Dynamic Scaling in Plant Growth Figure 3. The normalized intra-plant leaf size distribution. Each symbol represents the relationship between the normalized position (relative number of leaves counted from the bottom to top of the stem, where 0 = bottom, 0.5 = middle and 1.0 = top of the stem) and the normalized leaf area (area of an individual leaf divided by the averaged leaf area for the plant) of each leaf (n = 208). Each series shows an entire set of leaves for each plant (n = 29). The bold curve represents the fitted curve estimated by using the gam function in the mgcv package of R [29] (r2 = 0.792). doi:10.1371/journal.pone.0045317.g003 PLOS ONE | www.plosone.org 3 September 2012 | Volume 7 | Issue 9 | e45317 Figure 4. Log-log relationship between whole-plant leaf area and total leaf number. Each open circle represents one individual plant. The solid line shows the standardized major axis regression (r2 = 0.93, n = 29). doi:10.1371/journal.pone.0045317.g004 a single-leaf plant would have r = 1.0 (the lowest position). Instead, by Eq. 1, the single leaf on a single-leaf plant has r = 0.5 (the middle position). The rationale for this definition lies in the fact that a single leaf occupied each position from the top (r = 0) to the bottom (r = 1) on the plant, such that the mean value 0.5 should be applied. To examine the relationship between the normalized position of each leaf area and the normalized leaf area, we utilized an additive model [29]. The additive model was assessed with the mgcv package [29] using R version 2.14.2 [30]. Results Whole-plant leaf area varied by .200-fold (27.6–5690 cm2). In support of the dynamic scaling law, the relationship between normalized leaf position and normalized leaf area on each plant was similar among the different-sized plants (Fig. 3). On the basis of the additive model, the effect of normalized leaf position was highly significant, and normalized leaf area was well explained (r2 = 0.792, p,0.001) (Fig. 3). In support of the power law, whole- plant leaf area (F) was a power function of total leaf number (t) 2 (Fig. 4). The SMA regression line (Log10F (cm ) = b Log10t + a) had a slope and intercept of b = 1.81 (95% CI: 1.62–2.01) and a = 1.62 (1.46–1.78), respectively. Fitting the OLS regression line gave a similar result: b = 1.74 (1.55–1.93) and a = 1.67 (1.51–1.83), respectively (r2 = 0.93, p,0.001). The slope (b) was larger than unity, indicating that mean individual leaf area (F/t) increased with t according to the power function: Log10 (F/t) = (b–1) Log10 (t) + a. Hence, both the size of the entire pattern (i.e., whole-plant