{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T06:34:30Z","timestamp":1789194870633,"version":"build-2803163510"},"reference-count":66,"publisher":"National Academy of Sciences","issue":"20","license":[{"start":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T00:00:00Z","timestamp":1778716800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN-2024-05054"],"award-info":[{"award-number":["RGPIN-2024-05054"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["CRC-2020-00234"],"award-info":[{"award-number":["CRC-2020-00234"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,5,19]]},"abstract":"<jats:p>\n                    Much ecological theory has pursued understanding the mechanisms that stabilize communities, yet empirical analyses reveal deterministic nonlinear dynamics such as oscillations and chaos to be widespread in free-living populations. How then does stability emerge in ecosystems when the building blocks are unstable? We analyzed the extent to which deterministic nonlinear fluctuations produce the ecological stability gained via portfolio effects in globally important sockeye salmon (\n                    <jats:italic toggle=\"yes\">Oncorhynchus nerka<\/jats:italic>\n                    ) stock complexes from Bristol Bay and the Fraser River. Using empirical dynamic modeling of 27 populations spanning six decades, we show that stability emerges at the regional scale not despite, but specifically because constituent populations are highly nonlinear and orbit a shared attractor asynchronously. This asynchrony produced the uncorrelated fluctuations that underpin the portfolio effect and deterministic nonlinearity was the main source of variation, with attractor reconstruction accounting for 81 to 89% of the variance in annual sockeye recruitment in Bristol Bay and 61 to 78% in the Fraser River. Furthermore, local population dynamics were primarily chaotic, but when aggregated at the regional scale where commercial fisheries and some predators operate, the dynamics stabilized and interannual variability decreased by 47%. These results indicate that portfolio effects can transform locally unstable dynamics into stable outcomes at higher levels of aggregation, and that deterministic nonlinear dynamics rather than strong linear stochastic forcing produce the variation that portfolio effects act upon. Given the ubiquity of nonlinearity, the averaging of uncorrelated fluctuations produced by asynchronous nonlinear dynamics may be an underappreciated mechanism driving stability in ecosystems.\n                  <\/jats:p>","DOI":"10.1073\/pnas.2535296123","type":"journal-article","created":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T18:10:33Z","timestamp":1778782233000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":1,"title":["Ecological stability through nonlinear fluctuations and the portfolio effect"],"prefix":"10.1073","volume":"123","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9961-7179","authenticated-orcid":false,"given":"Robert M.","family":"Hechler","sequence":"first","affiliation":[{"name":"Department of Ecology and Evolutionary Biology, University of Toronto","place":["Toronto, Canada"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7591-7954","authenticated-orcid":false,"given":"Martin","family":"Krkosek","sequence":"additional","affiliation":[{"name":"Department of Ecology and Evolutionary Biology, University of Toronto","place":["Toronto, Canada"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2026,5,14]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature09060"},{"key":"e_1_3_4_2_2","doi-asserted-by":"publisher","DOI":"10.1038\/35012234"},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.adg8488"},{"key":"e_1_3_4_4_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature04742"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.96.4.1463"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.1038\/261459a0"},{"key":"e_1_3_4_7_2","volume-title":"Stability and Complexity in Model Ecosystems","author":"May R. 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