A New Flexible Sigmoidal Growth Model

Liying Cao,Guifen Chen,Lin Li,Pei-Jian Shi

doi:10.3390/sym11020204

Liying Cao, Guifen Chen + Show 2 more

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https://doi.org/10.3390/sym11020204

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Abstract

Biological growth is driven by numerous functions, such as hormones and mineral nutrients, and is also involved in various ecological processes. Therefore, it is necessary to accurately capture the growth trajectory of various species in ecosystems. A new sigmoidal growth (NSG) model is presented here for describing the growth of animals and plants when the assumption is that the growth rate curve is asymmetric. The NSG model was compared with four classic sigmoidal growth models, including the logistic equation, Richards, Gompertz, and ontogenetic growth models. Results indicated that all models fit well with the empirical growth data of 12 species, except the ontogenetic growth model, which only captures the growth of animals. The estimated maximum asymptotic biomass w m a x of plants from the ontogenetic growth model was not reliable. The experiment result shows that the NSG model can more precisely estimate the value and time of reaching maximum biomass when growth rate becomes close to zero near the end of growth. The NSG model contains three other parameters besides the value and time of reaching maximum biomass, and thereby, it can be difficult to assign initial values for parameterization using local optimization methods (e.g., using Gauss–Newton or Levenberg–Marquardt methods). We demonstrate the use of a differential evolution algorithm for resolving this issue efficiently. As such, the NSG model can be applied to describing the growth patterns of a variety of species and estimating the value and time of achieving maximum biomass simultaneously.

Highlights

The growth of individual biomass is driven by numerous functions and processes, as well as interspecific interactions [1,2,3,4,5]
The five growth models can be divided into three groups depending on their number of parameters: the five-parameter new sigmoidal growth (NSG) model in Equation (5), the four-parameter Richards model in Equation (3), and three three-parameter models (logistic in Equation (1), Gompertz in Equation
In forcontrast, the crop species, the ontogenetic model could predict neither t for maximum growth rate nor for the crop species, the ontogenetic model could predict neitherm t for maximum growth rate nor thethe time ofof reaching summary,the the results suggested the NSG

Summary

Introduction

The growth of individual biomass is driven by numerous functions and processes, as well as interspecific interactions [1,2,3,4,5]. A complete trajectory of biomass growth resembles a sigmoidal curve [12,13]. Many sigmoidal growth models have been proposed to capture the growth trajectory with accuracy, such as the classical logistic equation and models proposed by Gompertz and by Richards [6,14]. The logistic equation describes the symmetric growth, whereas the Gompertz and ontogenetic growth equations depict asymmetric growth with fixed inflection points. The inflection point of the Richards equation is flexible and can be used for describing different levels of asymmetry in growth [15]. Reference presented a general ontogenetic growth equation based on the 3/4 power law of allometric scaling [16,17]

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