Navigating the Landscape of Fear

Animals searching for food must navigate through complex landscapes with varying terrain, food availability, predator activity, and shelter. One method for analyzing how foraging animals balance these competing interests is Optimal Foraging Theory, which posits that foragers make decisions that maximize some expected reward or utility. However, models have generally focused on simplified settings, especially regarding animal movement decisions, either ignoring spatial variability entirely or limiting the forager’s options to choosing among a few discrete habitat patches (or patch types) that are modeled as spatially uniform. In this paper, we present a model of optimal foraging in a continuous landscape for an animal that is subject to predation. Foraging animals thus must choose not only where to gather food, but also how to (safely) travel across the landscape. Furthermore, we explicitly model stochastic predator interactions, allowing us to predict optimal foraging trajectories conditional on the presence or absence of an immediate threat from a predator. We illustrate our model with numerical examples, one a hypothetical landscape with two regions of high food abundance and two areas of high predation risk on the direct route between the feeding areas and the forager’s overnight refuge, the other inspired by empirical data on foraging Samango monkeys ( Cercopithecus albogularis schwarzi ). We find that the shape of a forager’s utility function affects not only where it chooses to feed, but also the paths it takes to and from the optimal feeding ground. Thus, examining predicted optimal trajectories can provide additional information about what quantity, if any, animals optimize while foraging. We also develop and demonstrate a preliminary model for an animal that depletes the food supply in its local environment.