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A dynamical model for bark beetle outbreaks
Vlastimil Křivan1, Mark Lewis2, Barbara J Bentz3
1Institute of Entomology, Biology Centre, Czech Academy of Sciences, Branišovská 31, 370 05 České Budějovice, Czech Republic; Faculty of Sciences, University of South Bohemia, Branišovská 1760, 370 05 České Budějovice, Czech Republic.
Journal of Theoretical Biology
|July 12, 2016
Summary
Mathematical models reveal how environmental changes and beetle behavior drive forest outbreaks. Bark beetle populations can lead to forest recovery or endemic states, with intermediate rates causing bistability and hysteresis.
Area of Science:
- Forest Ecology
- Mathematical Modeling
- Epidemiology
Background:
- Bark beetles are significant disturbances in coniferous forests.
- Climate change impacts tree resistance and beetle outbreak dynamics.
- Nonlinear interactions, including beetle aggregation, complicate forest-beetle systems.
Purpose of the Study:
- To develop a novel mathematical model for bark beetle outbreaks.
- To analyze the influence of tree resistance and beetle aggregation on outbreak dynamics.
- To investigate beetle population dynamics under varying immigration and environmental conditions.
Main Methods:
- Developed a mathematical model analogous to epidemiological models.
- Applied singular perturbation methods to simplify the multiscale dynamical system.
- Incorporated a seed-bank for tree recruitment and considered two immigration scenarios.
Main Results:
- Low beetle immigration allows forest recovery; high immigration leads to endemic equilibrium.
- Intermediate immigration rates predict bistability, resulting in either a healthy or endemic forest state.
- Model demonstrates hysteresis and shows how less resistant stands can facilitate regional outbreaks.
Conclusions:
- The model captures complex bark beetle outbreak dynamics, including bistability and hysteresis.
- Environmental factors and beetle behavior critically influence forest ecosystem stability.
- Understanding these dynamics is crucial for managing forest health under climate change.
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