Powell J, Kennedy B, White P, Bentz B, Logan J, Roberts D
Department of Mathematics and Statistics, Utah State University, Logan, UT 84322-3900, USA.
J Theor Biol. 2000 Jun 21;204(4):601-20. doi: 10.1006/jtbi.2000.1080.
Three different mathematical approaches are combined to develop a spatial framework in which risk of mountain pine beetle (MPB) attack on individual hosts may be assessed. A density-based partial differential equation model describes the dispersal and focusing behavior of MPB. A local projection onto a system of ordinary differential equations predicts the consequences of the density equations at individual hosts. The bifurcation diagram of these equations provides a natural division into categories of risk for each host. A stem-competition model links host vigor to stand age and demographics. Coupled together, these models illuminate spatial risk structures which may also shed light on the role of climatic variables in population outbreaks. Preliminary results suggest that stand microclimate has much greater influence on risk of attack than host vigor and stand age.
结合三种不同的数学方法来构建一个空间框架，在该框架中可以评估单株寄主遭受山松甲虫（MPB）攻击的风险。基于密度的偏微分方程模型描述了山松甲虫的扩散和聚集行为。对常微分方程组的局部投影预测了密度方程在单株寄主上的结果。这些方程的分岔图为每个寄主的风险类别提供了自然划分。一个树干竞争模型将寄主活力与林分年龄和种群统计学联系起来。这些模型结合在一起，阐明了空间风险结构，这也可能有助于揭示气候变量在种群爆发中的作用。初步结果表明，林分小气候对攻击风险的影响远大于寄主活力和林分年龄。
