{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T14:18:44Z","timestamp":1788445124792,"version":"build-2803163510"},"reference-count":40,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100012659","name":"Foundation for Innovative Research Groups of the National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Biosciences"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.mbs.2026.109754","type":"journal-article","created":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T16:02:39Z","timestamp":1782748959000},"page":"109754","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["The hydra and hormetic effects in a single discrete-time overcompensation model"],"prefix":"10.1016","volume":"400","author":[{"given":"Liwen","family":"Song","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sanyi","family":"Tang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9610-0289","authenticated-orcid":false,"given":"Changcheng","family":"Xiang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.mbs.2026.109754_bib0001","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.ecocom.2013.02.002","article-title":"Harvesting, census timing and \u201chidden\u201d hydra effects","volume":"14","author":"Hilker","year":"2013","journal-title":"Ecol. Complex."},{"key":"10.1016\/j.mbs.2026.109754_bib0002","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.fishres.2008.01.003","article-title":"A review of harvest policies: understanding relative performance of control rules","volume":"94","author":"Deroba","year":"2008","journal-title":"Fish. Res."},{"issue":"6","key":"10.1016\/j.mbs.2026.109754_bib0003","doi-asserted-by":"crossref","first-page":"1585","DOI":"10.1890\/08-1467.1","article-title":"When can efforts to control nuisance and invasive species backfire?","volume":"19","author":"Zipkin","year":"2009","journal-title":"Ecol. Appl."},{"issue":"5","key":"10.1016\/j.mbs.2026.109754_bib0004","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1139\/f54-039","article-title":"Stock and recruitment","volume":"11","author":"Ricker","year":"1954","journal-title":"J. Fish. Res. Board Can."},{"issue":"5560","key":"10.1016\/j.mbs.2026.109754_bib0005","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1038\/261459a0","article-title":"Simple mathematical models with very complicated dynamics","volume":"261","author":"May","year":"1976","journal-title":"Nature"},{"issue":"1","key":"10.1016\/j.mbs.2026.109754_bib0006","first-page":"39","article-title":"Temporally structured density-dependence and population management","volume":"36","author":"Jonz\u00e9n","year":"1999","journal-title":"Ann. Zool. Fenn."},{"key":"10.1016\/j.mbs.2026.109754_bib0007","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.mbs.2013.12.003","article-title":"Harvest timing and its population dynamic consequences in a discrete single-species model","volume":"248","author":"Cid","year":"2014","journal-title":"Math. Biosci."},{"issue":"157","key":"10.1016\/j.mbs.2026.109754_bib0008","doi-asserted-by":"crossref","DOI":"10.1098\/rsif.2019.0468","article-title":"A general model of hormesis in biological systems and its application to pest management","volume":"16","author":"Tang","year":"2019","journal-title":"J. R. Soc. Interface"},{"issue":"1","key":"10.1016\/j.mbs.2026.109754_bib0009","doi-asserted-by":"crossref","first-page":"174","DOI":"10.3934\/dcdsb.2023092","article-title":"Understanding the hydra effect in predator-dependent functional response models","volume":"29","author":"Pal","year":"2024","journal-title":"Discrete Contin. Dyn. Syst. B"},{"issue":"5","key":"10.1016\/j.mbs.2026.109754_bib0010","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1111\/j.1461-0248.2009.01282.x","article-title":"When does greater mortality increase population size? the long history and diverse mechanisms underlying the hydra effect","volume":"12","author":"Abrams","year":"2009","journal-title":"Ecol. Lett."},{"issue":"1","key":"10.1016\/j.mbs.2026.109754_bib0011","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1146\/annurev.pharmtox.43.100901.140223","article-title":"Hormesis: the dose-response revolution","volume":"43","author":"Calabrese","year":"2003","journal-title":"Annu. Rev. Pharmacol. Toxicol."},{"issue":"2","key":"10.1016\/j.mbs.2026.109754_bib0012","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1191\/0960327102ht217oa","article-title":"Defining hormesis","volume":"21","author":"Calabrese","year":"2002","journal-title":"Hum. Exp. Toxicol."},{"issue":"7","key":"10.1016\/j.mbs.2026.109754_bib0013","doi-asserted-by":"crossref","first-page":"1451","DOI":"10.1897\/07-541.1","article-title":"Hormesis: why it is important to toxicology and toxicologists","volume":"27","author":"Calabrese","year":"2008","journal-title":"Environ. Toxicol. Chem."