Social Aggregation in Pea Aphids: Experiment and Random Walk Modeling
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{"title"=>"Social aggregation in pea aphids: Experiment and random walk modeling", "type"=>"journal", "authors"=>[{"first_name"=>"Christa", "last_name"=>"Nilsen", "scopus_author_id"=>"56025076600"}, {"first_name"=>"John", "last_name"=>"Paige", "scopus_author_id"=>"56023932100"}, {"first_name"=>"Olivia", "last_name"=>"Warner", "scopus_author_id"=>"56024759600"}, {"first_name"=>"Benjamin", "last_name"=>"Mayhew", "scopus_author_id"=>"56024667900"}, {"first_name"=>"Ryan", "last_name"=>"Sutley", "scopus_author_id"=>"56023625400"}, {"first_name"=>"Matthew", "last_name"=>"Lam", "scopus_author_id"=>"56024525600"}, {"first_name"=>"Andrew J.", "last_name"=>"Bernoff", "scopus_author_id"=>"6701690191"}, {"first_name"=>"Chad M.", "last_name"=>"Topaz", "scopus_author_id"=>"6508146488"}], "year"=>2013, "source"=>"PLoS ONE", "identifiers"=>{"pui"=>"372245290", "arxiv"=>"1308.4917", "issn"=>"19326203", "doi"=>"10.1371/journal.pone.0083343", "scopus"=>"2-s2.0-84893353582", "pmid"=>"24376691", "sgr"=>"84893353582"}, "id"=>"077790ed-b03a-333b-91e2-f805f820168a", "abstract"=>"From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid, Acyrthosiphon pisum. Specifically, we conduct experiments to track the motion of aphids walking in a featureless circular arena in order to deduce individual-level rules. We observe that each aphid transitions stochastically between a moving and a stationary state. Moving aphids follow a correlated random walk. The probabilities of motion state transitions, as well as the random walk parameters, depend strongly on distance to an aphid's nearest neighbor. For large nearest neighbor distances, when an aphid is essentially isolated, its motion is ballistic with aphids moving faster, turning less, and being less likely to stop. In contrast, for short nearest neighbor distances, aphids move more slowly, turn more, and are more likely to become stationary; this behavior constitutes an aggregation mechanism. From the experimental data, we estimate the state transition probabilities and correlated random walk parameters as a function of nearest neighbor distance. With the individual-level model established, we assess whether it reproduces the macroscopic patterns of movement at the group level. To do so, we consider three distributions, namely distance to nearest neighbor, angle to nearest neighbor, and percentage of population moving at any given time. For each of these three distributions, we compare our experimental data to the output of numerical simulations of our nearest neighbor model, and of a control model in which aphids do not interact socially. Our stochastic, social nearest neighbor model reproduces salient features of the experimental data that are not captured by the control.", "link"=>"http://www.mendeley.com/research/social-aggregation-pea-aphids-experiment-random-walk-modeling", "reader_count"=>22, "reader_count_by_academic_status"=>{"Researcher"=>4, "Student > Ph. D. Student"=>7, "Student > Master"=>3, "Other"=>2, "Student > Bachelor"=>2, "Lecturer"=>1, "Professor"=>3}, "reader_count_by_user_role"=>{"Researcher"=>4, "Student > Ph. D. Student"=>7, "Student > Master"=>3, "Other"=>2, "Student > Bachelor"=>2, "Lecturer"=>1, "Professor"=>3}, "reader_count_by_subject_area"=>{"Engineering"=>3, "Unspecified"=>2, "Environmental Science"=>3, "Mathematics"=>1, "Agricultural and Biological Sciences"=>8, "Medicine and Dentistry"=>1, "Arts and Humanities"=>1, "Physics and Astronomy"=>2, "Computer Science"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>3}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>8}, "Computer Science"=>{"Computer Science"=>1}, "Mathematics"=>{"Mathematics"=>1}, "Unspecified"=>{"Unspecified"=>2}, "Environmental Science"=>{"Environmental Science"=>3}, "Arts and Humanities"=>{"Arts and Humanities"=>1}}, "reader_count_by_country"=>{"United States"=>2, "China"=>1}, "group_count"=>0}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1325103"], "description"=>"<p>(A) Trajectories of 28 aphids during approximately 15 <i>min</i> of one experimental trial, as determined by motion tracking of video data. The green circle is the experimental arena with radius 20 <i>cm</i>. (B) Blow-up of a subset of a single aphid trajectory, shown in a 10 <i>cm</i> × 10 <i>cm</i> zoom.</p>", "links"=>[], "tags"=>["aphid"], "article_id"=>883926, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Christa Nilsen", "John Paige", "Olivia Warner", "Benjamin Mayhew", "Ryan Sutley", "Matthew Lam", "Andrew J. Bernoff", "Chad M. Topaz"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0083343.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Visualizations_of_aphid_movement_in_experiment_/883926", "title"=>"Visualizations of aphid movement in experiment.