A Two-Step Growth Curve: Approach to the von Bertalanffy and Gompertz EquationsReport as inadecuate




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Manycurves have been proposed and debated to model individual growth of marineinvertebrates. Broadly, they fall into two classes, first order e.g. vonBertalanffy and sigmoidal e.g. Gompertz. We provide an innovative approachwhich demonstrates that the growth curves are not mutually exclusive but that eithermay arise from a simple three-stage growth model with two steps k1 and k2 depending on the ratio of the growth parameters . The new approachpredicts sigmoidal growth when is close to 1, but if either growth from stageA to stage B or B to C is fast relative to the other, the slower of the twosteps becomes the growth limiting step and the model reduces to first ordergrowth. The resulting curves indicate that there is a substantial difference inthe estimated size at time t duringthe period of active growth. This novel two-step rate model generates a growthsurface that allows for changes in the rate parameters over time as reflectedin the new parameter nt = k1t - k2t. The added degree of freedom bringsabout individual growth trajectories across the growth surface that is noteasily mapped using conventional growth modeling techniques. This two or morestage growth model yields a growth surface that allows for a wide range ofgrowth trajectories, accommodating staged growth, growth lags, as well asindeterminate growth and can help resolve debates as to which growth curvesshould be used to model animal growth. This flexibility can improve estimatesof growth parameters used in population models influencing model outcomes andultimately management decisions.=

KEYWORDS

Growth Model, Growth Surface, Rate Equation, Staged Growth, Population Models

Cite this paper

Rogers-Bennett, L. and Rogers, D. 2016 A Two-Step Growth Curve: Approach to the von Bertalanffy and Gompertz Equations. Advances in Pure Mathematics, 6, 321-330. doi: 10.4236-apm.2016.65023.





Author: Laura Rogers-Bennett1,2*, Donald W. Rogers3,4

Source: http://www.scirp.org/



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