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Biology, Methodology or Chance? The Degree Distributions of Bipartite Ecological Networks

Publication Date: March 03, 2011
Journal: PLOS ONE
Author: Richard J. Williams
Volume: 6
Issue: 3
Pages: e17645
DOI: https://dx.plos.org/10.1371/journal.pone.0017645
Publisher URL: http://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0017645
PubMed: http://www.ncbi.nlm.nih.gov/pubmed/21390231
PubMed Central: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3048397
Europe PMC: http://europepmc.org/abstract/MED/21390231
Web of Science: 000287965200034
Scopus: 79952288065
Mendeley: http://www.mendeley.com/research/biology-methodology-chance-degree-distributions-bipartite-ecological-networks

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Mendeley 13905 May 09:08 UTC

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{"title"=>"Biology, methodology or chance? The degree distributions of bipartite ecological networks", "type"=>"journal", "authors"=>[{"first_name"=>"Richard J.", "last_name"=>"Williams", "scopus_author_id"=>"55612751800"}], "year"=>2011, "source"=>"PLoS ONE", "identifiers"=>{"sgr"=>"79952288065", "doi"=>"10.1371/journal.pone.0017645", "pmid"=>"21390231", "issn"=>"19326203", "scopus"=>"2-s2.0-79952288065", "pui"=>"361382328"}, "id"=>"9456cdd9-969a-3543-b7c9-17ffb22fc43f", "abstract"=>"The distribution of the number of links per species, or degree distribution, is widely used as a summary of the topology of complex networks. Degree distributions have been studied in a range of ecological networks, including both mutualistic bipartite networks of plants and pollinators or seed dispersers and antagonistic bipartite networks of plants and their consumers. The shape of a degree distribution, for example whether it follows an exponential or power-law form, is typically taken to be indicative of the processes structuring the network. The skewed degree distributions of bipartite mutualistic and antagonistic networks are usually assumed to show that ecological or co-evolutionary processes constrain the relative numbers of specialists and generalists in the network. I show that a simple null model based on the principle of maximum entropy cannot be rejected as a model for the degree distributions in most of the 115 bipartite ecological networks tested here. The model requires knowledge of the number of nodes and links in the network, but needs no other ecological information. The model cannot be rejected for 159 (69%) of the 230 degree distributions of the 115 networks tested. It performed equally well on the plant and animal degree distributions, and cannot be rejected for 81 (70%) of the 115 plant distributions and 78 (68%) of the animal distributions. There are consistent differences between the degree distributions of mutualistic and antagonistic networks, suggesting that different processes are constraining these two classes of networks. Fit to the MaxEnt null model is consistently poor among the largest mutualistic networks. Potential ecological and methodological explanations for deviations from the model suggest that spatial and temporal heterogeneity are important drivers of the structure of these large networks.", "link"=>"http://www.mendeley.com/research/biology-methodology-chance-degree-distributions-bipartite-ecological-networks", "reader_count"=>137, "reader_count_by_academic_status"=>{"Unspecified"=>2, "Professor > Associate Professor"=>8, "Student > Doctoral Student"=>14, "Researcher"=>24, "Student > Ph. D. Student"=>44, "Student > Postgraduate"=>7, "Student > Master"=>19, "Student > Bachelor"=>8, "Lecturer"=>2, "Lecturer > Senior Lecturer"=>1, "Professor"=>8}, "reader_count_by_user_role"=>{"Unspecified"=>2, "Professor > Associate Professor"=>8, "Student > Doctoral Student"=>14, "Researcher"=>24, "Student > Ph. D. Student"=>44, "Student > Postgraduate"=>7, "Student > Master"=>19, "Student > Bachelor"=>8, "Lecturer"=>2, "Lecturer > Senior Lecturer"=>1, "Professor"=>8}, "reader_count_by_subject_area"=>{"Unspecified"=>4, "Environmental Science"=>34, "Biochemistry, Genetics and Molecular Biology"=>1, "Mathematics"=>1, "Agricultural and Biological Sciences"=>76, "Medicine and Dentistry"=>1, "Business, Management and Accounting"=>1, "Physics and Astronomy"=>9, "Chemical Engineering"=>1, "Psychology"=>1, "Computer Science"=>6, "Earth and Planetary Sciences"=>2}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>9}, "Psychology"=>{"Psychology"=>1}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>76}, "Computer Science"=>{"Computer Science"=>6}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}, "Mathematics"=>{"Mathematics"=>1}, "Unspecified"=>{"Unspecified"=>4}, "Environmental Science"=>{"Environmental Science"=>34}, "Chemical Engineering"=>{"Chemical Engineering"=>1}}, "reader_count_by_country"=>{"Colombia"=>2, "United States"=>5, "Japan"=>1, "United Kingdom"=>2, "Switzerland"=>3, "Portugal"=>2, "India"=>1, "Spain"=>1, "New Zealand"=>1, "Venezuela"=>1, "Canada"=>2, "Sweden"=>1, "China"=>1, "Finland"=>1, "Brazil"=>6, "South Africa"=>1, "Italy"=>2, "Mexico"=>1, "Israel"=>1, "Slovenia"=>1, "France"=>2, "Germany"=>1}, "group_count"=>2}

