Relations between root length densities and root intersections with horizontal and vertical planes using root growth modelling in 3-dimensions

The root growth simulation model of Diggle (ROOTMAP; 1988) was modified to allow the numerical output of data on root intersections with horizontal and vertical planes. ROOTMAP was used to generate two three-dimensional model structures of fibrous root systems. The lateral roots were oriented randomly (geotropism index=0) but the main axes were positively gravitropic (geotropism index=0.6). The mean density of root intersections (n, cm-2) with the sides of a series of 5×5×5 cm cubic volumes was related approximately linearly to the root length density (Lt cm-2) within each volume by the equation Lt=2.3n (correlation coefficient, r=0.981). This compared with the relation of Lt=2n predicted theoretically for randomly oriented lines (Melhuish and Lang, 1968). Root length density was related to the intersection density by the equation Lt=2.43nv (r=0.940) for the vertical faces and Lt=1.88nh (r=0.984) for the horizontal faces. Lt/nv was greater than Lt/nh because of the preferential vertical orientation of the main root axes.The Melhuish and Lang (1968) equation does not generally give accurate prediction of root length density from field experiment data. Under field conditions, values have been reported in the ranges of 1.4 to 16 for Lt/nh, and 3.8 to 9 for Lt/nv. The most likely explanation for this difference is that only a small proportion (e.g. about 20–30%) of the actual number of roots are counted using the core-break and root mapping (including the trench wall) methods, due to the practical experimental difficulties of identifying individual fine roots under field conditions. Detailed experimental studies are needed to identify what portion of the root system is recorded using these field techniques (e.g. whether the main root axes are counted while the fine lateral roots remain undetected).Three-dimensional models of root growth provide a new method of studying the relations between Lt, nv and nh for root systems generated stochastically according to known geometrical rules. Using these models it will be possible to determine the effects of the degree of gravitropism and of root branching on the value and on the variability of Lt/nh and Lt/nv. The effectiveness of the statistical corrections that have been developed to correct for non-random root orientation can also be evaluated, as can the effects of sample position.

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