Internode morphometrics and allometry of Tonkin Cane Pseudosasa amabilis

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.