Continuous limits of large plant-pollinator random networks and some applications Article Swipe
Sylvain Billiard
,
Hélène Leman
,
Thomas Rey
,
Viet Chi Tran
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2201.05219
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2201.05219
We study a stochastic individual-based model of interacting plant and pollinator species through a bipartite graph: each species is a node of the graph, an edge representing interactions between a pair of species. The dynamics of the system depends on the between- and within-species interactions: pollination by insects increases plant reproduction rate but has a cost which can increase plant death rate, depending on the densities of pollinators. Pollinators reproduction is increased by the resources harvested on plants. Each species is characterized by a trait corresponding to its degree of generalism. This trait determines the structure of the interaction graph and the quantities of resources exchanged between species. Our model includes in particular nested or modular networks. Deterministic approximations of the stochastic measure-valued process by systems of ordinary differential equations or integro-differential equations are established and studied, when the population is large or when the graph is dense and can be replaced with a graphon. The long-time behaviors of these limits are studied and central limit theorems are established to quantify the difference between the discrete stochastic individual-based model and the deterministic approximations. Finally, studying the continuous limits of the interaction network and the resulting PDEs, we show that nested plant-pollinator communities are expected to collapse towards a coexistence between a single pair of species of plants and pollinators.
Related Topics
Concepts
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2201.05219
- https://arxiv.org/pdf/2201.05219
- OA Status
- green
- Cited By
- 1
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4221144409
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4221144409Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2201.05219Digital Object Identifier
- Title
-
Continuous limits of large plant-pollinator random networks and some applicationsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2022Year of publication
- Publication date
-
2022-01-13Full publication date if available
- Authors
-
Sylvain Billiard, Hélène Leman, Thomas Rey, Viet Chi TranList of authors in order
- Landing page
-
https://arxiv.org/abs/2201.05219Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2201.05219Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2201.05219Direct OA link when available
- Concepts
-
Pollinator, Mathematics, Environmental science, Pollination, Biology, Pollen, EcologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
-
2024: 1Per-year citation counts (last 5 years)
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4221144409 |
|---|---|
| doi | https://doi.org/10.48550/arxiv.2201.05219 |
| ids.doi | https://doi.org/10.48550/arxiv.2201.05219 |
| ids.openalex | https://openalex.org/W4221144409 |
| fwci | |
| type | preprint |
| title | Continuous limits of large plant-pollinator random networks and some applications |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T10487 |
| topics[0].field.id | https://openalex.org/fields/11 |
| topics[0].field.display_name | Agricultural and Biological Sciences |
| topics[0].score | 0.9980000257492065 |
| topics[0].domain.id | https://openalex.org/domains/1 |
| topics[0].domain.display_name | Life Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1105 |
| topics[0].subfield.display_name | Ecology, Evolution, Behavior and Systematics |
| topics[0].display_name | Plant and animal studies |
| topics[1].id | https://openalex.org/T10702 |
| topics[1].field.id | https://openalex.org/fields/13 |
| topics[1].field.display_name | Biochemistry, Genetics and Molecular Biology |
