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

Most mathematical descriptions of predator-prey interactions fail to take into account the spatio-temporal structures of the populations, which can lead to errors or misinterpretations. For example, a compact pulse of prey migrating through a field of quasi-stationary predators may not be well described by standard predator-prey models, because the predators and prey are unlikely to be well mixed; that is, the prey may be exposed to only a fraction 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 of models of salmon smolts migrating through a reservoir arrayed with predators. The reservoir is divided into a number of longitudinal compartments or spatial cells, the length of each cell representing the upstream-downstream 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, and 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 analytic model. Both models showed sharp differences in the predicted mortality to a compact pulse of smolt prey moving through the reservoir, depending on the number of spatial cells in the model. In particular, models with fewer than about 10 cells vastly overpredicted the amount of mortality due to predators 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.