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

The total length of a linear structure contained in an unbounded, transparent reference space can be estimated from 'total vertical projections' obtained by rotating the linear structure about an arbitrary 'vertical' axis, and projecting the linear structure onto a plane parallel to the axis of rotation. The total number of intersections between cycloid arcs with their minor axis perpendicular to the axis of rotation and the projected linear structure then provides an unbiased estimator of the total length of the structure. In this study, a stereological procedure based on the method of 'total vertical projections' was used to non-destructively estimate total root length, number of branches, diameter distribution and mean root diameter of crested 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 counts over two projection directions per plant. Biological coefficients of variance for total length were between 30-70%, and were largely related to variation in the extent of branching.