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Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework

Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework
Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework
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.
Lévy walks, temporal discounting, optimal search, decision making, foraging theory
0027-8424
8747-8752
Namboodiri, Vijay Mohan K.
c82fd5f8-4f7d-4541-88b3-77aebbc6bdf0
Levy, Joshua M.
877ec004-ede3-4161-8fd5-6f6799c3e8fb
Mihalas, Stefan
2926eb78-8b4e-4b35-a53f-328182fa5c60
Sims, David W.
7234b444-25e2-4bd5-8348-a1c142d0cf81
Hussain Shuler, Marshall G.
b4e288bb-eda8-4d55-93b1-2b4645c3b82a
Namboodiri, Vijay Mohan K.
c82fd5f8-4f7d-4541-88b3-77aebbc6bdf0
Levy, Joshua M.
877ec004-ede3-4161-8fd5-6f6799c3e8fb
Mihalas, Stefan
2926eb78-8b4e-4b35-a53f-328182fa5c60
Sims, David W.
7234b444-25e2-4bd5-8348-a1c142d0cf81
Hussain Shuler, Marshall G.
b4e288bb-eda8-4d55-93b1-2b4645c3b82a

Namboodiri, Vijay Mohan K., Levy, Joshua M., Mihalas, Stefan, Sims, David W. and Hussain Shuler, Marshall G. (2016) Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework. Proceedings of the National Academy of Sciences, 113 (31), 8747-8752. (doi:10.1073/pnas.1601664113).

Record type: Article

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.

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More information

Accepted/In Press date: 26 May 2016
e-pub ahead of print date: 6 July 2016
Published date: 2 August 2016
Keywords: Lévy walks, temporal discounting, optimal search, decision making, foraging theory
Organisations: Ocean and Earth Science

Identifiers

Local EPrints ID: 400466
URI: http://eprints.soton.ac.uk/id/eprint/400466
ISSN: 0027-8424
PURE UUID: e8a35abc-13e9-4d02-8aee-8536522b9177

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Date deposited: 14 Sep 2016 15:27
Last modified: 08 Jan 2022 12:41

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Contributors

Author: Vijay Mohan K. Namboodiri
Author: Joshua M. Levy
Author: Stefan Mihalas
Author: David W. Sims
Author: Marshall G. Hussain Shuler

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