| topics[1].score | 0.963699996471405 |
| topics[1].domain.id | https://openalex.org/domains/1 |
| topics[1].domain.display_name | Life Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/1311 |
| topics[1].subfield.display_name | Genetics |
| topics[1].display_name | Insect and Arachnid Ecology and Behavior |
| topics[2].id | https://openalex.org/T10064 |
| topics[2].field.id | https://openalex.org/fields/31 |
| topics[2].field.display_name | Physics and Astronomy |
| topics[2].score | 0.9423999786376953 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/3109 |
| topics[2].subfield.display_name | Statistical and Nonlinear Physics |
| topics[2].display_name | Complex Network Analysis Techniques |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C102789151 |
| concepts[0].level | 4 |
| concepts[0].score | 0.7208273410797119 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q1141466 |
| concepts[0].display_name | Pollinator |
| concepts[1].id | https://openalex.org/C33923547 |
| concepts[1].level | 0 |
| concepts[1].score | 0.38436588644981384 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[1].display_name | Mathematics |
| concepts[2].id | https://openalex.org/C39432304 |
| concepts[2].level | 0 |
| concepts[2].score | 0.3509688377380371 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q188847 |
| concepts[2].display_name | Environmental science |
| concepts[3].id | https://openalex.org/C168197293 |
| concepts[3].level | 3 |
| concepts[3].score | 0.3217843770980835 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q134624 |
| concepts[3].display_name | Pollination |
| concepts[4].id | https://openalex.org/C86803240 |
| concepts[4].level | 0 |
| concepts[4].score | 0.21405616402626038 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q420 |
| concepts[4].display_name | Biology |
| concepts[5].id | https://openalex.org/C2780618852 |
| concepts[5].level | 2 |
| concepts[5].score | 0.1540643870830536 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q79932 |
| concepts[5].display_name | Pollen |
| concepts[6].id | https://openalex.org/C18903297 |
| concepts[6].level | 1 |
| concepts[6].score | 0.1498132050037384 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q7150 |
| concepts[6].display_name | Ecology |
| keywords[0].id | https://openalex.org/keywords/pollinator |
| keywords[0].score | 0.7208273410797119 |
| keywords[0].display_name | Pollinator |
| keywords[1].id | https://openalex.org/keywords/mathematics |
| keywords[1].score | 0.38436588644981384 |
| keywords[1].display_name | Mathematics |
| keywords[2].id | https://openalex.org/keywords/environmental-science |
| keywords[2].score | 0.3509688377380371 |
| keywords[2].display_name | Environmental science |
| keywords[3].id | https://openalex.org/keywords/pollination |
| keywords[3].score | 0.3217843770980835 |
| keywords[3].display_name | Pollination |
| keywords[4].id | https://openalex.org/keywords/biology |
| keywords[4].score | 0.21405616402626038 |
| keywords[4].display_name | Biology |
| keywords[5].id | https://openalex.org/keywords/pollen |
| keywords[5].score | 0.1540643870830536 |
| keywords[5].display_name | Pollen |
| keywords[6].id | https://openalex.org/keywords/ecology |
| keywords[6].score | 0.1498132050037384 |
| keywords[6].display_name | Ecology |
| language | en |
| locations[0].id | pmh:oai:arXiv.org:2201.05219 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4306400194 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | arXiv (Cornell University) |
| locations[0].source.host_organization | https://openalex.org/I205783295 |
| locations[0].source.host_organization_name | Cornell University |
| locations[0].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[0].license | |
| locations[0].pdf_url | https://arxiv.org/pdf/2201.05219 |
| locations[0].version | submittedVersion |
| locations[0].raw_type | text |
| locations[0].license_id | |
| locations[0].is_accepted | False |
