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A Two-Step Growth c.rve: Approac. to the von Bertalanffy and Gompertz Equations

Advanc.s in Pure Mathematic. 2016年第5期6卷 321-330页

作者： Laura Rogers-Bennett Donald W. Rogers california department of fish and wildlife and karen c. drayer Wildlife Health Center UC Davis CA USA Bodega Marine Laboratory Bodega Bay CA USA c.emistry department Long Island University Brooklyn NY USA Friday Harbor Laboratories Whiteley Center University of Washington Friday Harbor WA USA

Many c.rves have been proposed and debated to model individual growth of marine invertebrates. Broadly, they fall into two c.asses, first order (e.g. von Bertalanffy) and sigmoidal (e.g. Gompertz). We provide an innovative approac. whic. demonstrates that the growth c.rves are not mutually exc.usive but that either may arise from a simple three-stage growth model with two steps (k1 and k2) depending on the ratio of the growth parameters . The new approac. predic.s sigmoidal growth when is c.ose to 1, but if either growth from stage A to stage B or B to c.is fast relative to the other, the slower of the two steps bec.mes the growth limiting step and the model reduc.s to first order growth. The resulting c.rves indic.te that there is a substantial differenc. in the estimated size at time t during the period of ac.ive growth. This novel two-step rate model generates a growth surfac. that allows for c.anges in the rate parameters over time as reflec.ed in the new parameter n(t) = k1(t) - k2(t). The added degree of freedom brings about individual growth trajec.ories ac.oss the growth surfac. that is not easily mapped using c.nventional growth modeling tec.niques. This two (or more) stage growth model yields a growth surfac. that allows for a wide range of growth trajec.ories, ac.ommodating staged growth, growth lags, as well as indeterminate growth and c.n help resolve debates as to whic. growth c.rves should be used to model animal growth. This flexibility c.n improve estimates of growth parameters used in population models influenc.ng model outc.mes and ultimately management dec.sions.=

关键词： Growth Model Growth Surfac. Rate Equation Staged Growth Population Models

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