{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T16:01:39Z","timestamp":1791475299879,"version":"4.3.4"},"reference-count":89,"publisher":"National Academy of Sciences","issue":"41","license":[{"start":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T00:00:00Z","timestamp":1791417600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"name":"NSF","award":["DMR-2218849."],"award-info":[{"award-number":["DMR-2218849."]}]}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,10,13]]},"abstract":"<jats:p>Classical ecological models predict that diverse communities should be unstable, presenting a central challenge to explaining the stable biodiversity seen in nature. We revisit this long-standing problem by extending the generalized Lotka\u2013Volterra model to include both spatial structure and environmental fluctuations across space and time. We find that neither space nor environmental noise alone can resolve the tension between diversity and stability, but that together they permit arbitrarily many species to stably coexist in a sufficiently large system, despite strongly disordered competitive interactions. We analytically characterize the noise-induced transition to coexistence, showing that spatiotemporal noise drives power-law abundance fluctuations, leading to an anomalous scaling of moments known empirically as Taylor\u2019s law. At the metacommunity level, this manifests as an emergent sublinear self-inhibition that stabilizes diversity and renders the interaction disorder irrelevant in the high-diversity limit. Spatiotemporal noise thus provides a resolution to the diversity-stability paradox and a generic mechanism by which complex communities can persist.<\/jats:p>","DOI":"10.1073\/pnas.2619598123","type":"journal-article","created":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T15:42:01Z","timestamp":1791474121000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["Spatiotemporal noise stabilizes unbounded diversity in strongly competitive communities"],"prefix":"10.1073","volume":"123","author":[{"given":"Amer","family":"Al-Hiyasat","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/042nb2s44","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics, Massachusetts Institute of Technology","place":["Cambridge"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel W.","family":"Swartz","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/042nb2s44","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics, Massachusetts Institute of Technology","place":["Cambridge"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jeff","family":"Gore","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/042nb2s44","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics, Massachusetts Institute of Technology","place":["Cambridge"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1112-5912","authenticated-orcid":false,"given":"Mehran","family":"Kardar","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/042nb2s44","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Physics, Massachusetts Institute of Technology","place":["Cambridge"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2026,10,8]]},"reference":[{"key":"e_1_3_4_1_2","volume-title":"The Diversity of Life","author":"Wilson E. O.","year":"1999","unstructured":"E. O. Wilson, The Diversity of Life (WW Norton & Company, 1999)."},{"key":"e_1_3_4_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/9781444325508.ch4"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.142680199"},{"key":"e_1_3_4_4_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature08821"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.131.3409.1292"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.1038\/238413a0"},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.5962\/bhl.title.4489"},{"key":"e_1_3_4_8_2","doi-asserted-by":"publisher","DOI":"10.2307\/1935608"},{"key":"e_1_3_4_9_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41559-021-01535-8"},{"key":"e_1_3_4_10_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.abm7841"},{"key":"e_1_3_4_11_2","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.ecolsys.31.1.343"},{"key":"e_1_3_4_12_2","doi-asserted-by":"publisher","DOI":"10.1038\/35012234"},{"key":"e_1_3_4_13_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1188321"},{"key":"e_1_3_4_14_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature10832"},{"key":"e_1_3_4_15_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1220529"},{"key":"e_1_3_4_16_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