| locations[0].is_published | False |
| locations[0].raw_source_name | |
| locations[0].landing_page_url | http://arxiv.org/abs/2201.05219 |
| locations[1].id | pmh:oai:HAL:hal-03525607v1 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S4306402512 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | HAL (Le Centre pour la Communication Scientifique Directe) |
| locations[1].source.host_organization | https://openalex.org/I1294671590 |
| locations[1].source.host_organization_name | Centre National de la Recherche Scientifique |
| locations[1].source.host_organization_lineage | https://openalex.org/I1294671590 |
| locations[1].license | other-oa |
| locations[1].pdf_url | |
| locations[1].version | submittedVersion |
| locations[1].raw_type | info:eu-repo/semantics/preprint |
| locations[1].license_id | https://openalex.org/licenses/other-oa |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | https://hal-cnrs.archives-ouvertes.fr/hal-03525607 |
| locations[1].landing_page_url | https://hal-cnrs.archives-ouvertes.fr/hal-03525607 |
| locations[2].id | pmh:oai:HAL:hal-03525607v2 |
| locations[2].is_oa | True |
| locations[2].source.id | https://openalex.org/S4306402512 |
| locations[2].source.issn | |
| locations[2].source.type | repository |
| locations[2].source.is_oa | False |
| locations[2].source.issn_l | |
| locations[2].source.is_core | False |
| locations[2].source.is_in_doaj | False |
| locations[2].source.display_name | HAL (Le Centre pour la Communication Scientifique Directe) |
| locations[2].source.host_organization | https://openalex.org/I1294671590 |
| locations[2].source.host_organization_name | Centre National de la Recherche Scientifique |
| locations[2].source.host_organization_lineage | https://openalex.org/I1294671590 |
| locations[2].license | other-oa |
| locations[2].pdf_url | |
| locations[2].version | submittedVersion |
| locations[2].raw_type | Journal articles |
| locations[2].license_id | https://openalex.org/licenses/other-oa |
| locations[2].is_accepted | False |
| locations[2].is_published | False |
| locations[2].raw_source_name | MathematicS In Action, In press |
| locations[2].landing_page_url | https://cnrs.hal.science/hal-03525607 |
| locations[3].id | pmh:oai:lilloa.univ-lille.fr:20.500.12210/122383 |
| locations[3].is_oa | True |
| locations[3].source.id | https://openalex.org/S4306402203 |
| locations[3].source.issn | |
| locations[3].source.type | repository |
| locations[3].source.is_oa | False |
| locations[3].source.issn_l | |
| locations[3].source.is_core | False |
| locations[3].source.is_in_doaj | False |
| locations[3].source.display_name | LillOA (Université de Lille (University Of Lille)) |
| locations[3].source.host_organization | https://openalex.org/I4210123514 |
| locations[3].source.host_organization_name | Centre d'Etudes en Civilisations, Langues et Littératures Etrangères |
| locations[3].source.host_organization_lineage | https://openalex.org/I4210123514 |
| locations[3].license | other-oa |
| locations[3].pdf_url | |
| locations[3].version | submittedVersion |
| locations[3].raw_type | info:eu-repo/semantics/article |
| locations[3].license_id | https://openalex.org/licenses/other-oa |
| locations[3].is_accepted | False |
| locations[3].is_published | False |
| locations[3].raw_source_name | |
| locations[3].landing_page_url | |
| locations[4].id | pmh:oai:lilloa.univ-lille.fr:20.500.12210/59276 |
| locations[4].is_oa | True |
| locations[4].source.id | https://openalex.org/S4306402203 |
| locations[4].source.issn | |
| locations[4].source.type | repository |
| locations[4].source.is_oa | False |
| locations[4].source.issn_l | |
| locations[4].source.is_core | False |
| locations[4].source.is_in_doaj | False |
| locations[4].source.display_name | LillOA (Université de Lille (University Of Lille)) |
| locations[4].source.host_organization | https://openalex.org/I4210123514 |
| locations[4].source.host_organization_name | Centre d'Etudes en Civilisations, Langues et Littératures Etrangères |
