Dynamic Scaling in Plant Growth Figure 1. Ontogenetic growth trajectory of C. cordatum rosettes. The photographs show representative C. cordatum plants on 10 May 2010. Red scale bars superimposed on each photograph indicate a distance of 5 cm on each leaf. Leaf punch holes and ink markings used for other experiments appear on some of the leaves (photographs by K. Koyama, taken on 10 May 2010). doi:10.1371/journal.pone.0045317.g001 Prefectural Forest Experiment Station (36u259N, 136u389E; elevation: 220 m), Japan. Mean annual temperature and pre- cipitation at the study site are 13.0uC and 2438 mm, respectively (2003–2007). A more detailed site description has been given elsewhere [25]. Leaf measurements. A total of 208 leaves on 29 rosettes (1– 18 leaves per plant) of C. cordatum were sampled on 10 May 2010 (Fig. 1). The smallest plant with only a single leaf (leaf length = 8.8 cm, leaf area = 27.6 cm2) grew from a bulblet attached to another rosette (Fig. 1). The rosette of the largest plant was .0.8 m in diameter. The five largest rosettes (12–18 leaves) were bolting (i.e., flowering later in the summer); they did not regenerate the following year. Hence, at this study site, we investigated the entire ontogenetic size range of C. cordatum. Sampling included fully and partially expanded leaves. Un- developed leaves, in which laminae were not separate from the stem, were not counted. For smaller, non-flowering rosettes, all Figure 2. Similarity among individual leaves. Each open circle indicates one harvested leaf (n = 51). The solid line shows the ordinary least-squares regression, which was forced through the origin: Leaf area (cm2) = 0.717 (length 6 width) (r2 = 0.997, n = 51, p,0.01). doi:10.1371/journal.pone.0045317.g002 leaves had appeared prior to the sampling period. For larger, bolting rosettes, most leaves had appeared prior to the study period, although some additional leaves appeared after sampling as the flowering stem elongated. We measured leaf length (the length of the central vein on each lamina, excluding the petiole) and width (maximum lamina width perpendicular to the central vein) for each leaf. The absolute leaf position was defined by counting the order of appearance from the base of the rosette. Eight of the sampled plants were harvested, and 21 were left at the site for future study. Leaf area was defined as laminar area of one side of each leaf. Laminar area of 51 leaves from harvested plants was measured using a leaf area meter (Li-1300; LI-COR, Lincoln, USA). Individual leaf area is proportional to the product of leaf lamina length and width (Fig. 2). This indicates that individual leaf forms are similar, although the ratio of length to width may vary within an individual plant and population, as has been reported for other species [26,27]. We fitted an ordinary least squares (OLS) regression of width 6 length of leaf laminae, using SMATR [28]: Leaf area (cm2) = 0.717 (width 6 length) (r2 = 0.997, p,0.01, n = 51) (Fig. 2). Using this relationship, we calculated leaf area for plants that were not harvested. When the regression line was not forced through the origin, the slope and r2 values changed little (slope = 0.735, r2 = 0.989, respectively); the 95% confidence intervals of the intercept included the origin, thus the intercept of the regression line was set to zero. Data analysis. Whole-plant leaf area (F) was calculated as the sum of all individual leaf areas on each plant. To describe the log-log relationship between whole-plant leaf area and total leaf number among different-sized plants, both standardized major axis (SMA) and ordinary least squares (OLS) regression lines were fitted by SMATR [28]. For each leaf, we defined a normalized leaf area and a normalized position. Normalized leaf area was defined as the area of a leaf divided by the mean individual leaf area of the plant to which the leaf was attached. This value was used to describe the intra-plant leaf size distribution on a normalized scale. The normalized position (r) of each leaf was defined as r~ðp1=2Þ=t 1 ð Þ where p is the absolute position of each leaf on each plant, and t is the total leaf number of the plant to which the leaf was attached. The normalized position indicates the position of each leaf on a given plant (i.e. 0 = the top, 0.5 = the middle, and 1.0 = the bottom of the plant). If we were to define the normalized position as r = p/t, it would produce a bias in that the single leaf on PLOS ONE | www.plosone.org 2 September 2012 | Volume 7 | Issue 9 | e45317