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Alternative models for cyclic lemming dynamics.

Hao Wang1, Yang Kuang

  • 1Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA. wanghao@asu.edu

Mathematical Biosciences and Engineering : MBE
|July 31, 2007
PubMed
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Autonomous differential equations can effectively model lemming population cycles, suggesting seasonal factors are not the primary drivers. High predation and birth rates, coupled with low self-limitation, likely explain these population dynamics.

Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Natural population dynamics are often influenced by seasonal changes, typically modeled using nonautonomous differential equations.
  • High-amplitude, large-period fluctuations in lemming populations have been well-documented, prompting investigation into their underlying mechanisms.

Purpose of the Study:

  • To investigate whether autonomous differential equations can accurately capture the complex dynamics of lemming populations.
  • To identify the primary factors driving multi-year lemming cycles by analyzing the Barrow model.

Main Methods:

  • Developed a series of autonomous differential equation models based on the Barrow model for food-lemming interaction.
  • Utilized bifurcation analysis to examine the influence of various parameters on population dynamics.

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Main Results:

  • Demonstrated that an appropriately formulated autonomous system can approximate the moss-lemming dynamics observed at Point Barrow.
  • Bifurcation analysis indicated that seasonal factors and basic growth/death rates are unlikely to be the main causes of lemming cycles.

Conclusions:

  • Autonomous models can effectively represent complex population dynamics, including periodic solutions similar to those from nonautonomous models.
  • High lemming predation rates, high birth rates, and low self-limitation are suspected as the primary drivers of multi-year lemming cycles, rather than seasonal variations.