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，一种在日本广泛地区已经传播的松木疾病已经传播了几十年。该疾病是由松木线虫，木叶氏菌（Bursaphelenchus xylophilus）引起的，木质丝虫（Pine Sawyer）是载体，替代品。我们提出了一个数学模型，以描述松树和松树锯豆之间的宿主 - 寄生虫相互作用，这些锯齿携带了线虫，这些模型基于关于松树锯豆的种群动态的详细数据以及日本西北海岸的研究地点的松木疾病的发生率。通过分析该模型，我们模拟了疾病发生率的时间变化，并预测如何通过消除松树锯剂来控制流行病。主要结果是：1）最初的松树密度的最低阈值可成功入侵该疾病。但是，即使松密度超过最小阈值，由于松（Pine Sawyer）的密度非常低时，该疾病由于松（Pine Sawyer）的合同作用而在侵袭中失败。 2）最小阈值密度随着根除率的增加而不成比例地增加。 3）健康树从感染中逃脱直到流行病的概率随着初始松体密度的增加而急剧减少，而消除率很低。2。我们分析了入侵物种的扩展范围，并得出了一种物种持久性的条件，两种零散的环境：（1）将环境分割成皮带，具有良好且不利的斑块。（2）在水平和垂直轴上分段的环境，在水平轴和垂直轴上分布，并在水平形状和方形的良好的斑点中有正常分布的环境。