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Intermittent chaos in population dynamics

M Doebeli1

  • 1Zoologisches Institut der Universität, Basel, Switzerland.

Journal of Theoretical Biology
|February 7, 1994
PubMed
Summary
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Population models typically assume identical individuals. This study shows that introducing variation, like a mutant phenotype, can lead to a different route to chaos via intermittency.

Area of Science:

  • Population dynamics
  • Theoretical ecology
  • Mathematical biology

Background:

  • Single-species population models commonly assume discrete generations and identical individuals.
  • Dynamical behavior in these models often progresses from stable equilibrium to chaotic motion through bifurcations as parameters change.
  • The assumption of individual homogeneity simplifies models but may not reflect natural populations.

Purpose of the Study:

  • To investigate how phenotypic variation within a population alters the route to chaotic dynamics.
  • To explore the role of mutant invasions in driving population fluctuations.
  • To identify alternative pathways to chaos beyond those predicted by homogeneous models.

Main Methods:

  • Mathematical modeling of population dynamics.

Related Experiment Videos

  • Analysis of discrete-time population equations incorporating phenotypic variation.
  • Simulation of mutant phenotype invasion dynamics.

    • Main Results:

    • Phenotypic variation can introduce a novel route to chaos, distinct from standard bifurcation cascades.
    • Invasion of a mutant phenotype into a resident population can induce intermittent chaotic behavior.
    • Intermittency is characterized by extended periods of regular dynamics punctuated by short bursts of wild fluctuations.

    Conclusions:

    • The assumption of individual homogeneity in population models can obscure important dynamical behaviors.
    • Phenotypic variation is a critical factor that can lead to complex population dynamics, including intermittency and chaos.
    • Understanding routes to chaos in heterogeneous populations is essential for accurate ecological predictions.