Variation in internode length patterns: a data analysis of internode length and serial number in three bamboo species

Introduction: Bamboo is one of the fastest-growing plants on earth, and its young culms are formed by the elongation of internodes. However, the mathematical intricacies of its internode elongation are not well understood. Methods: This study investigated the internode length growth of Phyllostachys edulis, Phyllostachys iridescens, and Pseudosasa amabilis at ten different culm height developmental stages (G1–G10). Results and discussion: The tempo of internode elongation from the culm base to the tip generally followed a “slow-fast-slow” growth rhythm. The internode length and the serial number relationship showed a right-skewed curve. As the bamboo grows taller, the longest internode moves from the base to the middle of the culm. The relationship between relative internode number (RIN) and relative cumulative internode length (RCIL) displayed a typical S-shaped growth curve. The modified Brière (MBE) sigmoid equation achieved better goodness-of-fit than the logistic, power, and third-order functions in fitting the RIN-RCIL curves with the smallest average root mean square error (RMSE). The elongation rates of internodes varied not only with the growth of culm height, but also with the position of the bamboo culm from base to tip. In addition, as the bamboo grows in height, more internodes gradually contribute to the culm height growth. At G1 development stage, 24.01–38.23% of the internodes contributed 65.27–73.59% of the culm height, whereas at G10 stage, 49.28–61.07% of the internodes contributed 66.70–78.18% of the culm height. Our findings provide new insights into the mathematical characterization of bamboo internode elongation patterns involved in the rapid culm growth.