Mathematical expression for the relationship between internode number and internode length for bamboo, Phyllostachys pubescens

We analyzed the relationship between internode number and internode length for one of the largest bamboo, Phyllostachys pubescens Mazel ex Houz. For 50 sample culms with various sizes felled in a purest and of P. pubescens, the internode number was assigned from base totip and the length for each internode was directly measured. The result indicated that the internode length should be cumulated from base to tip,and then the cumulated internode length should be relativized by the total culm length. It was inappropriate to relativize the internode length by themaximum intenode length. In addition, the relationship between therelative internode number (the internode number relativized by the total number of internodes) and the relative cumulated internode length should be described not by a power function but by a sigmoid function such as the third-order function. The determined function enabled us to estimate the actual internode length, with the root mean squared error being 4 cm.In conclusion, the mathematical expression presented here, i.e., there lativization of the cumulated internode length by the total culm length and the application of the sigmoid function, will be useful in describing the relationship between internode number and internode length for P.pubescens.