title: On the analytical solution for the Pütter-Bertalanffy growth equation.
abstract: This study develops the basic idea of Pütter and Bertalanffy addressing the allometric scaling of anabolism and catabolism on somatic growth dynamics. We proposed a standardized form of the Pütter-Bertalanffy equation (PBE), which is given as the extended model of Richards function, and subsequently solved it. The analytical solution of the PBE was defined by an incomplete beta function and can take a wide range of shapes in its growth curve. The mathematical behavior of PBE due to the change in parameter values was briefly discussed. Most forms of solution consistently hold the implicit functional type with respect to the variable of body size.
authors.affiliation: School of Marine Science and Technology, Tokai University, Shimizu, Shizuoka 424-8610, Japan. Electronic address: ohnishi@scc.u-tokai.ac.jp.
authors.forename: Shuhei
authors.initials: S
authors.lastname: Ohnishi
authors.affiliation: Graduate School of Agricultural and Life Sciences, The University of Tokyo, Bunkyo, Tokyo 113-8657, Japan.
authors.forename: Takashi
authors.initials: T
authors.lastname: Yamakawa
authors.affiliation: National Research Institute of Fisheries Science, Fisheries Research Agency, Yokohama, Kanagawa 236-8648, Japan.
authors.forename: Tatsuro
authors.initials: T
authors.lastname: Akamine
mesh_terms: D048788:Growth and Development; D006801:Humans; D008954:Models, Biological
keywords: Allometry; Bertalanffy model; Ontogenetic growth; Pütter model; Richards model