Moreover, current research suggests that many sets of ecological data cannot statistically justify complex models. That is, although nature may appear to be complicated, real data often cannot prove that more complicated models give a better description than simpler models (Hilborn and Mangel, 1996). Whether this is because nature really is simple, or because our data are noisy, is irrelevant for many practical purposes. The fact is that, if we want useful quantitative descriptions of nature, it is typically the case that we need fewer than 10 parameters.

Current work in ecological modeling thus emphasizes close connections between theory and data, and the use of mathematical models as statistical hypotheses about nature. As a result, models that were once viewed as being of only intellectual interest may well become useful in pest management. To make this point concrete, I will review my own work on a virus disease of a forest pest, the gypsy moth Lymantria dispar.

Ecological models of insect diseases began with a simple model by Anderson and May (1981), which started with a model for human epidemics and added population dynamics of insects and pathogens. Anderson and May used the model to make the general point that pathogens may drive the dynamics of forest insects capable of significant outbreaks such as the larch budmoth, Zeiraphera diniana. Further research on this and other insects has instead suggested first that single-factor explanations for forest insect population dynamics are probably generally insufficient, and second that pathogens are not always important players in the population dynamics of forest insects (Hunter and Dwyer, 1998). Nevertheless, even though the original generalization is too sweeping, features of Anderson and May's model have been useful for understanding insect pathogens.

Specifically, Anderson and May's model assumed that the rate of horizontal transmission of the virus increases linearly with the density of the pathogen. This assumption provided a useful quantitative hypothesis, and it is nonetheless interesting even though data show that it is often incorrect. For example, data for the transmission of the gypsy moth virus reject a linear model but cannot reject a nonlinear model (Dwyer et al., 1997). Additional experiments, however, suggested that this nonlinearity arises because of variability among the host insects in their susceptibility to the virus, and a model that allows for this variability can accurately predict the timing and intensity of virus epidemics (or epizootics) in naturally occurring gypsy moth populations. Surprisingly, the resulting model requires only four parameters.

Although this model arose from efforts to answer questions of basic research, it is beginning to have practical applications. For example, efforts are being made to genetically engineer this and other viruses. Consequently, a question of environmental concern is, “Will engineered virus strains outcompete wild-type strains, thereby altering the ecological balance between host and pathogen?” Because the model can predict epidemics from experimental transmission data, it can be used to assess the risks of releasing engineered strains before any such strains have been released (Dwyer et al., in press). Preliminary work has suggested that at least one deletion mutant of the gypsy moth virus is unlikely to be a superior competitor, and work is now advancing



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