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A Dynamical Model for Bark Beetle Outbreaks
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- Author(s) / Creator(s)
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Tree-killing bark beetles are major disturbance agents affecting coniferous forest ecosystems. The
role of environmental conditions on driving beetle outbreaks is becoming increasingly important as
global climatic change alters environmental factors, such as drought stress, that, in turn, govern tree
resistance. Furthermore, dynamics between beetles and trees are highly nonlinear, due to complex
aggregation behaviors exhibited by beetles attacking trees. Models have a role to play in helping
unravel the effects of variable tree resistance and beetle aggregation on bark beetle outbreaks.
In this article we develop a new mathematical model for bark beetle outbreaks using an analogy
with epidemiological models. Because the model operates on several distinct time scales, singular
perturbation methods are used to simplify the model. The result is a dynamical system that tracks
populations of uninfested and infested trees. A limiting case of the model is a discontinuous function
of state variables, leading to solutions in the Filippov sense. The model assumes an extensive seedbank
so that tree recruitment is possible even if trees go extinct. Two scenarios are considered for
immigration of new beetles. The first is a single tree stand with beetles immigrating from outside
while the second considers two forest stands with beetle dispersal between them. For the seed-bank
driven recruitment rate, when beetle immigration is low, the forest stand recovers to a beetle-free
state. At high beetle immigration rates beetle populations approach an endemic equilibrium state.
At intermediate immigration rates, the model predicts bistability as the forest can be in either of
the two equilibrium states: a healthy forest, or a forest with an endemic beetle population. The
model bistability leads to hysteresis. Interactions between two stands show how a less resistant
stand of trees may provide an initial toe-hold for the invasion, which later leads to a regional beetle
outbreak in the resistant stand. -
- Date created
- 2016-06-13
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- Type of Item
- Article (Draft / Submitted)