1253497"},{"key":"e_1_3_4_17_2","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms12285"},{"key":"e_1_3_4_18_2","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms12031"},{"key":"e_1_3_4_19_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature23273"},{"key":"e_1_3_4_20_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.118.028103"},{"key":"e_1_3_4_21_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1915313117"},{"key":"e_1_3_4_22_2","doi-asserted-by":"publisher","DOI":"10.1002\/ecy.70064"},{"key":"e_1_3_4_23_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.51.6.1207"},{"key":"e_1_3_4_24_2","doi-asserted-by":"publisher","DOI":"10.1086\/282900"},{"key":"e_1_3_4_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/0040-5809(85)90030-9"},{"key":"e_1_3_4_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12080-022-00549-7"},{"key":"e_1_3_4_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tpb.2024.12.005"},{"key":"e_1_3_4_28_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1007827"},{"key":"e_1_3_4_29_2","doi-asserted-by":"publisher","DOI":"10.1103\/PRXLife.2.013014"},{"key":"e_1_3_4_30_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.199.4335.1302"},{"key":"e_1_3_4_31_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.96.4.1463"},{"key":"e_1_3_4_32_2","unstructured":"F. Ferraro C. Grilletta A. Maritan S. Suweis S. Azaele Will a time-varying complex system be stable? arXiv [Preprint] (2026). https:\/\/arxiv.org\/abs\/2603.28464 (Accessed 10 April 2026)."},{"key":"e_1_3_4_33_2","doi-asserted-by":"publisher","DOI":"10.1086\/283778"},{"key":"e_1_3_4_34_2","doi-asserted-by":"publisher","DOI":"10.1006\/tpbi.1994.1013"},{"key":"e_1_3_4_35_2","doi-asserted-by":"publisher","DOI":"10.1086\/285949"},{"key":"e_1_3_4_36_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.94.038102"},{"key":"e_1_3_4_37_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2008.09.007"},{"key":"e_1_3_4_38_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12080-019-0420-9"},{"key":"e_1_3_4_39_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2022.111053"},{"key":"e_1_3_4_40_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.108.034404"},{"key":"e_1_3_4_41_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2221791120"},{"key":"e_1_3_4_42_2","doi-asserted-by":"crossref","unstructured":"E. Mallmin A. Traulsen S. De Monte Fluctuating growth rates link turnover and unevenness in species-rich communities. Ecol. Lett. 29 e70333 (2026).","DOI":"10.1111\/ele.70333"},{"key":"e_1_3_4_43_2","doi-asserted-by":"crossref","unstructured":"M. Asker M. Swailem U. C T\u00e4uber M. Mobilia Fixation and extinction in time-fluctuating spatially structured metapopulations. Phys. Rev. Res. 7 043205 (2025).","DOI":"10.1103\/6w4h-8xvk"},{"key":"e_1_3_4_44_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.75.10.5085"},{"key":"e_1_3_4_45_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tree.2012.08.014"},{"key":"e_1_3_4_46_2","doi-asserted-by":"publisher","DOI":"10.1086\/285580"},{"key":"e_1_3_4_47_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.95.042414"},{"key":"e_1_3_4_48_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2116954119"},{"key":"e_1_3_4_49_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41559-024-02618-y"},{"key":"e_1_3_4_50_2","doi-asserted-by":"publisher","DOI":"10.1046\/j.1461-0248.1999.22058.x"},{"key":"e_1_3_4_51_2","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/aada58"},{"key":"e_1_3_4_52_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.126.258301"},{"key":"e_1_3_4_53_2","doi-asserted-by":"publisher","DOI":"10.1086\/282171"},{"key":"e_1_3_4_54_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.102.052106"},{"key":"e_1_3_4_55_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.105.014417"},{"key":"e_1_3_4_56_2","doi-asserted-by":"publisher","DOI":"10.1038\/189732a0"},{"key":"e_1_3_4_57_2","doi-asserted-by":"publisher","DOI":"10.1080\/00018730801893043"},{"key":"e_1_3_4_58_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.adg8488"},{"key":"e_1_3_4_59_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.110.054403"},{"key":"e_1_3_4_60_2","doi-asserted-by":"publisher","DOI":"10.1038\/23876"},{"key":"e_1_3_4_61_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1461-0248.2004.00608.x"},{"key":"e_1_3_4_62_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2200390119"},{"key":"e_1_3_4_63_2","unstructured":"T. A. de Pirey Self-organized criticality in complex model ecosystems. arXiv [Preprint] (2025). https:\/\/arxiv.org\/abs\/2512.06961 (Accessed 9 December 2026)."