A Bayesian model of navigation in squirrels

A Bayesian model of navigation in squirrels Anna S. Waisman (annawais@uw.edu) Institute for Learning and Brain Sciences, Portage Bay Building, Room 450 Seattle, WA 98195 USA Christopher G. Lucas (cglucas@gmail.com) Department of Educational Psychology, Baker Hall 342c Pittsburgh, PA 15213 USA Thomas L. Griffiths (tom_griffiths@berkeley.edu) Lucia F. Jacobs (jacobs@berkeley.edu) Department of Educational Psychology, 3210 Tolman Hall #1650 Berkeley, CA 94720 USA Abstract Fox squirrels have an impressive ability to remember the location of stored food. In doing so, they combine information from landmarks of different types. We deﬁne a Bayesian model that indicates how an ideal observer would optimally integrate landmark cues, and fit this model to the decisions made by squirrels in a spatial memory task. The resulting model provides a unifying framework for characterizing different strategies to cue integration, and a tool for investigating the circumstances under which particular cues are used. We show that the best fitting models changed depending on the season at testing and the details of the task. These analyses support previous claims that squirrels adopt flexible strategies in landmark use. Keywords: spatial cognition; Bayesian modeling; spatial memory; animal cognition; navigation Introduction Animals of many kinds display remarkable skill at spatial navigation, and formal models of how animals navigate have many potential uses. For example, one can use them to develop robots capable of autonomous movement (Thrun, 2005) and to aid in designing new animal conservation principles (Fevre, Bronsvoort, Hamilton & Cleaveland, 2006; Simons, 2004). In this paper, we analyze the problem of identifying a spatial location from memory as a kind of Bayesian inference. This approach provides a way to quantify degrees of belief and uncertainty, and thus provides a natural framework in which to develop an “ideal observer” model. In cases where multiple kinds of landmarks are available, the Bayesian approach allows us to take into account the perceived reliabilities of each landmark or landmark type. This information can be used to identify the location most consistent with the animal’s memory. Formalizing spatial memory in these terms gives us a tool for identifying which types of landmarks animals use in navigation, what factors influence the use of these landmarks, and what kinds of strategies animals are using based on how they use those landmarks in combination. Birds and other animals that are either nectar-feeding or store food have excellent spatial memory abilities due to natural selection pressures, and have often been used in spatial memory experiments. Traditionally, such animals have been described as using landmarks in a hierarchical fashion by which the animal works its way down its preference hierarchy of landmark types until it finds the rewarded location (Brodbeck, 1994; Clayton & Krebs, 1994; Herz, Zanette & Sherry 1994). Bats, hummingbirds, and squirrels have shown such preference hierarchies (Healy & Hurly, 1998; Jacobs & Shiflett, 1999; Thiele & Winter, 2005; Vlasak, 2006a). This traditional hierarchical model has recently been challenged by converging evidence in favor of the plasticity of landmark use in both mammals and birds (Pigeons: Legge, Spetch & Batty, 2009; Chickadees: LaDage, Roth, Fox & Pravosudov, 2009; Flying Squirrel: Gibbs, Lea & Jacobs, 2007; Fox Squirrel: Waisman & Jacobs, 2008). We were interested in exploring in more detail how different combinations of landmark types trade off in guiding search behavior and whether animals might be using Bayesian inference to determine their search strategy. This would explain the flexibility in their search strategies, and predict their strategies in a wide range of novel situations. The plan of the paper is as follows. In the first section, we briefly explain the general structure of a Bayesian model of landmark use. In the second section, we describe a series of cue combination experiments with squirrels and the specific model that we used to characterize their behavior. In the third section, we demonstrate how the model can be used to examine factors that influence the use of landmarks. The final section concludes the paper. A Bayesian analysis of cue combination in squirrel spatial navigation To construct a Bayesian model of squirrel spatial navigation we must first define the problem of squirrel spatial navigation in Bayesian terms. For simplicity, the model presented here will focus on the navigation problem encountered by a single species – the fox squirrel. A squirrel must rely on environmental landmarks and its memory of those landmarks when searching for food. Environments change and a squirrel’s memory has finite precision. This leads to a navigational problem for which the ideal solution