{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T04:03:34Z","timestamp":1773029014210,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1011458","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T00:00:00Z","timestamp":1694736000000}}],"reference-count":57,"publisher":"Public Library of Science (PLoS)","issue":"9","license":[{"start":{"date-parts":[[2023,9,5]],"date-time":"2023-09-05T00:00:00Z","timestamp":1693872000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100019217","name":"Institut de Valorisation des Donn\u00e9es","doi-asserted-by":"publisher","award":["PhD-2019a-5993304626"],"award-info":[{"award-number":["PhD-2019a-5993304626"]}],"id":[{"id":"10.13039\/501100019217","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Computational Biodiversity Science and Services program"},{"name":"Canadian Institute for Ecology & Evolution"},{"DOI":"10.13039\/501100021783","name":"Courtois Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100021783","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"crossref","award":["Discovery Grants and Discovery Accelerator Supplement"],"award-info":[{"award-number":["Discovery Grants and Discovery Accelerator Supplement"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Food webs are complex ecological networks whose structure is both ecologically and statistically constrained, with many network properties being correlated with each other. Despite the recognition of these invariable relationships in food webs, the use of the principle of maximum entropy (MaxEnt) in network ecology is still rare. This is surprising considering that MaxEnt is a statistical tool precisely designed for understanding and predicting many types of constrained systems. This principle asserts that the least-biased probability distribution of a system\u2019s property, constrained by prior knowledge about that system, is the one with maximum information entropy. MaxEnt has been proven useful in many ecological modeling problems, but its application in food webs and other ecological networks is limited. Here we show how MaxEnt can be used to derive many food-web properties both analytically and heuristically. First, we show how the joint degree distribution (the joint probability distribution of the numbers of prey and predators for each species in the network) can be derived analytically using the number of species and the number of interactions in food webs. Second, we present a heuristic and flexible approach of finding a network\u2019s adjacency matrix (the network\u2019s representation in matrix format) based on simulated annealing and SVD entropy. We built two heuristic models using the connectance and the joint degree sequence as statistical constraints, respectively. We compared both models\u2019 predictions against corresponding null and neutral models commonly used in network ecology using open access data of terrestrial and aquatic food webs sampled globally (N = 257). We found that the heuristic model constrained by the joint degree sequence was a good predictor of many measures of food-web structure, especially the nestedness and motifs distribution. Specifically, our results suggest that the structure of terrestrial and aquatic food webs is mainly driven by their joint degree distribution.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1011458","type":"journal-article","created":{"date-parts":[[2023,9,5]],"date-time":"2023-09-05T17:32:52Z","timestamp":1693935172000},"page":"e1011458","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":3,"title":["What constrains food webs? 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