Game-Theoretic Methods for Functional Response and Optimal Foraging Behavior
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{"title"=>"Game-theoretic methods for functional response and optimal foraging behavior", "type"=>"journal", "authors"=>[{"first_name"=>"Ross", "last_name"=>"Cressman", "scopus_author_id"=>"7004645382"}, {"first_name"=>"Vlastimil", "last_name"=>"Křivan", "scopus_author_id"=>"7005974801"}, {"first_name"=>"Joel S.", "last_name"=>"Brown", "scopus_author_id"=>"7409448841"}, {"first_name"=>"József", "last_name"=>"Garay", "scopus_author_id"=>"7006975887"}], "year"=>2014, "source"=>"PLoS ONE", "identifiers"=>{"pui"=>"372643407", "sgr"=>"84896519707", "issn"=>"19326203", "pmid"=>"24586390", "scopus"=>"2-s2.0-84896519707", "doi"=>"10.1371/journal.pone.0088773"}, "id"=>"33b7d93a-db34-3f64-9d9d-dbc2434dd5b0", "abstract"=>"We develop a decision tree based game-theoretical approach for constructing functional responses in multi-prey/multi-patch environments and for finding the corresponding optimal foraging strategies. Decision trees provide a way to describe details of predator foraging behavior, based on the predator's sequence of choices at different decision points, that facilitates writing down the corresponding functional response. It is shown that the optimal foraging behavior that maximizes predator energy intake per unit time is a Nash equilibrium of the underlying optimal foraging game. We apply these game-theoretical methods to three scenarios: the classical diet choice model with two types of prey and sequential prey encounters, the diet choice model with simultaneous prey encounters, and a model in which the predator requires a positive recognition time to identify the type of prey encountered. For both diet choice models, it is shown that every Nash equilibrium yields optimal foraging behavior. Although suboptimal Nash equilibrium outcomes may exist when prey recognition time is included, only optimal foraging behavior is stable under evolutionary learning processes.", "link"=>"http://www.mendeley.com/research/gametheoretic-methods-functional-response-optimal-foraging-behavior-4", "reader_count"=>28, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>1, "Researcher"=>2, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>13, "Other"=>2, "Student > Master"=>3, "Student > Bachelor"=>1, "Professor"=>4}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>1, "Researcher"=>2, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>13, "Other"=>2, "Student > Master"=>3, "Student > Bachelor"=>1, "Professor"=>4}, "reader_count_by_subject_area"=>{"Unspecified"=>1, "Environmental Science"=>1, "Agricultural and Biological Sciences"=>21, "Psychology"=>1, "Computer Science"=>4}, "reader_count_by_subdiscipline"=>{"Psychology"=>{"Psychology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>21}, "Computer Science"=>{"Computer Science"=>4}, "Unspecified"=>{"Unspecified"=>1}, "Environmental Science"=>{"Environmental Science"=>1}}, "reader_count_by_country"=>{"Canada"=>1, "Luxembourg"=>1, "Malaysia"=>1, "Portugal"=>1, "Switzerland"=>1, "Germany"=>1}, "group_count"=>0}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1402609"], "description"=>"<p>The first level gives the prey encounter distribution. The second level gives the predator activity distribution. The final row of the diagram gives the probability of each predator activity event and so sum to . Since each entry here is simply the product of the probabilities along the path leading to this endpoint, we do not provide them in the decision trees from now on. With random prey distribution and large, and . If prey is the more profitable type, the edge in the decision tree corresponding to not attacking this type of prey is never followed at optimal foraging (indicated by the dotted edge in the tree). The reduced tree is then the resulting diagram with this edge removed.</p>", "links"=>[], "tags"=>["ecology", "theoretical ecology", "Evolutionary biology", "Animal behavior", "Population biology", "Population Dynamics", "Predator-prey dynamics", "Population modeling", "Theoretical biology", "Zoology", "Applied mathematics", "Decision theory", "game theory", "prey"], "article_id"=>947853, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Ross Cressman", "Vlastimil Křivan", "Joel S. Brown", "József Garay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0088773.g001", "stats"=>{"downloads"=>2, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_decision_tree_for_two_prey_types_/947853", "title"=>"The decision tree for two prey types.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-28 02:49:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/1402610"], "description"=>"<p>Panel (a) assumes that in which case the optimal strategy and NE is In panel (c), and the optimal strategy (and NE) is The arrows in each panel indicate the direction of increasing energy intake per unit time at points in the unit square. For completeness, the figure also includes the threshold case, panel (b), where (i.e. the density of prey is at the switching threshold). Although this case is rarely considered by ecologists, its inclusion here is important to understand the optimal outcomes in our more complicated models. In panel (b), the optimal strategy is where , corresponding to the solid right-hand edge of the unit square that forms a set of NE points.