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{"files"=>["https://ndownloader.figshare.com/files/397132"], "description"=>"<div>The distribution of the number of links per species, or degree distribution, is widely used as a summary of the topology of complex networks. Degree distributions have been studied in a range of ecological networks, including both mutualistic bipartite networks of plants and pollinators or seed dispersers and antagonistic bipartite networks of plants and their consumers. The shape of a degree distribution, for example whether it follows an exponential or power-law form, is typically taken to be indicative of the processes structuring the network. The skewed degree distributions of bipartite mutualistic and antagonistic networks are usually assumed to show that ecological or co-evolutionary processes constrain the relative numbers of specialists and generalists in the network. I show that a simple null model based on the principle of maximum entropy cannot be rejected as a model for the degree distributions in most of the 115 bipartite ecological networks tested here. The model requires knowledge of the number of nodes and links in the network, but needs no other ecological information. The model cannot be rejected for 159 (69%) of the 230 degree distributions of the 115 networks tested. It performed equally well on the plant and animal degree distributions, and cannot be rejected for 81 (70%) of the 115 plant distributions and 78 (68%) of the animal distributions. There are consistent differences between the degree distributions of mutualistic and antagonistic networks, suggesting that different processes are constraining these two classes of networks. Fit to the MaxEnt null model is consistently poor among the largest mutualistic networks. Potential ecological and methodological explanations for deviations from the model suggest that spatial and temporal heterogeneity are important drivers of the structure of these large networks. </div>", "links"=>[], "tags"=>["methodology", "distributions", "bipartite", "networks"], "article_id"=>138441, "categories"=>["Biological Sciences", "Ecology", "Genetics"], "users"=>["Richard J. Williams"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0017645", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Biology_Methodology_or_Chance_The_Degree_Distributions_of_Bipartite_Ecological_Networks/138441", "title"=>"Biology, Methodology or Chance? The Degree Distributions of Bipartite Ecological Networks", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-03-03 02:20:41"}
{"files"=>["https://ndownloader.figshare.com/files/793402"], "description"=>"Solid line is linear regression, dotted lines are upper and lower confidence intervals. In (a) R2 = 0.25, p<0.001, in (b) R2 = 0.10, p = 0.015.", "links"=>[], "tags"=>["width", "distributions", "antagonistic", "networks", "mutualistic"], "article_id"=>463773, "categories"=>["Biological Sciences", "Ecology", "Genetics"], "users"=>["Richard J. Williams"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0017645.g003", "stats"=>{"downloads"=>1, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Relative_width_W_95_versus_number_of_species_S_for_the_animal_distributions_of_a_antagonistic_networks_and_b_mutualistic_networks_with_S_/463773", "title"=>"Relative width W95 versus number of species S for the animal distributions of (a) antagonistic networks and (b) mutualistic networks with S<135.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-03-03 01:02:53"}
{"files"=>["https://ndownloader.figshare.com/files/793593"], "description"=>"Both fG<0.95 and −1<W95<1 are required for the degree distribution to be considered a good fit to the MaxEnt model.", "links"=>[], "tags"=>["networks", "well-fit", "maxent", "distributions"], "article_id"=>463964, "categories"=>["Biological Sciences", "Ecology", "Genetics"], "users"=>["Richard J. Williams"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0017645.t001", "stats"=>{"downloads"=>2, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Number_and_fraction_of_networks_well_fit_by_the_MaxEnt_model_for_plant_and_animal_degree_distributions_in_networks_with_S_140_/463964", "title"=>"Number and (fraction) of networks well-fit by the MaxEnt model for plant and animal degree distributions in networks with S<135 and S>140.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-03-03 01:06:04"}
{"files"=>["https://ndownloader.figshare.com/files/793241"], "description"=>"Schematic showing (a) two bipartite networks coupled in (b) by making the most general animal species (marked with a dotted circle in (a)) be the only node shared across the two subwebs.", "links"=>[], "tags"=>["bipartite", "networks", "coupled", "making", "dotted", "node"], "article_id"=>463606, "categories"=>["Biological Sciences", "Ecology", "Genetics"], "users"=>["Richard J. Williams"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0017645.g001", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_showing_a_two_bipartite_networks_coupled_in_b_by_making_the_most_general_animal_species_marked_with_a_dotted_circle_in_a_be_the_only_node_shared_across_the_two_subwebs_/463606", "title"=>"Schematic showing (a) two bipartite networks coupled in (b) by making the most general animal species (marked with a dotted circle in (a)) be the only node shared across the two subwebs.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-03-03 01:00:06"}
{"files"=>["https://ndownloader.figshare.com/files/793495"], "description"=>"Shading of data points shows the goodness of fit fG of the MaxEnt model.", "links"=>[], "tags"=>["width", "distributions", "17", "networks"], "article_id"=>463862, "categories"=>["Biological Sciences", "Ecology", "Genetics"], "users"=>["Richard J. Williams"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0017645.g004", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Relative_width_W_95_versus_number_of_species_S_of_a_plant_distributions_and_b_animal_distributions_for_17_networks_with_S_140_/463862", "title"=>"Relative width W95 versus number of species S of (a) plant distributions and (b) animal distributions for 17 networks with S>140.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-03-03 01:04:22"}
{"files"=>["https://ndownloader.figshare.com/files/793296"], "description"=>"Shading of the data points shows the number of species in the networks.", "links"=>[], "tags"=>["width", "goodness", "maxent", "distributions", "98", "networks"], "article_id"=>463666, "categories"=>["Biological Sciences", "Ecology", "Genetics"], "users"=>["Richard J. Williams"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0017645.g002", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Relative_width_W_95_versus_goodness_of_fit_f_G_of_the_MaxEnt_model_for_a_plant_distributions_and_b_animal_distributions_of_98_networks_with_S_/463666", "title"=>"Relative width W95 versus goodness of fit fG of the MaxEnt model for (a) plant distributions and (b) animal distributions of 98 networks with S<135.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-03-03 01:01:06"}

PMC Usage Stats 81917 Feb 16:07 UTC

PMC Usage Stats | Further Information

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Relative Metric 61432010 May 16:24 UTC

Relative Metric

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F1000Prime24 Feb 12:17 UTC

F1000Prime

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