},{"key":"e_1_3_4_64_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.105.024307"},{"key":"e_1_3_4_65_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2312822121"},{"key":"e_1_3_4_66_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tree.2010.07.009"},{"key":"e_1_3_4_67_2","unstructured":"J. F. Henderson A. Tiffeau-Mayer Fluctuating environments are sufficient to drive substantial variability in species abundance across locations. arXiv [Preprint] (2026). https:\/\/arxiv.org\/abs\/2603.02403 (Accessed 3 March 2026)."},{"key":"e_1_3_4_68_2","doi-asserted-by":"publisher","DOI":"10.2307\/2845026"},{"key":"e_1_3_4_69_2","unstructured":"R. Calvo Microbiome association diversity reflects proximity to the edge of instability. arXiv [Preprint] (2026). https:\/\/arxiv.org\/abs\/2601.22918 (Accessed 15 April 2026)."},{"key":"e_1_3_4_70_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1521291113"},{"key":"e_1_3_4_71_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41559-018-0587-2"},{"key":"e_1_3_4_72_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-020-18529-y"},{"key":"e_1_3_4_73_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-025-59253-9"},{"key":"e_1_3_4_74_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.1110760"},{"key":"e_1_3_4_75_2","doi-asserted-by":"publisher","DOI":"10.1093\/jxb\/10.2.290"},{"key":"e_1_3_4_76_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.70.12.3590"},{"key":"e_1_3_4_77_2","volume-title":"The Unified Neutral Theory of Biodiversity and Biogeography (MPB-32)","author":"Hubbell S. P.","year":"2001","unstructured":"S. P. Hubbell, The Unified Neutral Theory of Biodiversity and Biogeography (MPB-32) (Princeton University Press, 2001), vol. 32."},{"key":"e_1_3_4_78_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.293.5539.2413"},{"key":"e_1_3_4_79_2","doi-asserted-by":"publisher","DOI":"10.1086\/589746"},{"key":"e_1_3_4_80_2","doi-asserted-by":"publisher","DOI":"10.1111\/ele.12439"},{"key":"e_1_3_4_81_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.133.167101"},{"key":"e_1_3_4_82_2","doi-asserted-by":"publisher","DOI":"10.1103\/5h2c-thdw"},{"key":"e_1_3_4_83_2","unstructured":"J. Hairston G. Nelson S. P. Ellner C. M. Kearns \u201cOverlapping generations: The storage effect and the maintenance of biotic diversity\u201d in Population Dynamics in Ecological Space and Time O. E. Rhodes Jr. R. K. Chesser M. H. Smith Eds. (University of Chicago Press Chicago IL 1996) pp. 109\u2013145."},{"key":"e_1_3_4_84_2","first-page":"011037","article-title":"Many-species ecological fluctuations as a jump process from the brink of extinction","volume":"14","author":"de Pirey T. A.","year":"2024","unstructured":"T. A. de Pirey, G. Bunin, Many-species ecological fluctuations as a jump process from the brink of extinction. Phys. Rev. X 14, 011037 (2024).","journal-title":"Phys. Rev. X"},{"key":"e_1_3_4_85_2","doi-asserted-by":"publisher","DOI":"10.1209\/epl\/i1998-00123-2"},{"key":"e_1_3_4_86_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.78.274"},{"key":"e_1_3_4_87_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.38.373"},{"key":"e_1_3_4_88_2","doi-asserted-by":"publisher","DOI":"10.1038\/nphys2592"},{"key":"e_1_3_4_89_2","unstructured":"A. Al-Hiyasat D. Swartz J. Gore M. Kardar Supplemental data for \u201cSpatiotemporal noise stabilizes unbounded diversity in strongly-competitive communities\u201d. Figshare. https:\/\/doi.org\/10.6084\/m9.figshare.33350109.v1. Deposited 19 September 2026."}],"container-title":["Proceedings of the National Academy of Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.2619598123","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T15:42:31Z","timestamp":1791474151000},"score":1,"resource":{"primary":{"URL":"https:\/\/pnas.org\/doi\/10.1073\/pnas.2619598123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,8]]},"references-count":89,"journal-issue":{"issue":"41","published-print":{"date-parts":[[2026,10,13]]}},"alternative-id":["10.1073\/pnas.2619598123"],"URL":"https:\/\/doi.org\/10.1073\/pnas.2619598123","relation":{},"ISSN":["0027-8424","1091-6490"],"issn-type":[{"value":"0027-8424","type":"print"},{"value":"1091-6490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,8]]},"assertion":[{"value":"2026-06-08","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-08-28","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-10-08","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e2619598123"}}