RUI: The Dynamics of Biological Invasions

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Schreiber0077986 The investigator develops mathematical methods fordifference and differential equation models to better predictunder what conditions biological invasions succeed and theimplications of successful invasions on the structure ofecological communities. An emphasis is placed on methods that arerobust to structural perturbations of the population equationsand that apply to systems with nonlinear dynamics (e.g.,periodicity, quasiperiodicity, and chaos). The methods involvethe use and development of techniques from smooth ergodic theory.Application of these methods to models of host-parasitoidinteractions and tritrophic food webs is pursued. Two aspects ofhost-parasitoid interactions are examined. First, becauseparasitoids experience egg limitation when released in systemswith highly variable host densities (the typical situation whenan exotic insect has reached pest status), a model ofhost-parasitoid interactions that incorporates thisegg-limitation is considered. As successful biological controlonly occurs after a parasitoid population has established itself,the proposed analysis of the model intends to determine howvariability in the dynamics of the host population influences theinvasion rate of the parasitoid population. Second, previous workon the coevolution of patch selection strategies inhost-parasitoid systems is extended to include two importantbiological factors, the sex-allocation strategies of parasitoidsand plant dynamics. The key issue is whether the manipulation ofcrop heterogeneity can lead to the coevolution of behavioraltraits that simultaneously stabilize the system and increase cropyields. Third, to better understand how ecological communitiesassemble due to invasions, this proposal undertakes the study oftritrophic systems with more than one species at each trophiclevel. In these systems, three ecological forces (apparentcompetition, resource competition and intraguild predation) playan important role and can lead to successional intransitivites(e.g., a sequence of invasions that takes community A tocommunity B, B to C and C back to A). Emphasis is placed on theinfluence of habitat productivity and the timing of invasions onthe community assembly process. In addition, the project includesa program designed to stimulate undergraduate research. Invading non-native species in the United States causeestimated economic losses of 138 billion dollars annually inagriculture, forestry and several other segments of the U.S.economy. Exotic insect species alone are estimated to cause 13billion dollars in crop losses annually and approximately 42% ofthe species on the threatened or endangered species lists are atrisk primarily because of nonnative species. As biologicalinvasions often involve nonlinear interactions between severalspecies, mathematical models, as simple caricatures, allow one toinexpensively answer questions such as: What characteristics makea species a successful invader? Which ecological communities aremost susceptible to large long-term changes following aninvasion? How can crop heterogeneity be manipulated to minimizethe economic impact of non-native pests? The project proposes todevelop analytical methods, and to apply these methods to modelsthat address these and other questions of current interest tocommunity ecology, restoration ecology, biological control, andevolutionary biology.