title: Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework.
abstract: Understanding the exploration patterns of foragers in the wild provides fundamental insight into animal behavior. Recent experimental evidence has demonstrated that path lengths (distances between consecutive turns) taken by foragers are well fitted by a power law distribution. Numerous theoretical contributions have posited that "Lévy random walks"-which can produce power law path length distributions-are optimal for memoryless agents searching a sparse reward landscape. It is unclear, however, whether such a strategy is efficient for cognitively complex agents, from wild animals to humans. Here, we developed a model to explain the emergence of apparent power law path length distributions in animals that can learn about their environments. In our model, the agent's goal during search is to build an internal model of the distribution of rewards in space that takes into account the cost of time to reach distant locations (i.e., temporally discounting rewards). For an agent with such a goal, we find that an optimal model of exploration in fact produces hyperbolic path lengths, which are well approximated by power laws. We then provide support for our model by showing that humans in a laboratory spatial exploration task search space systematically and modify their search patterns under a cost of time. In addition, we find that path length distributions in a large dataset obtained from free-ranging marine vertebrates are well described by our hyperbolic model. Thus, we provide a general theoretical framework for understanding spatial exploration patterns of cognitively complex foragers.
authors.affiliation: Department of Psychiatry, University of North Carolina, Chapel Hill, NC 27599; Neuroscience Center, University of North Carolina, Chapel Hill, NC 27599;
authors.forename: Vijay Mohan K
authors.initials: VM
authors.lastname: Namboodiri
authors.affiliation: Department of Neuroscience, Johns Hopkins University, Baltimore, MD 21205;
authors.forename: Joshua M
authors.initials: JM
authors.lastname: Levy
authors.affiliation: Allen Institute for Brain Science, Seattle, WA 98109;
authors.forename: Stefan
authors.initials: S
authors.lastname: Mihalas
authors.affiliation: Marine Biological Association of the United Kingdom, The Laboratory, Plymouth PL1 2PB, United Kingdom; Ocean and Earth Science, National Oceanography Centre Southampton, University of Southampton, Southampton SO14 3ZH, United Kingdom; Centre for Biological Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom.
authors.forename: David W
authors.initials: DW
authors.lastname: Sims
authors.affiliation: Department of Neuroscience, Johns Hopkins University, Baltimore, MD 21205; shuler@jhmi.edu.
authors.forename: Marshall G
authors.initials: MG
authors.lastname: Hussain Shuler
mesh_terms: D000328:Adult; D000465:Algorithms; D000818:Animals; D000835:Animals, Wild; D017753:Ecosystem; D005106:Exploratory Behavior / Q000502:physiology*; D005247:Feeding Behavior / Q000502:physiology*; D020387:Food Chain; D006801:Humans; D008386:Marine Biology / Q000379:methods; D008962:Models, Theoretical; D011235:Predatory Behavior / Q000502:physiology*; D013037:Spatial Behavior / Q000502:physiology*; D055815:Young Adult
keywords: Lévy walks; decision making; foraging theory; optimal search; temporal discounting