| locations[4].source.host_organization_lineage | https://openalex.org/I4210123514 |
| locations[4].license | other-oa |
| locations[4].pdf_url | |
| locations[4].version | submittedVersion |
| locations[4].raw_type | info:eu-repo/semantics/workingPaper |
| locations[4].license_id | https://openalex.org/licenses/other-oa |
| locations[4].is_accepted | False |
| locations[4].is_published | False |
| locations[4].raw_source_name | |
| locations[4].landing_page_url | http://hdl.handle.net/20.500.12210/59276 |
| locations[5].id | doi:10.48550/arxiv.2201.05219 |
| locations[5].is_oa | True |
| locations[5].source.id | https://openalex.org/S4306400194 |
| locations[5].source.issn | |
| locations[5].source.type | repository |
| locations[5].source.is_oa | True |
| locations[5].source.issn_l | |
| locations[5].source.is_core | False |
| locations[5].source.is_in_doaj | False |
| locations[5].source.display_name | arXiv (Cornell University) |
| locations[5].source.host_organization | https://openalex.org/I205783295 |
| locations[5].source.host_organization_name | Cornell University |
| locations[5].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[5].license | cc-by |
| locations[5].pdf_url | |
| locations[5].version | |
| locations[5].raw_type | article |
| locations[5].license_id | https://openalex.org/licenses/cc-by |
| locations[5].is_accepted | False |
| locations[5].is_published | |
| locations[5].raw_source_name | |
| locations[5].landing_page_url | https://doi.org/10.48550/arxiv.2201.05219 |
| indexed_in | arxiv, datacite |
| authorships[0].author.id | https://openalex.org/A5082444550 |
| authorships[0].author.orcid | https://orcid.org/0000-0003-2135-3246 |
| authorships[0].author.display_name | Sylvain Billiard |
| authorships[0].countries | FR |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I4210148734 |
| authorships[0].affiliations[0].raw_affiliation_string | Évolution, Écologie et Paléontologie (Evo-Eco-Paleo) - UMR 8198 |
| authorships[0].institutions[0].id | https://openalex.org/I4210148734 |
| authorships[0].institutions[0].ror | https://ror.org/04y91dy23 |
| authorships[0].institutions[0].type | facility |
| authorships[0].institutions[0].lineage | https://openalex.org/I1294671590, https://openalex.org/I2279609970, https://openalex.org/I4210137101, https://openalex.org/I4210139971, https://openalex.org/I4210148734 |
| authorships[0].institutions[0].country_code | FR |
| authorships[0].institutions[0].display_name | Unité Évolution, Écologie et Paléontologie |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Sylvain Billiard |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | Évolution, Écologie et Paléontologie (Evo-Eco-Paleo) - UMR 8198 |
| authorships[1].author.id | https://openalex.org/A5033988037 |
| authorships[1].author.orcid | |
| authorships[1].author.display_name | Hélène Leman |
| authorships[1].countries | FR |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I4210160577 |
| authorships[1].affiliations[0].raw_affiliation_string | Unité de Mathématiques Pures et Appliquées |
| authorships[1].affiliations[1].raw_affiliation_string | Inria Lyon |
| authorships[1].institutions[0].id | https://openalex.org/I4210160577 |
| authorships[1].institutions[0].ror | https://ror.org/05n21n105 |
| authorships[1].institutions[0].type | facility |
| authorships[1].institutions[0].lineage | https://openalex.org/I113428412, https://openalex.org/I1294671590, https://openalex.org/I203339264, https://openalex.org/I4210160577 |
| authorships[1].institutions[0].country_code | FR |
| authorships[1].institutions[0].display_name | Unité de Mathématiques Pures et Appliquées |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Hélène Leman |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | Inria Lyon, Unité de Mathématiques Pures et Appliquées |
| authorships[2].author.id | https://openalex.org/A5041065788 |
| authorships[2].author.orcid | https://orcid.org/0000-0001-7849-2090 |
