Fermat’s Principle of Least Time Predicts Refraction of Ant Trails at Substrate Borders
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{"title"=>"Fermat's Principle of Least Time Predicts Refraction of Ant Trails at Substrate Borders", "type"=>"journal", "authors"=>[{"first_name"=>"Jan", "last_name"=>"Oettler", "scopus_author_id"=>"15923686100"}, {"first_name"=>"Volker S.", "last_name"=>"Schmid", "scopus_author_id"=>"26531803700"}, {"first_name"=>"Niko", "last_name"=>"Zankl", "scopus_author_id"=>"55627377500"}, {"first_name"=>"Olivier", "last_name"=>"Rey", "scopus_author_id"=>"35180461400"}, {"first_name"=>"Andreas", "last_name"=>"Dress", "scopus_author_id"=>"57197170815"}, {"first_name"=>"Jürgen", "last_name"=>"Heinze", "scopus_author_id"=>"7103141463"}], "year"=>2013, "source"=>"PLoS ONE", "identifiers"=>{"sgr"=>"84875198855", "doi"=>"10.1371/journal.pone.0059739", "issn"=>"19326203", "pui"=>"368562432", "pmid"=>"23527263", "scopus"=>"2-s2.0-84875198855"}, "id"=>"ed6718db-6a25-3251-8379-6a539f09a3d8", "abstract"=>"Fermat's principle of least time states that light rays passing through different media follow the fastest (and not the most direct) path between two points, leading to refraction at medium borders. Humans intuitively employ this rule, e.g., when a lifeguard has to infer the fastest way to traverse both beach and water to reach a swimmer in need. Here, we tested whether foraging ants also follow Fermat's principle when forced to travel on two surfaces that differentially affected the ants' walking speed. Workers of the little fire ant, Wasmannia auropunctata, established \"refracted\" pheromone trails to a food source. These trails deviated from the most direct path, but were not different to paths predicted by Fermat's principle. Our results demonstrate a new aspect of decentralized optimization and underline the versatility of the simple yet robust rules governing the self-organization of group-living animals.", "link"=>"http://www.mendeley.com/research/fermats-principle-least-time-predicts-refraction-ant-trails-substrate-borders", "reader_count"=>48, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>2, "Researcher"=>9, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>15, "Student > Postgraduate"=>2, "Student > Master"=>3, "Other"=>7, "Student > Bachelor"=>3, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>2, "Professor"=>3}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>2, "Researcher"=>9, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>15, "Student > Postgraduate"=>2, "Student > Master"=>3, "Other"=>7, "Student > Bachelor"=>3, "Lecturer"=>1, "Lecturer > Senior Lecturer"=>2, "Professor"=>3}, "reader_count_by_subject_area"=>{"Engineering"=>1, "Biochemistry, Genetics and Molecular Biology"=>1, "Agricultural and Biological Sciences"=>24, "Medicine and Dentistry"=>2, "Neuroscience"=>1, "Physics and Astronomy"=>10, "Psychology"=>1, "Chemistry"=>2, "Computer Science"=>4, "Earth and Planetary Sciences"=>1, "Linguistics"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>1}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>2}, "Neuroscience"=>{"Neuroscience"=>1}, "Chemistry"=>{"Chemistry"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>10}, "Psychology"=>{"Psychology"=>1}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>24}, "Computer Science"=>{"Computer Science"=>4}, "Linguistics"=>{"Linguistics"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}}, "reader_count_by_country"=>{"El Salvador"=>1, "United States"=>3, "Luxembourg"=>1, "Brazil"=>2, "Israel"=>1, "Germany"=>2, "Spain"=>1}, "group_count"=>3}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/993189"], "description"=>"<p><i>W. auropunctata</i> foragers realized time budgets closer to the optimum <i>ρ</i> than to the direct path <i>α</i> in 13 out of 18 trials. When moving across glass-felt, travel times were closer to <i>ρ</i> than for other surface combinations, and the ants performed better at the larger <i>α</i> angle.</p>", "links"=>[], "tags"=>["times", "ant", "trails"], "article_id"=>656696, "categories"=>["Physics", "Biophysics", "Mathematics", "Physiology", "Neuroscience", "Evolutionary Biology"], "users"=>["Jan Oettler", "Volker S. Schmid", "Niko Zankl", "Olivier Rey", "Andreas Dress", "Jürgen Heinze"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0059739.g003", "stats"=>{"downloads"=>2, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Directions_and_estimated_travel_times_of_ant_trails_961_8217_relative_to_the_prediction_961_0_and_the_direct_path_945_100_/656696", "title"=>"Directions and estimated travel times of ant trails (<i>ρ’</i>) relative to the prediction (<i>ρ</i>, 0%) and the direct path (<i>α</i>, 100%).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-21 04:50:42"}
