Modeling spatio-temporal pattern of biological invasions that involve short-and long-distance dispersals

入侵物种的范围扩张表现出不同的时空模式，这取决于生物的扩散和繁殖方式。为了定量地掌握入侵的空间格局及其扩散速度，我们构建了两种不同的数学模型，分别是：1)分层扩散模型和2)基于积分核的模型，分别用于处理短程和长距离扩散以及Allee效应和/或人口统计学随机性。通过对这些模型进行解析或数值求解，我们推导出了传播速率的公式，并利用它们来探索远距离传播和繁殖如何相互作用以加速传播速度，或者Allee效应或人口统计学随机性如何减慢传播速度。将上述两种模型的思想与细胞自动机模型相结合，对日本Inbaragi县松材萎蔫病的传播进行了模拟。松材枯萎病是由松材线虫引起的，松材线虫是松材刺虫的载体。甲虫的传播通常包括两种方式：短程传播和远距离传播。我们根据现场资料估计了远距离散布者在病媒（松锯蝽）种群中的比例。因此，我们得出结论，甲虫的传播距离对疾病的传播速度有重要影响，随着甲虫长距离传播的比例从零增加，疾病的传播速度急剧扩大。

The range expansion of an invading species shows a variety of spatio-temporal patterns depending on how the dispersal and reproduction of the organisms take place. To grasp the spatial pattern of invasion and its rate of spread quantitatively, we have constructed two different mathematical models that deal with short-and long-distance dispersals as well as the Allee effect and/or demographic stochasticity : 1)the stratified diffusion model and 2)the integral-kernel-based models. By solving these models either analytically or numerically, we derived formulae for the rate of spread and used them to explore how long-distance dispersal and reproduction interplay to accelerate the speed, or how the Allee effect or demographic stochasticity decelerates it.Integrating the ideas of the above two models together with a cell-automaton model, we carried out simulations for the spread of pine wilt disease in Inbaragi Prefecture, Japan. Pine wilt disease is caused by the pinewood nematode that is vectored by the pine sawyer beetle. The dispersal of the beetle often involves two modes, short-range dispersal and long-range dispersal. We estimated the proportion of long-range dispersers in the population of the disease vector (the pine sawyer beetle) on the basis of field data. Thus we concluded that the dispersal distance of beetles critically affects the expansion speed of the disease, which is sharply amplified, as the fraction of beetles undergoing long distance dispersal increases from zero.