Ontogenetic growth functions provide basic information in biological and ecological studies. Various growth functions classified into the Pütter model have been used historically, regardless of controversies over their appropriateness. Here, we present a novel growth function for fish and aquatic organisms (generalised q-VBGF) by considering an allocation schedule of allometrically produced surplus energy between somatic growth and reproduction. The generalised q-VBGF can track growth trajectories in different life history strategies from determinate to indeterminate growth by adjusting the value of the ‘growth indeterminacy exponent’ q. The timing of maturation and attainable body size can be adjusted by the ‘maturation timing parameter’ τ while maintaining a common growth trajectory before maturation. The generalised q-VBGF is a comprehensive growth function in which exponentials in the traditional monomolecular, von Bertalanffy, Gompertz, logistic, and Richards functions are replaced with q-exponentials defined in the non-extensive Tsallis statistics, and it fits to actual data more adequately than these conventional functions. The relationship between the estimated parameter values τ and rq forms a unique hyperbola, which provides a new insight into the continuum of life history strategies of organisms.
A new practical growth model through the partial reconstruction for the von Bertalanffy function (VBF) has been proposed. In numerous studies on various species, VBF has been recognized as an appropriate function to describe growth. Here the difference in growth dynamics between soft and hard tissues is considered using VBF. A differential equation in which the growth rates of these two tissue types are described, gives a four parameter model. This advanced model showed characteristics such as: (i) S-shape curve similar to the Gompertz model; (ii) unfixed point of inflection; and (iii) definition as an implicit function. The characteristic indicated in (iii) makes it impossible to apply the method of least squares to data analysis. Therefore, a solution was introduced combining Lagrange's method of indeterminate coefficients and the Newton method. Data analysis for verifying the performance of the advanced model was conducted on published data on growth of the bivalve Spisula sachalinensis. As a result of the comparison among the existing growth models, the advanced model produced the minimum value of Akaike information criterion (AIC).
Before constructing growth formulae with time-varying growth coe‹cient, the gain in body length should be examined using data. For this purpose, it is necessary to apply an auxiliary analysis model while constraining the ‰uctuation of body expansion in time. This paper presents an analysis model which has a ‰exibleˆtness for the ‰uctuation in length. In general, the time-varying growth coe‹cient has been described by a periodic function. On the contrary, we employed theˆrst-order diŠerences of growth coe‹cient, which follows the probability distribution. Here, we describe the parameter estimation and model selection based on Bayes' Theorem and MarginalLikelihood. In order to compare the result of the Bayesian approach with that given by the conventional way, we introduced the body length data of masu salmon. In a case where only unreliable growth information has been obtained, it is necessary to extract the biological characters from data, which is useful for model exploration and construction. Through the auxiliary utilization of the Bayesian model, the biological features related to the complicated mechanism of growth may be speciˆed.
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