into account much of the root system complexity.

The root branching density functions of simulated root systems were similar to data from real root systems. The error which could be seen to increase occasionally

Acknowledgements

This work was financed by grants from the French Government (DERF Projects “Peuplier” and “Le Pin et le Vent”) and the E.U. (Eco-Slopes project, QLK5-2001-00289). L. Dupuy was funded by a CIFRE PhD bursary. We thank F. Lagane, C. Espagnet, B. Issenhuth, M. Curtet, M. M’Houdoir, P. Pougné, T. Carnus and H. Bignalet for help with the root measurements.

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