  • {"files"=>["https://ndownloader.figshare.com/files/993191"], "description"=>"<p>The position of the food is on the rough felt. Note that the density of workers on the rough felt is higher than on the smooth felt because travel speed is lower. In addition it appears, although not very obvious, as if the ants on the rough felt ‘float’ on top of the felt hairs, indicating the difficulty of walking on this substrate. Photograph kindly provided by Simon Tragust.</p>", "links"=>[], "tags"=>["workers"], "article_id"=>656698, "categories"=>["Physics", "Biophysics", "Mathematics", "Physiology", "Neuroscience", "Evolutionary Biology"], "users"=>["Jan Oettler", "Volker S. Schmid", "Niko Zankl", "Olivier Rey", "Andreas Dress", "Jürgen Heinze"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0059739.g004", "stats"=>{"downloads"=>1, "page_views"=>20, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Refracted_trail_of_W_auropunctata_workers_at_the_medium_border_between_smooth_white_and_rough_green_felt_/656698", "title"=>"“Refracted” trail of <i>W. auropunctata</i> workers at the medium border between smooth (white) and rough (green) felt.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-21 04:51:32"}
  • {"files"=>["https://ndownloader.figshare.com/files/993193"], "description"=>"<div><p>Fermat’s principle of least time states that light rays passing through different media follow the fastest (and not the most direct) path between two points, leading to refraction at medium borders. Humans intuitively employ this rule, e.g., when a lifeguard has to infer the fastest way to traverse both beach and water to reach a swimmer in need. Here, we tested whether foraging ants also follow Fermat’s principle when forced to travel on two surfaces that differentially affected the ants’ walking speed. Workers of the little fire ant, <i>Wasmannia auropunctata</i>, established “refracted” pheromone trails to a food source. These trails deviated from the most direct path, but were not different to paths predicted by Fermat’s principle. Our results demonstrate a new aspect of decentralized optimization and underline the versatility of the simple yet robust rules governing the self-organization of group-living animals.</p> </div>", "links"=>[], "tags"=>["refraction", "ant", "trails", "substrate", "borders"], "article_id"=>656700, "categories"=>["Physics", "Biophysics", "Mathematics", "Physiology", "Neuroscience", "Evolutionary Biology"], "users"=>["Jan Oettler", "Volker S. Schmid", "Niko Zankl", "Olivier Rey", "Andreas Dress", "Jürgen Heinze"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0059739", "stats"=>{"downloads"=>2, "page_views"=>21, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Fermat_s_Principle_of_Least_Time_Predicts_Refraction_of_Ant_Trails_at_Substrate_Borders__/656700", "title"=>"Fermat’s Principle of Least Time Predicts Refraction of Ant Trails at Substrate Borders", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-03-21 04:52:45"}
  • {"files"=>["https://ndownloader.figshare.com/files/993186"], "description"=>"<p>The ants crossed two kinds of surfaces to gather food. The dotted yellow line indicates the trail expected according to Fermat’s principle. With decreasing walking speed ratio (<i>v</i><sub>1</sub>/<i>v</i><sub>2</sub>) point D (associated with the predicted trail angle <i>ρ</i>) will move to the left. If <i>v</i><sub>1</sub>< <i>v</i><sub>2</sub>, <i>ρ</i> will be larger than <i>α</i> (the crossing angle of the shortest line between food and nest).</p>", "links"=>[], "tags"=>["two-surface", "illustrating", "geometric", "details", "deriving"], "article_id"=>656693, "categories"=>["Physics", "Biophysics", "Mathematics", "Physiology", "Neuroscience", "Evolutionary Biology"], "users"=>["Jan Oettler", "Volker S. Schmid", "Niko Zankl", "Olivier Rey", "Andreas Dress", "Jürgen Heinze"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0059739.g001", "stats"=>{"downloads"=>0, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_of_the_two_surface_test_illustrating_the_geometric_details_for_deriving_the_path_prediction_model_/656693", "title"=>"Schematic of the two-surface test illustrating the geometric details for deriving the path prediction model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-21 04:50:00"}
  • {"files"=>["https://ndownloader.figshare.com/files/993187"], "description"=>"<p>Given for each surface combination are <i>α</i>, <i>ρ</i> and <i>ρ'</i> of each of three colonies (bars = median, whiskers = minimum and maximum). <i>ρ</i> varied largely due to colony differences in walking speed.</p>", "links"=>[], "tags"=>["forced", "colonies", "ant", "formed", "trails", "optimum", "15", "18", "followed", "moving"], "article_id"=>656694, "categories"=>["Physics", "Biophysics", "Mathematics", "Physiology", "Neuroscience", "Evolutionary Biology"], "users"=>["Jan Oettler", "Volker S. Schmid", "Niko Zankl", "Olivier Rey", "Andreas Dress", "Jürgen Heinze"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0059739.g002", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_When_forced_to_move_across_different_surfaces_colonies_of_the_ant_W_auropunctata_formed_trails_with_an_angle_961_closer_to_the_optimum_961_in_15_out_of_18_trials_than_to_the_angle_945_they_would_have_followed_if_moving_to_the_food_source_on_a_straight_li/656694", "title"=>"When forced to move across different surfaces, colonies of the ant <i>W. auropunctata</i> formed trails with an angle <i>ρ'</i> closer to the optimum <i>ρ</i> (in 15 out of 18 trials) than to the angle <i>α</i> they would have followed if moving to the food source on a straight line.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-21 04:50:15"}

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