The neoclassical theory of population dynamics in spatially homogeneous environments. (I) Derivation of universal laws and monotonic growth

Peter Vadasz, A. S. Vadasz

Research output: Contribution to journalArticle

13 Citations (Scopus)

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 (Quart. Rev. Biol. II(4) (1927) 532-548) featuring growth followed by decay. Comparisons of the solutions obtained from the proposed neoclassical equation with 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)329-359
Number of pages31
JournalPhysica A: Statistical Mechanics and its Applications
Volume309
Issue number3-4
DOIs
StatePublished - Jun 15 2002
Externally publishedYes

Fingerprint

Population Dynamics
Monotonic
derivation
inflection points
Point of inflection
Logistic curve
Experimental Data
logistics
Logistic Growth
curves
Growth Curve
Phase-lag
Nonautonomous Systems
First-principles
time lag
Experiment
Logarithmic
oscillations
Decay
Oscillation

Keywords

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

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

@article{91998e2ab1814f6998b05a6a83be7f42,
title = "The neoclassical theory of population dynamics in spatially homogeneous environments. (I) Derivation of universal laws and monotonic growth",
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 (Quart. Rev. Biol. II(4) (1927) 532-548) featuring growth followed by decay. Comparisons of the solutions obtained from the proposed neoclassical equation with 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.",
keywords = "Lag phase, Logistic growth, Neoclassical growth, Oscillations and overhooting, Population dynamics",
author = "Peter Vadasz and Vadasz, {A. S.}",
year = "2002",
month = "6",
day = "15",
doi = "10.1016/S0378-4371(02)00586-1",
language = "English (US)",
volume = "309",
pages = "329--359",
journal = "Physica A: Statistical Mechanics and its Applications",
issn = "0378-4371",
publisher = "Elsevier",
number = "3-4",

}

TY - JOUR

T1 - The neoclassical theory of population dynamics in spatially homogeneous environments. (I) Derivation of universal laws and monotonic growth

AU - Vadasz, Peter

AU - Vadasz, A. S.

PY - 2002/6/15

Y1 - 2002/6/15

N2 - 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 (Quart. Rev. Biol. II(4) (1927) 532-548) featuring growth followed by decay. Comparisons of the solutions obtained from the proposed neoclassical equation with 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.

AB - 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 (Quart. Rev. Biol. II(4) (1927) 532-548) featuring growth followed by decay. Comparisons of the solutions obtained from the proposed neoclassical equation with 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.

KW - Lag phase

KW - Logistic growth

KW - Neoclassical growth

KW - Oscillations and overhooting

KW - Population dynamics

UR - http://www.scopus.com/inward/record.url?scp=0037097298&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037097298&partnerID=8YFLogxK

U2 - 10.1016/S0378-4371(02)00586-1

DO - 10.1016/S0378-4371(02)00586-1

M3 - Article

AN - SCOPUS:0037097298

VL - 309

SP - 329

EP - 359

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 3-4

ER -