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Population cycles caused by selection by density dependent competitive interactions.

L Witting1

  • 1Greenland Institute of Natural Resources, P. O. Box 570, DK-3900 Nuuk, Greenland. larsw@natur.gl

Bulletin of Mathematical Biology
|December 29, 2000
PubMed
Summary
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This study presents a new population dynamic equation explaining cyclic population dynamics and life history trait variations. The model, based on natural selection and density-dependent competition, accurately predicts Lepidoptera cycles and supports the Calder hypothesis.

Area of Science:

  • Ecology
  • Evolutionary Biology
  • Population Dynamics

Background:

  • Animal populations exhibit cyclic dynamics in abundance and life history traits.
  • Existing theories lack a unified equation explaining these cycles from basic ecological principles.

Purpose of the Study:

  • To deduce a population dynamic equation explaining cyclic abundance and life history trait variations.
  • To elucidate the mechanisms driving these cycles, whether evolutionary or plastic.

Main Methods:

  • Formulated a population dynamic equation based on density-dependent competitive interactions.
  • Integrated Fisher's fundamental theorem of natural selection as a foundational principle.
  • Model explains cycles through genotypic evolution or phenotypic plasticity.

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Main Results:

  • The derived equation explains cyclic dynamics in both population abundance and life history traits.
  • Predicted cycle periods align with observed Lepidoptera population cycles.
  • The Calder hypothesis (cycle period proportional to body mass to the 1/4 power) is derived from first principles.

Conclusions:

  • Density-dependent competition and natural selection provide a unified framework for understanding population cycles.
  • The model offers a mechanistic explanation for phase-related cycles in life history traits.
  • This work bridges population dynamics, evolutionary theory, and ecological constraints.