A diffusion process to model generalized von Bertalanffy growth patterns: Fitting to real data

JOURNAL OF THEORETICAL BIOLOGY

卷:263

Article

Roman-Roman, Patricia¹  Romero, Desiree¹  Torres-Ruiz, Francisco¹ 

[1] Univ Granada, Fac Ciencias, Dept Estadist & Invest Operat, E-18071 Granada, Spain

关键词: Diffusion process;    Stochastic growth;    Von Bertalanffy curve;   

DOI  :  10.1016/j.jtbi.2009.12.009

来源: Elsevier

【 摘 要 】

The von Bertalanffy growth curve has been commonly used for modeling animal growth (particularly fish). Both deterministic and stochastic models exist in association with this curve, the latter allowing for the inclusion of fluctuations or disturbances that might exist in the system under consideration which are not always quantifiable or may even be unknown. This curve is mainly used for modeling the length variable whereas a generalized version, including a new parameter b >= 1, allows for modeling both length and weight for some animal species in both isometric (b = 3) and allometric (b not equal 3) situations. In this paper a stochastic model related to the generalized von Bertalanffy growth curve is proposed. This model allows to investigate the time evolution of growth variables associated both with individual behaviors and mean population behavior. Also, with the purpose of fitting the above-mentioned model to real data and so be able to forecast and analyze particular characteristics, we study the maximum likelihood estimation of the parameters of the model. In addition, and regarding the numerical problems posed by solving the likelihood equations, a strategy is developed for obtaining initial solutions for the usual numerical procedures. Such strategy is validated by means of simulated examples. Finally, an application to real data of mean weight of sword fish is presented. (C) 2009 Elsevier Ltd. All rights reserved.

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