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Mathematical Study of Spatial Spread of Biological Invasion

生物入侵空间传播的数学研究

基本信息

批准号：
08640804
负责人：
SHIGESADA Nanako
金额：
$ 1.6万
依托单位：
Nara Women's University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1997
项目状态：
已结题

项目摘要

1. An epidemic of pine wilt disease has been spreading in wide areas of Japan for several decades. The disease is caused by the pinewood nematode, Bursaphelenchus xylophilus, which the pine sawyer, Monochamus alternatus, as vector. We present a mathematical model to describe the host-parasite interaction between pines and pine sawyers carrying nematodes based on detailed data on the population dynamics of pine sawyers and the incidence of pine wilt disease at a study site located on the northwest coast of Japan. By analyzing the model we simulate the temporal change in the incidence of the disease and predict how the epidemic could be controlled by eradication of the pine sawyer. The main results are : 1) There is a minimum threshold of the initial pine density for successful invasion of the disease. However, even if the pine density exceeds the minimum threshold, the disease fails in invasion due to the Allee effect of the pine sawyer when its density is very low. 2) The minimum threshold density increases disproportionately with increase in the eradication rate. 3) The probability for a healthy tree to escape from infection until the epidemic dies out decreases sharply with increase in the initial pine density, when the eradication rate is low.2. We analyzed the range expansion of an invading species and derived the conditions for persistence of a species two kinds of fragmented environments :(1) an environment segmented into belts, with favorable and unfavorable patches arranged alterately.(2) an environment segmented in both horizontal and vertical axs, with square-shaped favorable patches regularly distributed within the unfavorable environment.

1. 几十年来，松树枯萎病一直在日本的广大地区蔓延。本病是由松材线虫引起的，松材线虫以松锯蝇（Monochamus alternatus）为媒介。基于对日本西北海岸松材线虫种群动态和松材枯萎病发病率的详细数据，提出了一个描述松材线虫与松材线虫之间寄主-寄生虫相互作用的数学模型。通过对模型的分析，我们模拟了该疾病发病率的时间变化，并预测了如何通过根除松树来控制该流行病。主要结果是：1)存在一个林木初始密度的最小阈值，使病害能够成功侵袭；然而，即使松材密度超过最小阈值，当松材密度很低时，由于松材的Allee效应，病害也无法入侵。2)最小阈值密度随根除率的增加而不成比例地增加。(3)当根治率较低时，随着初始松木密度的增加，健康树木躲过感染直至疫情消失的概率急剧下降。分析了入侵物种的活动范围扩展，得出了两种破碎化环境的生存条件：(1)有利斑块和不利斑块交替排列的带状环境。(2)在水平轴和垂直轴上分割的环境，在不利环境中有规律地分布方形的有利斑块。