Invasion theory and biological control

William F. Fagan Mark A. Lewis Michael G. Neubert and P. van den Driessche Department of Biology, Arizona State University, Tempe, AZ 85287±1501, USA. Tel. 480-965-8263. Fax +480-965-2519. E-mail [email protected] Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA. Current Address: Department Mathematical Sciences and Department Biological Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada. Biology Department, Woods Hole Oceanographic Institution, Woods Hole, MA 02543±1049, USA. Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3P4, Canada Abstract Recent advances in the mathematical theory of invasion dynamics have much to offer to biological control. Here we synthesize several results concerning the spatiotemporal dynamics that occur when a biocontrol agent spreads into a population of an invading pest species. We outline conditions under which specialist and generalist predators can in ̄uence the density and rate of spatial spread of the pest, including the rather stringent conditions under which a specialist predator can successfully reverse a pest invasion. We next discuss the connections between long distance dispersal and invasive spread, emphasizing the different consequences of fast spreading pests and predators. Recent theory has considered the effects of population stage-structure on invasion dynamics, and we discuss how population demography affects the biological control of invading pests. Because low population densities generally characterize early stages of an invasion, we discuss the lessons invasion theory teaches concerning the detectability of invasions. Stochasticity and density-dependent dynamics are common features of many real invasions, in ̄uencing both the spatial character (e.g. patchiness) of pest invasions and the success of biocontrol agents. We conclude by outlining theoretical results delineating how stochastic effects and complex dynamics generated by density dependence can facilitate or impede biological pest control.