Root tapering between branching points should be included in fractal root system analysis

Abstract

The proportionality factor ( p) is a parameter used for fractal root system modelling. It describes tapering along root axes and is calculated by the ratio of total cross sectional area (CSA) before and after branching. The exact point where the area of the parent branch is measured is often not defined. By measurement of the CSA adjacent to a branching point tapering without branching is not included in factor p. In this study p was measured on six tropical tree species ( Clethra revoluta, Graffenrieda emarginata, Vismia tomentosa, Weinmannia loxensis, Clusia sp. and Styrax foveolaria). The measurement was conducted in three different ways, quantifying (i) tapering of roots by branching ( p branch), (ii) tapering without branching ( p within), and (iii) total root tapering ( p total). For five species p total was significantly higher than p branch ( p < 0.05). For three species p within contributed significantly more to p total than p branch. There was only a weak correlation between p and root segment diameter. The slope of the regression line was often higher for p within than for p branch. The results suggest that the exclusive use of p branch in fractal branching models leads to an underestimation of total root system tapering and to an overestimation of total root system biomass and root length in fractal branching models. Furthermore in some species self-similarity decreases when tapering without branching is included in the proportionality factor p. This may imply that models should allow p to change with increasing diameter.