Material derivative of Actin11 and EF1β transcript densities. Convective (A, B) and dilutive (C, D) components of the material derivative (E, F) - the net accumulation rate of Actin11 and EF1β transcripts, respectively - as a function of the distance from the root tip (Eulerian specification). The material derivative and its components are expressed in arbitrary unit mm-1 min-1. The black lines were calculated from the mean values of each parameter using equation (3). Box-and-whisker plots are the distribution of 1000 replicates (obtained by random resampling). The central mark is the median, the edges are the 25th and 75th percentiles, and the whiskers extend to 10th and the 90th percentiles.