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AOBPreview published online on May 14, 2004
Annals of Botany, doi:10.1093/aob/mch116
© 2004 by Annals of Botany Company
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Submitted on December 22, 2003
Revised on February 9, 2004
Accepted on March 13, 2004

Modelling Applicability of Fractal Analysis to Efficiency of Soil Exploration by Roots

THOMAS C. WALK1, ERIK VAN2, and JONATHAN P. LYNCH1*

Affiliation of the authors: 1 Department of Horticulture, Pennsylvania State University, University Park, PA 16802, USA; 2 Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA

* To whom correspondence should be addressed. E-mail: jpl4{at}psu.edu.

• Background and Aims Fractal analysis allows calculation of fractal dimension, fractal abundance and lacunarity. Fractal analysis of plant roots has revealed correlations of fractal dimension with age, topology or genotypic variation, while fractal abundance has been associated with root length. Lacunarity is associated with heterogeneity of distribution, and has yet to be utilized in analysis of roots. In this study, fractal analysis was applied to the study of root architecture and acquisition of diffusion-limited nutrients. The hypothesis that soil depletion and root competition are more closely correlated with a combination of fractal parameters than by any one alone was tested.

• Model The geometric simulation model SimRoot was used to dynamically model roots of various architectures growing for up to 16 d in three soil types with contrasting nutrient mobility. Fractal parameters were calculated for whole roots, projections of roots and vertical slices of roots taken at 0, 2·5 and 5 cm from the root origin. Nutrient depletion volumes, competition volumes, and relative competition were regressed against fractal parameters and root length.

• Key Results Root length was correlated with depletion volume, competition volume and relative competition at all times. In analysis of three-dimensional, projected roots and 0 cm slices, log(fractal abundance) was highly correlated with log(depletion volume) when times were pooled. Other than this, multiple regression yielded better correlations than regression with single fractal parameters. Correlations decreased with age of roots and distance of vertical slices from the root origin. Field data were also examined to see if fractal dimension, fractal abundance and lacunarity can be used to distinguish common bean genotypes in field situations. There were significant differences in fractal dimension and fractal abundance, but not in lacunarity.

• Conclusions These results suggest that applying fractal analysis to research of soil exploration by root systems should include fractal abundance, and possibly lacunarity, along with fractal dimension.
Key words: Fractal dimension, fractal abundance, lacunarity, phosphorus, depletion, competition, Phaseolus vulgaris, SimRoot, simulation modelling.


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