| authorships[2].author.display_name | Thomas Rey |
| authorships[2].countries | FR, US |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I4210101304 |
| authorships[2].affiliations[0].raw_affiliation_string | Reliable numerical approximations of dissipative systems |
| authorships[2].affiliations[1].institution_ids | https://openalex.org/I4210145948 |
| authorships[2].affiliations[1].raw_affiliation_string | Laboratoire Paul Painlevé - UMR 8524 |
| authorships[2].institutions[0].id | https://openalex.org/I4210145948 |
| authorships[2].institutions[0].ror | https://ror.org/043n4fm24 |
| authorships[2].institutions[0].type | facility |
| authorships[2].institutions[0].lineage | https://openalex.org/I1294671590, https://openalex.org/I1294671590, https://openalex.org/I1326498283, https://openalex.org/I2279609970, https://openalex.org/I4210141950, https://openalex.org/I4210145948 |
| authorships[2].institutions[0].country_code | FR |
| authorships[2].institutions[0].display_name | Laboratoire Paul Painlevé |
| authorships[2].institutions[1].id | https://openalex.org/I4210101304 |
| authorships[2].institutions[1].ror | https://ror.org/01abzsb47 |
| authorships[2].institutions[1].type | company |
| authorships[2].institutions[1].lineage | https://openalex.org/I4210101304 |
| authorships[2].institutions[1].country_code | US |
| authorships[2].institutions[1].display_name | Prediction Systems (United States) |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Thomas Rey |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | Laboratoire Paul Painlevé - UMR 8524, Reliable numerical approximations of dissipative systems |
| authorships[3].author.id | https://openalex.org/A5005255840 |
| authorships[3].author.orcid | https://orcid.org/0000-0002-3558-9420 |
| authorships[3].author.display_name | Viet Chi Tran |
| authorships[3].countries | FR |
| authorships[3].affiliations[0].institution_ids | https://openalex.org/I4210144844 |
| authorships[3].affiliations[0].raw_affiliation_string | Laboratoire Analyse et Mathématiques Appliquées |
| authorships[3].institutions[0].id | https://openalex.org/I4210144844 |
| authorships[3].institutions[0].ror | https://ror.org/0581g8849 |
| authorships[3].institutions[0].type | facility |
| authorships[3].institutions[0].lineage | https://openalex.org/I1294671590, https://openalex.org/I1294671590, https://openalex.org/I197681013, https://openalex.org/I4210141950, https://openalex.org/I4210144844, https://openalex.org/I4210154111 |
| authorships[3].institutions[0].country_code | FR |
| authorships[3].institutions[0].display_name | Laboratoire d’Analyse et de Mathématiques Appliquées |
| authorships[3].author_position | last |
| authorships[3].raw_author_name | Viet-Chi Tran |
| authorships[3].is_corresponding | False |
| authorships[3].raw_affiliation_strings | Laboratoire Analyse et Mathématiques Appliquées |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://arxiv.org/pdf/2201.05219 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Continuous limits of large plant-pollinator random networks and some applications |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T06:51:31.235846 |
| primary_topic.id | https://openalex.org/T10487 |
| primary_topic.field.id | https://openalex.org/fields/11 |
| primary_topic.field.display_name | Agricultural and Biological Sciences |
| primary_topic.score | 0.9980000257492065 |
| primary_topic.domain.id | https://openalex.org/domains/1 |
| primary_topic.domain.display_name | Life Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1105 |
| primary_topic.subfield.display_name | Ecology, Evolution, Behavior and Systematics |
| primary_topic.display_name | Plant and animal studies |
| related_works | https://openalex.org/W4292317591, https://openalex.org/W2153195003, https://openalex.org/W4381426054, https://openalex.org/W2587663446, https://openalex.org/W2254704327, https://openalex.org/W3045147376, https://openalex.org/W1990639689, https://openalex.org/W2379331219, https://openalex.org/W2903980083, https://openalex.org/W1974535339 |
