Importance of the predator's ecological neighborhood in modeling predationon migrating prey

Most mathematical descriptions of predator-prey interactions fail to take i nto account the spatio-temporal structures of the populations, which can le ad to errors or misinterpretations. For example, a compact pulse of prey mi grating through a field of quasi-stationary predators may not be well descr ibed by standard predator-prey models, because the predators and prey are u nlikely to be well mixed; that is, the prey may be exposed to only a fracti on of the predator population at a time. This underscores the importance of properly accounting for the ecological neighborhood, or effective feeding range, of predators in models. We illustrate this situation with a series o f models of salmon smolts migrating through a reservoir arrayed with predat ors. The reservoir is divided into a number of longitudinal compartments or spatial cells, the length of each cell representing the upstream-downstrea m range over which predators can forage. In this series of models a 100-km- long reservoir is divided, successively into 2, 5, 10, 25, 50, 100, 200, an d 400 cells, with respective cell lengths of 50, 20, 10, 4, 2, 1, 0.5, and 0.25 km. We used a detailed individual-based simulation model at first, but to ensure robustness of results we supplemented this with a simple analyti c model. Both models showed sharp differences in the predicted mortality to a compact pulse of smolt prey moving through the reservoir, depending on t he number of spatial cells in the model. In particular, models with fewer t han about 10 cells vastly overpredicted the amount of mortality due to pred ators with activity ranges of not more than a few kilometers. These results corroborate recent theoretical and simulation studies on the importance of spatial scale and behavior in modeling predator-prey dynamics.