</p>", "links"=>[], "tags"=>["ecology", "theoretical ecology", "Evolutionary biology", "Animal behavior", "Population biology", "Population Dynamics", "Predator-prey dynamics", "Population modeling", "Theoretical biology", "Zoology", "Applied mathematics", "Decision theory", "game theory", "outcomes", "optimal", "foraging", "prey", "types", "probability", "profitable"], "article_id"=>947854, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Ross Cressman", "Vlastimil Křivan", "Joel S. Brown", "József Garay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0088773.g002", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Qualitative_outcomes_of_the_optimal_foraging_strategy_for_the_classical_foraging_model_1_with_two_prey_types_as_a_function_of_the_encounter_probability_with_the_most_profitable_prey_i_e_of_/947854", "title"=>"Qualitative outcomes of the optimal foraging strategy for the classical foraging model (1) with two prey types as a function of the encounter probability with the most profitable prey (i.e. of ).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-28 02:49:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/1402611"], "description"=>"<p>At optimal foraging, two edges of this tree diagram are never followed. These are indicated by dotted lines in the tree. The reduced tree is then the resulting diagram with these edges removed.</p>", "links"=>[], "tags"=>["ecology", "theoretical ecology", "Evolutionary biology", "Animal behavior", "Population biology", "Population Dynamics", "Predator-prey dynamics", "Population modeling", "Theoretical biology", "Zoology", "Applied mathematics", "Decision theory", "game theory", "simultaneous"], "article_id"=>947855, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Ross Cressman", "Vlastimil Křivan", "Joel S. Brown", "József Garay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0088773.g003", "stats"=>{"downloads"=>4, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_decision_tree_for_the_simultaneous_encounter_game_/947855", "title"=>"The decision tree for the simultaneous encounter game.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-28 02:49:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/1402612"], "description"=>"<p>In these plots, the energetic value of resource B varies in the interval from to (i.e. ). The critical values of are ; ; ; . The arrows in each panel indicate the direction of increasing energy intake per unit time at points in the unit square. In each case shown, these arrows lead to a single vertex indicated by the filled in circle which corresponds to the optimal foraging behavior (and unique NE). (a) For , and . Thus and . (b) For , and . Thus and . The dashed line denotes As increases, moves to the right until it coincides with the vertical line when . At this critical value of (not shown), all points on this vertical line are optimal foraging strategies (and NE). (c) For , and . Thus and . (d) For , and Thus and . The dashed line denotes (e) For , and . Thus and .</p>", "links"=>[], "tags"=>["ecology", "theoretical ecology", "Evolutionary biology", "Animal behavior", "Population biology", "Population Dynamics", "Predator-prey dynamics", "Population modeling", "Theoretical biology", "Zoology", "Applied mathematics", "Decision theory", "game theory", "qualitative", "outcomes", "optimal", "foraging"], "article_id"=>947856, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Ross Cressman", "Vlastimil Křivan", "Joel S. Brown", "József Garay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0088773.g004", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_All_qualitative_outcomes_of_the_optimal_foraging_strategy_8_and_10_with_parameters_/947856", "title"=>"All qualitative outcomes of the optimal foraging strategy (8) and (10) with parameters .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-28 02:49:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/1402613"], "description"=>"<p>Panel A assumes a larger handling time of prey type A (, ), while panel B assumes the opposite case (, ). Other parameters </p>", "links"=>[], "tags"=>["ecology", "theoretical ecology", "Evolutionary biology", "Animal behavior", "Population biology", "Population Dynamics", "Predator-prey dynamics", "Population modeling", "Theoretical biology", "Zoology", "Applied mathematics", "Decision theory", "game theory", "optimal", "foraging", "dashed", "profitable", "prey"], "article_id"=>947857, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Ross Cressman", "Vlastimil Křivan", "Joel S. Brown", "József Garay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0088773.g005", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dependence_of_the_optimal_foraging_strategy_8_solid_line_and_10_dashed_line_on_the_energy_content_of_the_less_profitable_prey_type_B_/947857", "title"=>"Dependence of the optimal foraging strategy ((8), solid line) and ((10), dashed line) on the energy content of the less profitable prey type B.