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Aggregation unveiled: A sequential modelling approach to bark beetle outbreaks.

Mahdi Salehzadeh1, John M Stockie1, Ailene MacPherson1

  • 1Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, V5A 1S6, British Columbia, Canada.

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Bark beetle outbreaks cause widespread forest mortality. This study introduces a new model showing beetle aggregation significantly impacts outbreak risk, depending on both emergence rate and initial density.

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Area of Science:

  • Ecology
  • Forestry
  • Epidemiology

Background:

  • Tree-killing bark beetles cause significant coniferous forest mortality, impacting ecosystems and services.
  • Predictive models for bark beetle outbreaks are vital for forest management and conservation.
  • The non-linear interaction between beetle aggregation and host defenses makes outbreak dynamics poorly understood.

Purpose of the Study:

  • To develop a mathematically tractable model for bark beetle aggregation within an epidemiological framework.
  • To investigate how beetle aggregation influences outbreak probability and severity.
  • To determine the critical factors triggering bark beetle outbreaks.

Main Methods:

  • Applied the principle of distributed delays to model beetle aggregation.
  • Developed a novel epidemiological framework for bark beetle dynamics.
  • Utilized a stochastic model to validate deterministic predictions in finite populations.

Main Results:

  • Derived a critical outbreak threshold based on the beetle emergence rate, analogous to R0.
  • Demonstrated that beetle aggregation alters outbreak potential, making it dependent on both emergence rate and initial beetle density.
  • Confirmed the robustness of deterministic model predictions through stochastic simulations.

Conclusions:

  • Beetle aggregation is a critical factor modulating bark beetle outbreak dynamics.
  • The developed model provides new insights into predicting and managing bark beetle infestations.
  • Understanding these epidemiological interactions is key to mitigating forest loss.