| cited_by_count | 1 |
| counts_by_year[0].year | 2024 |
| counts_by_year[0].cited_by_count | 1 |
| locations_count | 6 |
| best_oa_location.id | pmh:oai:arXiv.org:2201.05219 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306400194 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | arXiv (Cornell University) |
| best_oa_location.source.host_organization | https://openalex.org/I205783295 |
| best_oa_location.source.host_organization_name | Cornell University |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| best_oa_location.license | |
| best_oa_location.pdf_url | https://arxiv.org/pdf/2201.05219 |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | text |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | |
| best_oa_location.landing_page_url | http://arxiv.org/abs/2201.05219 |
| primary_location.id | pmh:oai:arXiv.org:2201.05219 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306400194 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | arXiv (Cornell University) |
| primary_location.source.host_organization | https://openalex.org/I205783295 |
| primary_location.source.host_organization_name | Cornell University |
| primary_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| primary_location.license | |
| primary_location.pdf_url | https://arxiv.org/pdf/2201.05219 |
| primary_location.version | submittedVersion |
| primary_location.raw_type | text |
| primary_location.license_id | |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | |
| primary_location.landing_page_url | http://arxiv.org/abs/2201.05219 |
| publication_date | 2022-01-13 |
| publication_year | 2022 |
| referenced_works_count | 0 |
| abstract_inverted_index.a | 2, 13, 19, 29, 54, 83, 153, 207, 210 |
| abstract_inverted_index.We | 0 |
| abstract_inverted_index.an | 24 |
| abstract_inverted_index.be | 150 |
| abstract_inverted_index.by | 46, 72, 82, 124 |
| abstract_inverted_index.in | 111 |
| abstract_inverted_index.is | 18, 70, 80, 140, 146 |
| abstract_inverted_index.of | 6, 21, 31, 35, 66, 89, 96, 103, 119, 126, 158, 188, 213, 215 |
| abstract_inverted_index.on | 39, 63, 76 |
| abstract_inverted_index.or | 114, 130, 142 |
| abstract_inverted_index.to | 86, 169, 204 |
| abstract_inverted_index.we | 196 |
| abstract_inverted_index.Our | 108 |
| abstract_inverted_index.The | 33, 155 |
| abstract_inverted_index.and | 9, 42, 100, 135, 148, 163, 179, 192, 217 |
| abstract_inverted_index.are | 133, 161, 167, 202 |
| abstract_inverted_index.but | 52 |
| abstract_inverted_index.can | 57, 149 |
| abstract_inverted_index.has | 53 |
| abstract_inverted_index.its | 87 |
| abstract_inverted_index.the | 22, 36, 40, 64, 73, 94, 97, 101, 120, 138, 144, 171, 174, 180, 185, 189, 193 |
| abstract_inverted_index.Each | 78 |
| abstract_inverted_index.This | 91 |
| abstract_inverted_index.cost | 55 |
| abstract_inverted_index.each | 16 |
| abstract_inverted_index.edge | 25 |
| abstract_inverted_index.node | 20 |
| abstract_inverted_index.pair | 30, 212 |
| abstract_inverted_index.rate | 51 |
| abstract_inverted_index.show | 197 |
| abstract_inverted_index.that | 198 |
| abstract_inverted_index.when | 137, 143 |
| abstract_inverted_index.with | 152 |
| abstract_inverted_index.PDEs, | 195 |
| abstract_inverted_index.death | 60 |
| abstract_inverted_index.dense | 147 |
| abstract_inverted_index.graph | 99, 145 |
| abstract_inverted_index.large | 141 |
| abstract_inverted_index.limit | 165 |
| abstract_inverted_index.model | 5, 109, 178 |
| abstract_inverted_index.plant | 8, 49, 59 |
| abstract_inverted_index.rate, | 61 |
| abstract_inverted_index.study | 1 |
| abstract_inverted_index.these | 159 |
| abstract_inverted_index.trait | 84, 92 |
| abstract_inverted_index.which | 56 |
| abstract_inverted_index.degree | 88 |
| abstract_inverted_index.graph, | 23 |
| abstract_inverted_index.graph: | 15 |