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-20 03:52:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1325104"], "description"=>"<p>(A) <i>P<sub>MS</sub></i>, the probability that an aphid moving in a given timestep becomes stationary at the next timestep. Each data point represents the probability within a bin of 800 elements from our experimental data set, where the data are binned by <i>d</i>. The probability is calculated via a simple frequency count according to <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083343#pone.0083343.e004\" target=\"_blank\">Eq. (1)</a>. The overall dependence of the data on <i>d</i> is modeled with <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083343#pone.0083343.e005\" target=\"_blank\">Eq. (2)</a>, which describes an increased probability of an aphid settling if a neighbor is nearby. Best fit parameters appear in the text; the coefficient of determination is <i>R</i><sup>2</sup> = 0.92. To give a further sense of the efficacy of the fit, we display each point according to the standard error of the mean within the bin it represents. If the model curve passes within two standard errors of the estimated value, we show it as a green square; otherwise, it is a red dot. (B) Like (A), but for the probability <i>P<sub>SM</sub></i> that a stationary aphid starts moving. The model is <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083343#pone.0083343.e015\" target=\"_blank\">Eq. (4)</a>, describing higher aphid mobility at very short and very long <i>d</i>. Here, <i>R</i><sup>2</sup> = 0.52; see text for discussion.</p>", "links"=>[], "tags"=>["probabilities", "nearest"], "article_id"=>883927, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Christa Nilsen", "John Paige", "Olivia Warner", "Benjamin Mayhew", "Ryan Sutley", "Matthew Lam", "Andrew J. Bernoff", "Chad M. Topaz"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0083343.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_State_transition_probabilities_P_MS_and_P_MS_as_a_function_of_distance_to_an_aphid_s_nearest_neighbor_d_in_m_/883927", "title"=>"State transition probabilities <i>P<sub>MS</sub></i> and <i>P<sub>MS</sub></i> as a function of distance to an aphid's nearest neighbor, <i>d</i> (in <i>m</i>).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-20 03:52:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1325105"], "description"=>"<p>Each data point represents the mean step length within a bin of 800 elements from our experimental data set, where the data are binned by <i>d</i>. The overall dependence of the data on <i>d</i> is modeled with <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083343#pone.0083343.e023\" target=\"_blank\">Eq. (5)</a>, which captures the tendency of aphids to aggregate simply by traveling less when in the vicinity of others. Best fit parameters appear in the text; the coefficient of determination is <i>R</i><sup>2</sup> = 0.82. To give a further sense of the efficacy of the fit, we display data points according to the same scheme used in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083343#pone-0083343-g002\" target=\"_blank\">Fig. 2</a>. Green squares (red dots) represent data bins for which the model prediction falls within (outside) two standard errors of the experimental mean.</p>", "links"=>[], "tags"=>["nearest"], "article_id"=>883928, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Christa Nilsen", "John Paige", "Olivia Warner", "Benjamin Mayhew", "Ryan Sutley", "Matthew Lam", "Andrew J. Bernoff", "Chad M. Topaz"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0083343.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Correlated_random_walk_step_length_in_m_per_frame_as_a_function_of_distance_to_an_aphid_s_nearest_neighbor_d_in_m_/883928", "title"=>"Correlated random walk step length (in <i>m</i>) per frame as a function of distance to an aphid's nearest neighbor <i>d</i> (in <i>m</i>).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-20 03:52:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1325106"], "description"=>"<p>(A) Turning angle distribution parameter 0<<i>ρ</i><1 as a function of distance to an aphid's nearest neighbor. Here, <i>ρ</i> is a parameter in the zero-mean wrapped Cauchy distribution <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083343#pone.0083343.e032\" target=\"_blank\">Eq. (6)</a> used to model turning angle <i>θ</i>. Each data point represents the experimentally measured value of <i>ρ</i> within a bin of 2400 elements from our experimental data set, where the data are binned by <i>d</i>. The overall dependence of the data on <i>d</i> is modeled with <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083343#pone.0083343.e034\" target=\"_blank\">Eq. (7)</a>, which captures the tendency of aphids to aggregate by taking wider turns when in the vicinity of others, leading to motion that is more diffusive and less ballistic. Best fit parameters appear in the text; the coefficient of determination is <i>R</i><sup>2</sup> = 0.99. Green circles (red dots) points represent data bins for which the model prediction falls within (outside) a 95% confidence interval around the experimentally measured <i>ρ</i>, where the interval is constructed by resampling our original data 20,000 times. (B) Normalized histogram showing the experimental turning angle distribution within the data bin corresponding to the magenta triangle in (A). The blue curve shows the wrapped Cauchy distribution predicted by our model. (C) Like (B), but for the magenta diamond.