Maximum size-density relationship in bamboo forests: Case study of Phyllostachys pubescens forests in Japan

Bamboo forests are likely to be subjected to self-thinning due to their rapid growth rate. In fully stocked bamboo forests, the stand density (ρ) was suggested to be inversely proportional to the square of mean diameter at breast height (D) (ρ ∝ D−2), differing from the conventional power-law for trees, i.e., Reineke equation (ρ ∝ D−1.6). Nevertheless, the validity and mechanism of the inverse-square law remained unclear, despite its significance for managing bamboo forests. In this study, we derived an allometric model that predicts the slope of the maximum size-density relationship (MSDR) between D and ρ on double logarithmic coordinates based on well-known ecological laws. The model indicates that the slope of −2 for bamboo is theoretically valid, with the difference in the slope between bamboo and trees being caused by their differences in inner-culm (or inner-stem) structure. We also determined the MSDR empirically by compiling data of 415 Phyllostachys pubescens Mazel ex Houz. pure stands across Japan. The obtained MSDR describes the upper boundary of the D-ρ relationship well, with a slope of −1.996 that is very close to − 2. We further established a stand density management diagram of P. pubescens stands based on the MSDR. This diagram allows forest managers to regulate ρ depending on D as well as management purposes (production of bamboo shoot, bamboo charcoal and culm wood).