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An open-ended logistic-based growth function: Analytical solutions and the power-law logistic model

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  • Thornley, John H.M.
  • Shepherd, John J.
  • France, J.

Abstract

An open-ended form of the logistic equation was recently proposed, using a model comprising two differential equations [Thornley, J.H.M., France, J., 2005. An open-ended logistic-based growth function. Ecol. Model. 184, 257–261]. The equations represent the two processes of growth and development, and are coupled. In this note, an analytical solution is developed for constant parameters. The solution can be expressed as a targetted single-differential-equation model, the θ-logistic or power-law logistic model, which is a well-known empirical growth equation in ecology and elsewhere. The analysis may facilitate mechanistic interpretation and application of the power-law logistic model as well as the original open two-differential-equation model.

Suggested Citation

  • Thornley, John H.M. & Shepherd, John J. & France, J., 2007. "An open-ended logistic-based growth function: Analytical solutions and the power-law logistic model," Ecological Modelling, Elsevier, vol. 204(3), pages 531-534.
    • Handle: RePEc:eee:ecomod:v:204:y:2007:i:3:p:531-534
    DOI: 10.1016/j.ecolmodel.2006.12.026
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    References listed on IDEAS

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    1. Rodrigues, João & Domingos, Tiago & Conceição, Pedro & Belbute, José, 2005. "Constraints on dematerialisation and allocation of natural capital along a sustainable growth path," Ecological Economics, Elsevier, vol. 54(4), pages 382-396, September.
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    Cited by:

    1. Barker, Daniel & Sibly, Richard M., 2008. "The effects of environmental perturbation and measurement error on estimates of the shape parameter in the theta-logistic model of population regulation," Ecological Modelling, Elsevier, vol. 219(1), pages 170-177.
    2. Miškinis, Paulius & Vasiliauskienė, Vaida, 2017. "The analytical solutions of the harvesting Verhulst’s evolution equation," Ecological Modelling, Elsevier, vol. 360(C), pages 189-193.
    3. Shi, Pei-Jian & Fan, Mei-Ling & Ratkowsky, David A. & Huang, Jian-Guo & Wu, Hsin-I & Chen, Lei & Fang, Shui-Yuan & Zhang, Chun-Xia, 2017. "Comparison of two ontogenetic growth equations for animals and plants," Ecological Modelling, Elsevier, vol. 349(C), pages 1-10.
    4. Moriguchi, Kai, 2018. "An approach for deriving growth equations for quantities exhibiting cumulative growth based on stochastic interpretation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1150-1163.
    5. Shi, Pei-Jian & Men, Xing-Yuan & Sandhu, Hardev S. & Chakraborty, Amit & Li, Bai-Lian & Ou-Yang, Fang & Sun, Yu-Cheng & Ge, Feng, 2013. "The “general” ontogenetic growth model is inapplicable to crop growth," Ecological Modelling, Elsevier, vol. 266(C), pages 1-9.
    6. Han, Yong & Sun, Zhiyu & Fang, Hongwei & Bai, Sen & Huang, Lei & He, Guojian, 2020. "Habitat succession of the Yangtze finless porpoise in Poyang Lake under the changing hydrodynamic and feeding environment," Ecological Modelling, Elsevier, vol. 424(C).
    7. Thornley, John H.M. & France, James, 2013. "Use of growth functions to describe disease vector population dynamics—Additional assumptions are required and are important," Ecological Modelling, Elsevier, vol. 266(C), pages 97-102.

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