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DYNAMICS OF AN LPAA MODEL FOR TRIBOLIUM GROWTH: INSIGHTS INTO POPULATION CHAOS.

Samantha J Brozak1, Sophia Peralta2, Tin Phan3

  • 1School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ.

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|November 28, 2024
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Summary

Flour beetles exhibit complex population dynamics. While chaos is possible, this study suggests it

Keywords:
37N2592B05LPA modelTriboliumdiscrete modelflour beetlematrix model

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Area of Science:

  • Mathematical Biology
  • Ecological Research
  • Population Dynamics

Background:

  • Flour beetles (Tribolium) are established model organisms in ecological and mathematical biology research.
  • Previous work utilized the larvae-pupae-adult (LPA) model to induce chaos in laboratory beetle populations.
  • The intrinsic propensity of flour beetles to exhibit chaotic dynamics remains an open question.

Purpose of the Study:

  • To extend the LPA model by incorporating adult population stratification and mature adult cannibalism.
  • To analyze the population dynamics of flour beetles using a refined mathematical model.
  • To investigate the conditions under which chaotic behavior may arise in flour beetle populations.

Main Methods:

  • Developed an extended LPA model with stratified adults (newly emerged and mature) and mature adult cannibalism.
  • Fitted the model to longitudinal data of larvae, pupae, and adult flour beetle populations.
  • Performed local and global stability analyses for steady states and numerical exploration of bifurcations and limit cycles.

Main Results:

  • The extended LPA model successfully recapitulated the transient population dynamics of flour beetles.
  • Stability analyses revealed conditions for trivial and positive steady states.
  • Numerical simulations indicated that chaos is a rare phenomenon within experimentally derived parameter ranges.

Conclusions:

  • The refined LPA model provides a better fit to flour beetle population dynamics.
  • Chaos in flour beetle populations is unlikely to be an intrinsic property under typical experimental conditions.
  • Environmental factors, such as media changes and censusing, are more likely triggers for induced chaos.