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

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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.