A Dynamical Model for Bark Beetle Outbreaks

  • Author(s) / Creator(s)
  • 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
  • Subjects / Keywords
  • Type of Item
    Article (Draft / Submitted)
  • DOI
  • License
    Attribution-NonCommercial 4.0 International