</p>", "links"=>[], "tags"=>["turning"], "article_id"=>883929, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Christa Nilsen", "John Paige", "Olivia Warner", "Benjamin Mayhew", "Ryan Sutley", "Matthew Lam", "Andrew J. Bernoff", "Chad M. Topaz"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0083343.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Correlated_random_walk_turning_angle_952_/883929", "title"=>"Correlated random walk turning angle <i>θ</i>.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-20 03:52:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1325110"], "description"=>"<p>The circular experimental arena has a radius of 0.2 <i>m</i>. Only 10% of the data set corresponds to aphids within 2 <i>cm</i> (about five body lengths) of the boundary.</p>", "links"=>[], "tags"=>["aphids"], "article_id"=>883931, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Christa Nilsen", "John Paige", "Olivia Warner", "Benjamin Mayhew", "Ryan Sutley", "Matthew Lam", "Andrew J. Bernoff", "Chad M. Topaz"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0083343.g005"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Cumulative_distribution_of_aphids_as_a_function_of_distance_to_arena_boundary_in_m_for_experimental_data_set_/883931", "title"=>"Cumulative distribution of aphids as a function of distance to arena boundary (in <i>m</i>) for experimental data set.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-20 03:52:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1325111"], "description"=>"<p>(A) Cumulative distributions of distance to nearest neighbor <i>d</i> (in <i>m</i>) for experimental data set (solid blue), social interaction model (dashed green), and non-interacting model (dot-dashed red). (B) Like (A), but the cumulated quantity is angle to nearest neighbor <i>φ</i> (relative to an aphid's heading ). (C) Like (A), but the cumulated quantity is , fraction of the aphid population moving in a given frame. As compared to the curves in (A) and (B), the more staircase-like appearance of these curves arises simply from the fact that the variable being cumulated is discrete (percentage of aphids in a group of several dozen) as opposed to the continuous variables in (A) and (B). For (A)–(C), measures of the difference between the distributions are given in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083343#pone-0083343-t001\" target=\"_blank\">Tables 1</a>–<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083343#pone-0083343-t003\" target=\"_blank\">3</a> respectively.</p>", "links"=>[], "tags"=>["aphid", "group-level", "behaviors"], "article_id"=>883932, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Christa Nilsen", "John Paige", "Olivia Warner", "Benjamin Mayhew", "Ryan Sutley", "Matthew Lam", "Andrew J. Bernoff", "Chad M. Topaz"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0083343.g006"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Pea_aphid_group_level_behaviors_in_experiment_a_social_interaction_model_and_a_control_non_interacting_model_/883932", "title"=>"Pea aphid group-level behaviors in experiment, a social interaction model, and a control (non-interacting) model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-20 03:52:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1325112"], "description"=>"<p>By measures of the difference between median values , the Kolmogorov-Smirnov distance , and the Kullback-Leibler divergence , the cumulative distribution of <i>INT</i> comes closer to <i>EXP</i> than <i>NON</i> does. This is especially apparent in the and values. The three distributions are shown in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083343#pone-0083343-g006\" target=\"_blank\">Fig. 6(C)</a>.