The determination of relative elemental growth rate profiles from segmental growth rates - A methodological evaluation

Relative elemental growth rate (REGR) profiles describe spatial patterns of growth intensity; they are indispensable for causal growth analyses. Published methods of REGR profile determination from marking experiments fall in two classes: the profile is either described by a series of segmental growth rates, or calculated as the slope of a function describing the displacement velocities of points along the organ. The latter technique is usually considered superior for theoretical reasons, but to our knowledge, no comparative methodological study of the two approaches is currently available. We formulated a model REGR profile that resembles those reported from primary roots. We established the displacement velocity profile and derived growth trajectories, which enabled us to perform hypothetical marking experiments on the model with varying spacing of marks and durations of measurement. REGR profiles were determined from these data by alternative methods, and results were compared to the original profile. We find that with our model plotting of segmental relative growth rates versus segment position provides exact REGR profile estimations, if the initial segment length is less than 10% of the length of the whole growing zone, and if less than 20% of the growing zone is displaced past its boundary during the measurement. Based on our analysis, we discuss systematic errors that occur in marking experiments.