},{"issue":"5","key":"10.1016\/j.mbs.2026.109754_bib0014","doi-asserted-by":"crossref","first-page":"145","DOI":"10.15698\/mic2014.05.145","article-title":"Hormesis: a fundamental concept in biology","volume":"1","author":"Calabrese","year":"2014","journal-title":"Microb. Cell"},{"issue":"1","key":"10.1016\/j.mbs.2026.109754_bib0015","first-page":"1","article-title":"Temperature effects on the hormetic response of Myzus persicae after sublethal exposure to insecticides","volume":"5","author":"Silva","year":"2024","journal-title":"CABI Agric. Biosci."},{"issue":"4","key":"10.1016\/j.mbs.2026.109754_bib0016","doi-asserted-by":"crossref","first-page":"12","DOI":"10.56557\/upjoz\/2025\/v46i44800","article-title":"Harnessing hormesis: exploring insecticide dose-response dynamics for sustainable pest management","volume":"46","author":"Dey Roy","year":"2025","journal-title":"Uttar Pradesh J. Zool."},{"issue":"10","key":"10.1016\/j.mbs.2026.109754_bib0017","doi-asserted-by":"crossref","DOI":"10.1002\/ecy.2789","article-title":"How (co)evolution alters predator responses to increased mortality extinction thresholds and hydra effects","volume":"100","author":"Cortez","year":"2019","journal-title":"Ecology"},{"issue":"1\u20132","key":"10.1016\/j.mbs.2026.109754_bib0018","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.mbs.2008.06.004","article-title":"A paradox in discrete single species population dynamics with harvesting\/thinning","volume":"214","author":"Seno","year":"2008","journal-title":"Math. Biosci."},{"issue":"7","key":"10.1016\/j.mbs.2026.109754_bib0019","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1140\/epjp\/s13360-025-06615-3","article-title":"Hydra effect and stability analysis of a delayed predator\u2013prey model with Allee effect in the predator","volume":"140","author":"Mondal","year":"2025","journal-title":"Eur. Phys. J. Plus"},{"issue":"11","key":"10.1016\/j.mbs.2026.109754_bib0020","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1016\/j.tree.2014.08.006","article-title":"When less is more: positive population-level effects of mortality","volume":"29","author":"Schr\u00f6der","year":"2014","journal-title":"Trends Ecol. Evol."},{"issue":"12","key":"10.1016\/j.mbs.2026.109754_bib0021","doi-asserted-by":"crossref","DOI":"10.1073\/pnas.2003955118","article-title":"Stage-specific overcompensation, the hydra effect, and the failure to eradicate an invasive predator","volume":"118","author":"Grosholz","year":"2021","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"issue":"3","key":"10.1016\/j.mbs.2026.109754_bib0022","doi-asserted-by":"crossref","first-page":"E59","DOI":"10.1086\/520119","article-title":"Food-dependent growth leads to overcompensation in stage-specific biomass when mortality increases","volume":"170","author":"De Roos","year":"2007","journal-title":"Am Nat."},{"key":"10.1016\/j.mbs.2026.109754_bib0023","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.jtbi.2011.12.012","article-title":"Global dynamics in a stage-structured discrete-time population model with harvesting","volume":"297","author":"Liz","year":"2012","journal-title":"J. Theor. Biol."},{"key":"10.1016\/j.mbs.2026.109754_bib0024","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/S0304-3800(98)00089-1","article-title":"Seasonal density dependence, timing of death and sustainable harvesting","volume":"110","author":"Kokko","year":"1998","journal-title":"Ecol. Model."},{"issue":"2","key":"10.1016\/j.mbs.2026.109754_bib0025","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/s00285-011-0416-6","article-title":"The hydra effect in predator\u2013prey models","volume":"64","author":"Sieber","year":"2012","journal-title":"J. Math. Biol."},{"key":"10.1016\/j.mbs.2026.109754_bib0026","doi-asserted-by":"crossref","DOI":"10.1098\/rsif.2025.0169","article-title":"Hormesis and hydra effects revealed by intraspecific overcompensation models and dose-response curves","volume":"22","author":"Tang","year":"2025","journal-title":"J. R. Soc. Interface"},{"issue":"5","key":"10.1016\/j.mbs.2026.109754_bib0027","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.1890\/15-0648.1","article-title":"Hydra effects in stable communities and their implications for system dynamics","volume":"97","author":"Cortez","year":"2016","journal-title":"Ecology"},{"key":"10.1016\/j.mbs.2026.109754_bib0028","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1007\/s00285-011-0489-2","article-title":"The hydra effect, bubbles, and chaos in a simple discrete population model with constant effort harvesting","volume":"65","author":"Liz","year":"2012","journal-title":"J. Math. Biol."