Sequential decision-making in a variable environment: Modeling elk movement in Yellowstone National Park as a dynamic game

We develop a suite of models with varying complexity to predict elk movement behavior during the winter on the Northern Range of Yellowstone National Park (YNP). The models range from a simple representation of optimal patch choice to a dynamic game, and we show how the underlying theory in each is related by the presence or absence of state- and frequency-dependence. We compare predictions from each of the models for three variables that are of basic and applied interest: elk survival, aggregation, and use of habitat outside YNP. Our results suggest that despite low overall forage depletion in the winter, frequency-dependence is crucial to the predictions for elk movement and distribution. Furthermore, frequency-dependence interacts with mass-dependence in the predicted outcome of elk decision-making. We use these results to show how models that treat single movement decisions in isolation from the seasonal sequence of decisions are insufficient to capture landscape scale behavior.