| abstract_inverted_index.limits | 160, 187 |
| abstract_inverted_index.nested | 113, 199 |
| abstract_inverted_index.plants | 216 |
| abstract_inverted_index.single | 211 |
| abstract_inverted_index.system | 37 |
| abstract_inverted_index.between | 28, 106, 173, 209 |
| abstract_inverted_index.central | 164 |
| abstract_inverted_index.depends | 38 |
| abstract_inverted_index.insects | 47 |
| abstract_inverted_index.modular | 115 |
| abstract_inverted_index.network | 191 |
| abstract_inverted_index.plants. | 77 |
| abstract_inverted_index.process | 123 |
| abstract_inverted_index.species | 11, 17, 79, 214 |
| abstract_inverted_index.studied | 162 |
| abstract_inverted_index.systems | 125 |
| abstract_inverted_index.through | 12 |
| abstract_inverted_index.towards | 206 |
| abstract_inverted_index.Finally, | 183 |
| abstract_inverted_index.between- | 41 |
| abstract_inverted_index.collapse | 205 |
| abstract_inverted_index.discrete | 175 |
| abstract_inverted_index.dynamics | 34 |
| abstract_inverted_index.expected | 203 |
| abstract_inverted_index.graphon. | 154 |
| abstract_inverted_index.includes | 110 |
| abstract_inverted_index.increase | 58 |
| abstract_inverted_index.ordinary | 127 |
| abstract_inverted_index.quantify | 170 |
| abstract_inverted_index.replaced | 151 |
| abstract_inverted_index.species. | 32, 107 |
| abstract_inverted_index.studied, | 136 |
| abstract_inverted_index.studying | 184 |
| abstract_inverted_index.theorems | 166 |
| abstract_inverted_index.behaviors | 157 |
| abstract_inverted_index.bipartite | 14 |
| abstract_inverted_index.densities | 65 |
| abstract_inverted_index.depending | 62 |
| abstract_inverted_index.equations | 129, 132 |
| abstract_inverted_index.exchanged | 105 |
| abstract_inverted_index.harvested | 75 |
| abstract_inverted_index.increased | 71 |
| abstract_inverted_index.increases | 48 |
| abstract_inverted_index.long-time | 156 |
| abstract_inverted_index.networks. | 116 |
| abstract_inverted_index.resources | 74, 104 |
| abstract_inverted_index.resulting | 194 |
| abstract_inverted_index.structure | 95 |
| abstract_inverted_index.continuous | 186 |
| abstract_inverted_index.determines | 93 |
| abstract_inverted_index.difference | 172 |
| abstract_inverted_index.particular | 112 |
| abstract_inverted_index.pollinator | 10 |
| abstract_inverted_index.population | 139 |
| abstract_inverted_index.quantities | 102 |
| abstract_inverted_index.stochastic | 3, 121, 176 |
| abstract_inverted_index.Pollinators | 68 |
| abstract_inverted_index.coexistence | 208 |
| abstract_inverted_index.communities | 201 |
| abstract_inverted_index.established | 134, 168 |
| abstract_inverted_index.generalism. | 90 |
| abstract_inverted_index.interacting | 7 |
| abstract_inverted_index.interaction | 98, 190 |
| abstract_inverted_index.pollination | 45 |
| abstract_inverted_index.differential | 128 |
| abstract_inverted_index.interactions | 27 |
| abstract_inverted_index.pollinators. | 67, 218 |
| abstract_inverted_index.representing | 26 |
| abstract_inverted_index.reproduction | 50, 69 |
| abstract_inverted_index.Deterministic | 117 |
| abstract_inverted_index.characterized | 81 |
| abstract_inverted_index.corresponding | 85 |
| abstract_inverted_index.deterministic | 181 |
| abstract_inverted_index.interactions: | 44 |
| abstract_inverted_index.approximations | 118 |
| abstract_inverted_index.measure-valued | 122 |
| abstract_inverted_index.within-species | 43 |
| abstract_inverted_index.approximations. | 182 |
| abstract_inverted_index.individual-based | 4, 177 |
| abstract_inverted_index.plant-pollinator | 200 |
| abstract_inverted_index.integro-differential | 131 |
| cited_by_percentile_year | |
| countries_distinct_count | 2 |
| institutions_distinct_count | 4 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/2 |
| sustainable_development_goals[0].score | 0.6100000143051147 |
| sustainable_development_goals[0].display_name | Zero hunger |
| citation_normalized_percentile |