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-28 02:49:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/1402614"], "description"=>"<p>In the reduced tree, the dotted edges are deleted.</p>", "links"=>[], "tags"=>["ecology", "theoretical ecology", "Evolutionary biology", "Animal behavior", "Population biology", "Population Dynamics", "Predator-prey dynamics", "Population modeling", "Theoretical biology", "Zoology", "Applied mathematics", "Decision theory", "game theory", "prey"], "article_id"=>947858, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Ross Cressman", "Vlastimil Křivan", "Joel S. Brown", "József Garay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0088773.g006", "stats"=>{"downloads"=>3, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Decision_tree_for_prey_recognition_game_/947858", "title"=>"Decision tree for prey recognition game.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-28 02:49:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/1402615"], "description"=>"<p>Panel (a) assumes for which and . The optimal foraging strategy is at (i.e. always pay the cost of recognition and then never attack the less profitable prey type) and the NE component (shown as the gray line segment) (corresponding to the NE outcome of attacking immediately) is suboptimal. In each of the other three panels, the (union of the) thick edges forms a strict equilibrium set (SES, for definition see section Zero-one rule and the Nash equilibrium of <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0088773#pone.0088773.s001\" target=\"_blank\">Appendix S1</a>) that is the globally stable evolutionary outcome. Panel (b) assumes , and . The union of the two edges and forms one NE component corresponding to optimal foraging behavior. Panel (c) assumes , and . The edge forms a NE component corresponding to optimal foraging behavior. Panel (d) assumes for which and The edge forms a NE component corresponding to optimal foraging behavior. The arrows in each panel indicate the direction of increasing energy intake per unit time at points in the unit square. Other parameters , , , and .</p>", "links"=>[], "tags"=>["ecology", "theoretical ecology", "Evolutionary biology", "Animal behavior", "Population biology", "Population Dynamics", "Predator-prey dynamics", "Population modeling", "Theoretical biology", "Zoology", "Applied mathematics", "Decision theory", "game theory", "outcomes", "optimal", "foraging"], "article_id"=>947859, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Ross Cressman", "Vlastimil Křivan", "Joel S. Brown", "József Garay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0088773.g007", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Qualitative_outcomes_of_the_optimal_foraging_strategy_13_and_14_for_increasing_recognition_time_/947859", "title"=>"Qualitative outcomes of the optimal foraging strategy (13) and (14) for increasing recognition time .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-28 02:49:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/1402616"], "description"=>"<div><p>We develop a decision tree based game-theoretical approach for constructing functional responses in multi-prey/multi-patch environments and for finding the corresponding optimal foraging strategies. Decision trees provide a way to describe details of predator foraging behavior, based on the predator's sequence of choices at different decision points, that facilitates writing down the corresponding functional response. It is shown that the optimal foraging behavior that maximizes predator energy intake per unit time is a Nash equilibrium of the underlying optimal foraging game. We apply these game-theoretical methods to three scenarios: the classical diet choice model with two types of prey and sequential prey encounters, the diet choice model with simultaneous prey encounters, and a model in which the predator requires a positive recognition time to identify the type of prey encountered. For both diet choice models, it is shown that every Nash equilibrium yields optimal foraging behavior. Although suboptimal Nash equilibrium outcomes may exist when prey recognition time is included, only optimal foraging behavior is stable under evolutionary learning processes.</p></div>", "links"=>[], "tags"=>["ecology", "theoretical ecology", "Evolutionary biology", "Animal behavior", "Population biology", "Population Dynamics", "Predator-prey dynamics", "Population modeling", "Theoretical biology", "Zoology", "Applied mathematics", "Decision theory", "game theory", "methods", "optimal", "foraging"], "article_id"=>947860, "categories"=>["Biological Sciences", "Mathematics"], "users"=>["Ross Cressman", "Vlastimil Křivan", "Joel S. Brown", "József Garay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0088773", "stats"=>{"downloads"=>1, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Game_Theoretic_Methods_for_Functional_Response_and_Optimal_Foraging_Behavior_/947860", "title"=>"Game-Theoretic Methods for Functional Response and Optimal Foraging Behavior", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2014-02-28 02:49:47"}

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