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Symmetry 2019, 11(2), 204; https://doi.org/10.3390/sym11020204

A New Flexible Sigmoidal Growth Model

1
College of information and technology, Jilin Agricultural University, Changchun 130118, China
2
Department of Plant and Soil Science, Texas Tech University, Lubbock, TX 79409, USA
3
Co-Innovation Centre for Sustainable Forestry in Southern China, Bamboo Research Institute, Nanjing Forestry University, Nanjing 210037, China
*
Author to whom correspondence should be addressed.
Received: 14 December 2018 / Revised: 30 January 2019 / Accepted: 2 February 2019 / Published: 12 February 2019
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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. View Full-Text
Keywords: growth model; asymmetric growth rate curve; biological growth; new sigmoidal growth (NSG) growth model; asymmetric growth rate curve; biological growth; new sigmoidal growth (NSG)
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Cao, L.; Shi, P.-J.; Li, L.; Chen, G. A New Flexible Sigmoidal Growth Model. Symmetry 2019, 11, 204.

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