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

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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.