},{"issue":"3","key":"10.1016\/j.mbs.2026.109754_bib0029","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1080\/17513750903009169","article-title":"Native intra-and inter-specific reactions may cause the paradox of pest control with harvesting","volume":"4","author":"Seno","year":"2010","journal-title":"J. Biol. Dyn."},{"issue":"5","key":"10.1016\/j.mbs.2026.109754_bib0030","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1177\/096032719801700510","article-title":"Agricultural implications of pesticide-induced hormesis of insects and mites","volume":"17","author":"Morse","year":"1998","journal-title":"Hum. Exp. Toxicol."},{"issue":"2","key":"10.1016\/j.mbs.2026.109754_bib0031","doi-asserted-by":"crossref","first-page":"581","DOI":"10.2307\/4926","article-title":"Density-dependent processes and key factors in insect populations","volume":"57","author":"Stiling","year":"1988","journal-title":"J. Anim. Ecol."},{"issue":"2","key":"10.1016\/j.mbs.2026.109754_bib0032","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1111\/j.1570-7458.2005.00297.x","article-title":"Mortality dynamics and population regulation in Bemisia tabaci","volume":"116","author":"Naranjo","year":"2005","journal-title":"Entomol. Exp. Appl."},{"issue":"4","key":"10.1016\/j.mbs.2026.109754_bib0033","doi-asserted-by":"crossref","DOI":"10.1177\/15593258211062785","article-title":"A universal delayed difference model fitting dose-response curves","volume":"19","author":"Yang","year":"2021","journal-title":"Dose-Response"},{"key":"10.1016\/j.mbs.2026.109754_bib0034","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s10493-020-00496-0","article-title":"Light intensity influences feeding and fecundity of Tetranychus urticae","volume":"81","author":"Shibuya","year":"2020","journal-title":"Exp. Appl. Acarol."},{"key":"10.1016\/j.mbs.2026.109754_bib0035","doi-asserted-by":"crossref","first-page":"1040","DOI":"10.1186\/s12885-023-11542-6","article-title":"Hormetic and synergistic effects of cancer treatments","volume":"23","author":"Tang","year":"2023","journal-title":"BMC Cancer"},{"issue":"3","key":"10.1016\/j.mbs.2026.109754_bib0036","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1016\/j.envpol.2004.10.001","article-title":"Paradigm lost, paradigm found: the re-emergence of hormesis","volume":"138","author":"Calabrese","year":"2005","journal-title":"Environ. Pollut."},{"issue":"4","key":"10.1016\/j.mbs.2026.109754_bib0037","doi-asserted-by":"crossref","first-page":"1308","DOI":"10.1021\/es071148m","article-title":"A general approach to modeling biphasic relationships","volume":"42","author":"Beckon","year":"2008","journal-title":"Environ. Sci. Technol."},{"issue":"12","key":"10.1016\/j.mbs.2026.109754_bib0038","doi-asserted-by":"crossref","first-page":"2175","DOI":"10.1890\/11-0410.1","article-title":"Stage-specific biomass overcompensation by juveniles in response to increased adult mortality","volume":"92","author":"Ohlberger","year":"2011","journal-title":"Ecology"},{"issue":"1","key":"10.1016\/j.mbs.2026.109754_bib0039","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s11538-021-00975-4","article-title":"Disease-induced hydra effect with overcompensatory recruitment","volume":"84","author":"Jaramillo","year":"2022","journal-title":"Bull. Math. Biol."},{"issue":"6","key":"10.1016\/j.mbs.2026.109754_bib0040","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1007\/s00285-024-02074-z","article-title":"Infection-induced increases to population size during cycles in a discrete-time epidemic model","volume":"88","author":"Strube","year":"2024","journal-title":"J. Math. Biol."}],"container-title":["Mathematical Biosciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0025556426001446?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0025556426001446?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T13:59:10Z","timestamp":1788443950000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0025556426001446"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":40,"alternative-id":["S0025556426001446"],"URL":"https:\/\/doi.org\/10.1016\/j.mbs.2026.109754","relation":{},"ISSN":["0025-5564"],"issn-type":[{"value":"0025-5564","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"The hydra and hormetic effects in a single discrete-time overcompensation model","name":"articletitle","label":"Article Title"},{"value":"Mathematical Biosciences","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.mbs.2026.109754","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"109754"}}