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

Abstract

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 = 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 swordfish is presented.

New Insights into Tree Height Distribution Based on Mixed Effects Univariate Diffusion Processes

“…Traditionally used ordinary differential equation models are the Malthus, Mitscherlich, Gompertz, and Bertalanffy types [11–13] (see Appendix A). …”

“…Von Bertalanffy (for a review, see example in Román-Román et al [13]) hypothesized that the growth of an organism could be represented as the difference between the synthesis and degradation of its building materials. There are few theoretical equations formulated specifically for biology applications.…”

Inferring the effect of therapy on tumors showing stochastic Gompertzian growth

“…In Figure 3, 100 simulated sample paths of the modified version of process (14) are plotted, choosing C(t) = 0.03, ∀t ≥ t 1 = 0.…”

“…With the aim of validating the proposed strategy, we have simulated 100 sample paths of the modified version of process (14), choosing C(t) = 0.03 log(e +0.2t), ∀t ≥ t 1 = 0. The values of the parameters have been chosen arbitrarily but so that the therapy is effective, i.e.…”

“…This is the case, for example, of the dynamics of growth of individuals in the same species. It must be pointed out that the methodology used in Gutiérrez et al [6] can be extended to other contexts in order to model several modes of population growth (see, for instance, Roman et al [14]). …”