The neoclassical theory of population dynamics in spatially homogeneous environments. (II) Non-monotonic dynamics, overshooting and oscillations

Peter Vadasz, A. S. Vadasz

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

A neoclassical theory is proposed for the growth of populations in a spatially homogeneous environment. The proposed theory derives from first principles while extending and unifying the existing theories by addressing all the cases where the existing theories fall short in recovering qualitative as well as quantitative features that appear in experimental data. These features include in some cases overshooting and oscillations, in others the existence of a "Lag Phase" at the initial growth stages, as well as an inflection point in the "ln curve" of the population number, i.e., a logarithmic inflection point referred here as "Lip". The proposed neoclassical theory is derived to recover the Logistic Growth Curve as a special case. It also recovers results of a classical experiment reported by Pearl [Q. Rev. Biol. 2(4) (1927) 532] featuring growth followed by decay. Comparisons of the solutions obtained from the proposed neoclassical equation with the experimental data confirm its quantitative validity, as well as its ability to recover a wide range of qualitative features captured in experiments. This is the first non-autonomous system proposed so far that is shown to capture all these effects.

Original languageEnglish (US)
Pages (from-to)360-380
Number of pages21
JournalPhysica A: Statistical Mechanics and its Applications
Volume309
Issue number3-4
DOIs
StatePublished - Jun 15 2002
Externally publishedYes

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Keywords

  • Lag phase
  • Logistic growth
  • Neoclassical growth
  • Oscillations and overhooting
  • Population dynamics

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

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