Internode morphometrics and allometry of Tonkin Cane Pseudosasa amabilis

Abstract

Pseudosasa amabilis (McClure) (Poales: Gramineae) is a typical bamboo species naturally distributed in large area of south China and famous for its culm strength. Although bamboos were found to share the same development rule, the detailed internode morphology of bamboo culm was actually not fully expressed. We explored internode morphology of P. amabilis using 11 different physical parameters in different dimensions (1–4). As Taylor's power law (TPL) is generally applicable to describe relationship between mean and variance of population density, here we used TPL to evaluate the differences between internodes, and further, the relationship between dimension and TPL. Results showed that length (L), hollow radius (HR), hollow area (HA), hollow cylinder volume (HCV), total cylinder volume (TCV), density (De), and weight (W) all presented positive skewed distribution in varying degrees. For the basic one‐dimensional parameters, the 9th internode was the longest, the 7th the heaviest, while thickness (T) decreased with internodes. Diameter (D) decreased in general but with an inconspicuous local mode at the 5–6th internodes, potentially due to the rapid height growth. The longest (9th) internode was the “turning point” for T‐D and HR‐D relationships. Scatter plot changing trends of W to the one‐dimensional parameters after the heaviest (7th) internode were reversed, indicating a deceleration of growth speed. TPL was not holding well in one‐dimensional parameters (R 2: 0.5413–0.8125), but keep increasing as the parameter's dimension increasing (R 2 > 0.92 for two‐dimensional, R 2 > 0.97 for three‐dimensional, and R 2 > 0.99 for four‐dimensional parameters.), suggesting an emergence mechanism of TPL related to both the physical dimensions of morphological measures and the allometric growth of bamboo. From the physical fundamental level, all existences are the expression of energy distribution in different dimensions, implying a more general rule that energy distribution holds better TPL in higher dimension level.

Taylor’s Power Law for Leaf Bilateral Symmetry

“…Therefore, the scaling relationship of leaf weight and leaf area of bamboo plants is significantly stronger than those of the other two classes of plants based on the comparison of the coefficients of determination (i.e., R 2 ). Because the biomass (weight) is a better measurement than the area or length in describing TPL [18,23], plants with a better scaling relationship between leaf weight and leaf area will have a better TPL for describing leaf bilateral symmetry. If we could cut a leaf into different parts with equidistant intervals from the leaf base to leaf apex and measure their weights (see Figure 1), we believe that we would obtain a better goodness of fit for TPL by using the measures of leaf weight than using the measures of leaf area.…”

“…These studies related to TPL have added to our understanding of the variation of a large number of ecological and non-ecological measures, for example, animal and plant population density, biomass, poikilothermic developmental rate, crime, precipitation, released energies of aftershocks, trading activity of stock, and so on [13,[18][19][20][21][22]. In our recent studies, weight is a typical representative of energy for biological measures, so the variance-mean relationship based on weight measures should reflect TPL well [23].…”

Variation in individual biomass decreases faster than mean biomass with increasing density of bamboo stands

“…Taylor's power law (TPL) has been used to describe the relationship between the variance (V) and the mean (M) of population densities, and takes the form of V = aÁM b (Taylor 1961), where a represents a constant, and b is an empirical exponent ranging from 1 to 3 (Taylor 1981;Anderson et al 1982;Ballantyne and Kerkhoff 2007;Kaltz et al 2012;Giometto et al 2015;Cohen and Xu 2015;Xiao et al 2015;Shi et al 2016Shi et al , 2018Tippett and Cohen 2016). Taylor's power law has been applied and verified widely in many disciplines such as botany, ecology, economics, entomology, epidemiology, meteorology, and physics (Walgenbach 1994;Yamamura 2000;Eisler et al 2008;Kaltz et al 2012;Tippett and Cohen 2016;Cheng et al 2017;Cohen et al 2017a;Lin et al 2018;Shi et al 2017aShi et al , b, 2018. Multiple biological and ecological constraints affect the exponent b of TPL.…”

“…However, it remains unclear how TPL of plant biomass is related to other laws of plant dimensions such as leaf area, stem diameter and tree height. Cheng et al (2017) analyzed TPL with reference to the internode variables for a bamboo Pseudosasa amabilis, including internode diameter, length, thickness, and weight, and found that the physical dimensions of these measures could significantly affect the goodness of fit to the log-log linear regression of TPL. TPL for weight yielded a better fit than did other parameters because weight (and biomass) represents the highest physical dimension among these measures.…”

“…Recent work focused on the geographic distribution of different bamboo species and on variations in biomass and growth patterns. The mathematical analysis of population dynamics has not been equally emphasized, with the exception of the TPL morphmetrics of bamboo internodes (Inoue 2013;Cheng et al 2017). Although the self-thinning relationship between stand density and plant size has been verified for different bamboo species (Liu et al 2016), TPL has not been tested with reference to ground diameter or plant height or weight.…”