Dynamic Scaling in the Growth of a Non-Branching Plant, Cardiocrinum cordatum Kohei Koyama1,2*, Yoshiki Hidaka3, Masayuki Ushio2 1 Department of Environmental Science, Ishikawa Prefectural University, Nonoichi, Ishikawa, Japan, 2 Center for Ecological Research, Kyoto University, Otsu, Shiga, Japan, 3 Department of Applied Quantum Physics and Nuclear Engineering, Graduate School of Engineering, Kyushu University, Fukuoka, Japan Abstract We investigated whole-plant leaf area in relation to ontogenetic variation in leaf-size for a forest perennial herb, Cardiocrinum cordatum. The 200-fold ontogenetic variability in C. cordatum leaf area followed a power-law dependence on total leaf number, a measure of developmental stage. When we normalized for plant size, the function describing the size of single leaves along the stem was similar among different-sized plants, implying that the different-sized canopies observed at different times in the growth trajectory were fundamentally similar to each other. We conclude that the growth trajectory of a population of C. cordatum plant leaves obeyed a dynamic scaling law, the first reported for a growth trajectory at the whole-plant level. Citation: Koyama K, Hidaka Y, Ushio M (2012) Dynamic Scaling in the Growth of a Non-Branching Plant, Cardiocrinum cordatum. PLoS ONE 7(9): e45317. doi:10.1371/journal.pone.0045317 Editor: Christof Markus Aegerter, University of Zurich, Switzerland Received April 17, 2012; Accepted August 20, 2012; Published September 19, 2012 Copyright: 2012 Koyama et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: KK was funded by the JSPS Research Fellowship for Young Scientists. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: konpei.koyama@gmail.com Introduction Whole-plant leaf area is a major determinant of plant and ecosystem productivity [1–3], and use of allometric relationships to predict whole-plant leaf area is a central topic in plant ecology [4– 10]. However, one difficulty in modeling whole-plant leaf area is that individual leaves show considerable morphological plasticity in their size. Leaf size is determined by both developmental stage [11–15], and by position within a canopy [11–13]. To date, this leaf size variation has not been incorporated into whole-plant allometric scaling models [8,16]; current scaling models are based on the assumption that whole-plant leaf area is proportional to leaf number [6,7,16]. The omission of leaf size variation may help to explain why current whole-plant scaling theories do not reliably predict whole-plant leaf area (c.f. [10]). It has been suggested that the metabolic theories for plants will be further improved by incorporating leaf size variation [16]. In this paper, we adopt the concept of dynamic scaling in an attempt to establish such a cross- scale linkage. Dynamic scaling refers to a phenomenon in which observations of a growing system at different times are similar to each other [17]. Galeano et al. [18] analyzed dynamic scaling of the growth of plant calli (i.e., cultured plant cells). However, to the best of our knowledge, there have been no studies that have reported dynamic scaling at the whole-plant level. We hypothesized that geometric similarity through development would also be expected at the whole-plant level, to maintain overall plant structure to conserve the efficiency of the light-capturing foliar array and mechanical stability during ontogeny. In the present context, we investigated the possibility that one pattern (e.g., leaf size as a function of position within a plant, described by an unknown function), when observed at a particular developmental stage, has the same form when observed at another developmental stage. One commonly observed correlate of dynamic scaling is that the size of the unit pattern [17,19] and the size of the entire pattern [18] typically follow a power-law dependence on time. Hence, we investigated the possibility that whole-plant leaf area (the size of the pattern) can be expressed as a power function of total leaf number (a normalized time across developmental stages). Total leaf number across developmental stages is essentially equivalent to the plastochron index or plastochron age, which has been widely applied in studies of the foliar development of herbs [11,20]. To assess this possibility, we investigated the growth trajectory of the foliar array in a perennial, rosette-forming forest herb, Cardiocrinum cordatum. Specifically, we tested the following two hypotheses: (1) the within-plant distribution of leaf size observed at a particular time is described by the same function as that observed at another time (dynamic scaling); (2) whole-plant leaf area and mean individual leaf area are power functions of total leaf number across developmental stages (power law). Materials and Methods Species and Site Cardiocrinum cordatum (Liliaceae) is a monocarpic perennial herb [21–23] found in the forest understory. In this species, the entire leaf population dies before the onset of winter, and in the following spring, a new rosette forms with a larger leaf population. When a C. cordatum plant flowers, it sets seed and senesces, leaving small bulblets that are produced prior to bolting as asexual propagules [21–23]. We sampled a population of C. cordatum (Fig. 1) from a temperate forest dominated by Japanese alder (Alnus japonica, age: 50–60 yr; canopy height: 20 m [24]), located at the Ishikawa PLOS ONE | www.plosone.org 1 September 2012 | Volume 7 | Issue 9 | e45317