</p>", "links"=>[], "tags"=>["comparing", "cumulative", "distributions", "aphids", "moving", "noninteracting"], "article_id"=>883933, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Christa Nilsen", "John Paige", "Olivia Warner", "Benjamin Mayhew", "Ryan Sutley", "Matthew Lam", "Andrew J. Bernoff", "Chad M. Topaz"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0083343.t003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Measures_comparing_cumulative_distributions_of_fraction_of_aphids_moving_in_experiment_EXP_a_social_interaction_model_INT_and_a_noninteracting_control_model_NON_/883933", "title"=>"Measures comparing cumulative distributions of fraction of aphids moving in experiment (<i>EXP</i>), a social interaction model (<i>INT</i>) and a noninteracting control model (<i>NON</i>).", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-12-20 03:52:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1325114"], "description"=>"<p>By measures of the difference between median values , the Kolmogorov-Smirnov distance , and the Kullback-Leibler divergence , the cumulative distributions for <i>INT</i>, <i>NON</i>, and <i>EXP</i> are nearly identical. Since <i>φ</i> is an angle measured in radians, the values of should be compared to the value 2<i>π</i>. The three distributions are shown in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083343#pone-0083343-g006\" target=\"_blank\">Fig. 6(B)</a>.</p>", "links"=>[], "tags"=>["comparing", "cumulative", "distributions", "nearest", "noninteracting"], "article_id"=>883935, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Christa Nilsen", "John Paige", "Olivia Warner", "Benjamin Mayhew", "Ryan Sutley", "Matthew Lam", "Andrew J. Bernoff", "Chad M. Topaz"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0083343.t002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Measures_comparing_cumulative_distributions_of_angle_to_nearest_neighbor_966_in_experiment_EXP_a_social_interaction_model_INT_and_a_noninteracting_control_model_NON_/883935", "title"=>"Measures comparing cumulative distributions of angle to nearest neighbor <i>φ</i> in experiment (<i>EXP</i>), a social interaction model (<i>INT</i>) and a noninteracting control model (<i>NON</i>).", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-12-20 03:52:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1325115"], "description"=>"<p>By measures of the difference between median values (in <i>m</i>), the Kolmogorov-Smirnov distance , and the Kullback-Leibler divergence , the cumulative distribution of <i>INT</i> comes closer to <i>EXP</i> than <i>NON</i> does. Since is a dimensioned quantity, it is meaningful to compare values to an aphid body length, approximately 0.004 <i>m</i>. <i>EXP</i> and <i>INT</i> have median values that differ by a body length, while the other two comparison have median differences an order of magnitude larger. The three distributions are shown in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0083343#pone-0083343-g006\" target=\"_blank\">Fig. 6(A)</a>.</p>", "links"=>[], "tags"=>["comparing", "cumulative", "distributions", "nearest", "noninteracting"], "article_id"=>883936, "categories"=>["Biological Sciences", "Science Policy"], "users"=>["Christa Nilsen", "John Paige", "Olivia Warner", "Benjamin Mayhew", "Ryan Sutley", "Matthew Lam", "Andrew J. Bernoff", "Chad M. Topaz"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0083343.t001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Measures_comparing_cumulative_distributions_of_distance_to_nearest_neighbor_d_in_experiment_EXP_a_social_interaction_model_INT_and_a_noninteracting_control_model_NON_/883936", "title"=>"Measures comparing cumulative distributions of distance to nearest neighbor d in experiment (<i>EXP</i>), a social interaction model (<i>INT</i>) and a noninteracting control model (<i>NON</i>).", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-12-20 03:52:28"}

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  • {"unique-ip"=>"2", "full-text"=>"0", "pdf"=>"3", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"10"}
  • {"unique-ip"=>"5", "full-text"=>"6", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"7"}
  • {"unique-ip"=>"2", "full-text"=>"2", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"8"}
  • {"unique-ip"=>"6", "full-text"=>"11", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"12"}
  • {"unique-ip"=>"3", "full-text"=>"5", "pdf"=>"1", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"1", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"9"}
  • {"unique-ip"=>"1", "full-text"=>"1", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"2"}
  • {"unique-ip"=>"4", "full-text"=>"4", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"3"}
  • {"unique-ip"=>"6", "full-text"=>"5", "pdf"=>"2", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"4"}
  • {"unique-ip"=>"2", "full-text"=>"2", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"5"}
  • {"unique-ip"=>"3", "full-text"=>"3", "pdf"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"0", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2019", "month"=>"8"}

Relative Metric

{"start_date"=>"2013-01-01T00:00:00Z", "end_date"=>"2013-12-31T00:00:00Z", "subject_areas"=>[{"subject_area"=>"/Biology and life sciences/Zoology", "average_usage"=>[294, 473, 591, 693, 788, 883, 972, 1054, 1140, 1222, 1299, 1381, 1446]}, {"subject_area"=>"/Physical sciences/Physics", "average_usage"=>[254, 421, 527, 626, 720, 813, 900, 983, 1063, 1136, 1210, 1283, 1342]}]}
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