Non-destructive, stereological estimation of plant root lengths, branchingpattern and diameter distribution

The total length of a linear structure contained in an unbounded, transpare nt reference space can be estimated from 'total vertical projections' obtai ned by rotating the linear structure about an arbitrary 'vertical' axis, an d projecting the linear structure onto a plane parallel to the axis of rota tion. The total number of intersections between cycloid arcs with their min or axis perpendicular to the axis of rotation and the projected linear stru cture then provides an unbiased estimator of the total length of the struct ure. In this study, a stereological procedure based on the method of 'total vertical projections' was used to non-destructively estimate total root le ngth, number of branches, diameter distribution and mean root diameter of c rested wheatgrass plants (Agropyron cristatum L.) growing in a transparent medium. Root lengths, diameters, and number of branching points of various orders were determined at 3-day intervals over a 4-week growing period. The length estimator was very robust and efficient with sampling coefficients of error usually less than 5% for a total of 50-150 grid intersection count s over two projection directions per plant. Biological coefficients of vari ance for total length were between 30-70%, and were largely related to vari ation in the extent of branching.