Analysis of logistic growth models.

By A. Tsoularis, J. Wallace. Mathematical Biosciences, 2002

1,047 citations recorded by the source corpus.

A variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. Most predictive models are shown to be based on variations of the classical Verhulst logistic growth equation. We review and compare several such models and analyse properties of interest for these. We also identify and detail several associated limitations and restrictions.A generalized form of the logistic growth curve is introduced which incorporates these models as special cases. Several properties of the generalized growth are also presented. We furthermore prove that the new growth form incorporates additional growth models which are markedly different from the logistic growth and its variants, at least in their mathematical representation. Finally, we give a brief outline of how the new curve could be used for curve-fitting.

Subfields: Economics and Econometrics, Environmental Engineering, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/ce123f0547e55959c223fc39d084582ed36379dd

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Citations in the corpus

Nonlinear Regression Models and Applications in Agricultural Research (2015, background): “This has led to the development of numerous versions of a standard equation (e.g., Birch, 1999; Tsoularis, 2001; Supplemental Tables S1–S3).”
Global oil depletion - an assessment of the evidence for a near-term peak in global oil production (2009, methodology): “82 used to model growth processes (Meade, 1984; Tsoularis and Wallace, 2002).”
Least-squares fitting Gompertz curve (2004, background): “Gompertz curve is a special case of the so-called hyper-Gompertz curve, which is also known as a generalized ecological curve, or simply, a generalized Gompertz curve (see [15,16,17]).”
Superabsorbent hydrogels based on polysaccharides for application in agriculture as soil conditioner and nutrient carrier: A review (2015, background): “In static release experiments, the increase in the nutrient concentration ( C ( t )) as a function of the release time ( t ) may be considered analogous to the logistic growth of a population in the environment with limited resource [162].”
Nonlinear Growth Models for Modeling Oil Palm Yield Growth (2005, neutral): “Stannard ( ) ( ) 3 (t)= 1+exp - + t + ε [12]”
Growth rates of modern science: a latent piecewise growth curve approach to model publication numbers from established and new literature databases (2020, neutral): “The resolution of this differential equation leads to a functional relationship, which can be represented in the following statistical model (Tsoularis and Wallace, 2002, p. 28f.): yt ¼ f tð Þ ¼ e K eb0 eK eb0ð Þe b1 tþeb0 e εt ; εt N 0; σ2CORRεtεt 1 ð4Þ It can be seen from Eq.”
Almost automorphic solutions of dynamic equations on time scales (2013, neutral): “See [25] and [51], for more details.”
Improved evaluation of cover crop species by growth and root factors (2010, background): “Several empirical functions are available to characterize the logistic growth dynamics that are frequently observed in nature (e.g. Tsoularis and Wallace, 2002).”