RUI: The Dynamics of Biological Invasions

Western Washington University, Bellingham WA

Investigators

Abstract

Schreiber 0077986 The investigator develops mathematical methods for difference and differential equation models to better predict under what conditions biological invasions succeed and the implications of successful invasions on the structure of ecological communities. An emphasis is placed on methods that are robust to structural perturbations of the population equations and that apply to systems with nonlinear dynamics (e.g., periodicity, quasiperiodicity, and chaos). The methods involve the use and development of techniques from smooth ergodic theory. Application of these methods to models of host-parasitoid interactions and tritrophic food webs is pursued. Two aspects of host-parasitoid interactions are examined. First, because parasitoids experience egg limitation when released in systems with highly variable host densities (the typical situation when an exotic insect has reached pest status), a model of host-parasitoid interactions that incorporates this egg-limitation is considered. As successful biological control only occurs after a parasitoid population has established itself, the proposed analysis of the model intends to determine how variability in the dynamics of the host population influences the invasion rate of the parasitoid population. Second, previous work on the coevolution of patch selection strategies in host-parasitoid systems is extended to include two important biological factors, the sex-allocation strategies of parasitoids and plant dynamics. The key issue is whether the manipulation of crop heterogeneity can lead to the coevolution of behavioral traits that simultaneously stabilize the system and increase crop yields. Third, to better understand how ecological communities assemble due to invasions, this proposal undertakes the study of tritrophic systems with more than one species at each trophic level. In these systems, three ecological forces (apparent competition, resource competition and intraguild predation) play an important role and can lead to successional intransitivites (e.g., a sequence of invasions that takes community A to community B, B to C and C back to A). Emphasis is placed on the influence of habitat productivity and the timing of invasions on the community assembly process. In addition, the project includes a program designed to stimulate undergraduate research. Invading non-native species in the United States cause estimated economic losses of 138 billion dollars annually in agriculture, forestry and several other segments of the U.S. economy. Exotic insect species alone are estimated to cause 13 billion dollars in crop losses annually and approximately 42% of the species on the threatened or endangered species lists are at risk primarily because of nonnative species. As biological invasions often involve nonlinear interactions between several species, mathematical models, as simple caricatures, allow one to inexpensively answer questions such as: What characteristics make a species a successful invader? Which ecological communities are most susceptible to large long-term changes following an invasion? How can crop heterogeneity be manipulated to minimize the economic impact of non-native pests? The project proposes to develop analytical methods, and to apply these methods to models that address these and other questions of current interest to community ecology, restoration ecology, biological control, and evolutionary biology.