Discrete-Time Models for Biological Invasions: Variability and Multispecies Interactions

Neubert 9973212 研究人员系统地发展和分析生物入侵的数学模型。 他们的目的是了解三个关键因素（物种相互作用，环境异质性和人口统计随机性）如何影响入侵过程。 模型采用非线性积分差分方程组的形式。 他们用一次新生的、生物学上简单的入侵的数据来测试他们的模型：在1980年爆发后，羽扇豆和它的毛虫食草动物扩散到了圣海伦斯山的浮石平原地区。 外来物种的入侵--像斑马贻贝、舞毒蛾和紫色金钱草--比以往任何时候都更频繁地发生。 在最近的一年，4.56亿外来植物被进口到美国。 这些入侵的生物和经济后果可能是戏剧性的;估计外来物种对农作物造成的损失高达数十亿美元。 控制外来物种传播的关键是科学地理解决定它们在景观中传播速度的因素。 获得这种理解的方法之一是通过使用入侵过程的数学模型。研究人员构建和分析的入侵模型包含了一个在其他研究中经常被忽略的重要生物学事实：入侵者与猎物互动，并且经常与同时引入的捕食者和竞争者互动。 他们用圣海伦火山爆发后发生的实际生物入侵的数据来测试他们的模型的预测。 他们从这些研究中获得的洞察力将帮助环境管理者更有效地处理入侵的外来害虫物种。该项目得到了应用数学和计算数学计划以及MPS多学科活动办公室和BIO种群生物学和生态学计划的支持。

Neubert9973212 The investigators systematically develop and analyzemathematical models of biological invasions. Their aim is tounderstand how three key factors (species interactions,environmental heterogeneity, and demographic stochasticity)affect the invasion process. The models take the form of systemsof nonlinear integrodifference equations. They test their modelswith data from a nascent, biologically simple invasion: thespread of lupine and its caterpillar herbivore into the PumicePlains region of Mount St. Helens following its 1980 eruption. Invasions by exotic species -- species like zebra mussels,gypsy moths, and purple loosestrife -- are occurring morefrequently than ever before. In one recent year, 456 millionexotic plants were imported into the United States. Thebiological and economic consequences of these invasions can bedramatic; estimates of the damage done to agricultural crops byexotic species run in the billions of dollars. A key tocontrolling the spread of exotic species is a scientificunderstanding of the factors that determine how fast they spreadacross the landscape. One way to obtain this understanding isthrough the use of mathematical models of the invasion process.The investigators construct and analyze invasion models thatincorporate an important biological reality that has often beenmissing in other studies: the fact that invaders interact bothwith their prey and often with simultaneously introducedpredators and competitors. They test the predictions of theirmodels with data from actual biological invasions that occurredin the wake of the eruption of Mount St. Helens. The insightthey gain from these studies will help environmental managersdeal more effectively with invading nonnative pest species.The project is supported by the programs of Applied Mathematicsand of Computational Mathematics and the Office ofMultidisciplinary Activities in MPS and by the programs ofPopulation Biology and of Ecology in BIO.