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Examples of threshold behaviour arise in resource competition theory, epidemiological theory and environmentally driven population dynamics, to name a few. Although expected from theory, thresholds may be difficult to detect in real datasets due to stochasticity, finite population size and confounding effects that soften the observed shifts and introduce variability in the data. Here, we propose a modelling framework for threshold responses to environmental drivers that allows for a flexible treatment of the transition between regimes, including variation in the sharpness of the transition and the variance of the response. The model assumes two underlying stochastic processes whose mixture determines the system's response. For environmentally driven systems, the mixture is a function of an environmental covariate and the response may exhibit strong nonlinearity. When applied to two datasets for water-borne diseases, the model was able to capture the effect of rainfall on the mean number of cases as well as the variance. A quantitative description of this kind of threshold behaviour is of more general application to predict the response of ecosystems and human health to climate change.<\/jats:p>","DOI":"10.1098\/rsif.2007.1135","type":"journal-article","created":{"date-parts":[[2007,8,14]],"date-time":"2007-08-14T15:23:18Z","timestamp":1187104998000},"page":"247-252","update-policy":"https:\/\/doi.org\/10.1098\/crossmarkpolicy","source":"Crossref","is-referenced-by-count":39,"title":["A stochastic model for ecological systems with strong nonlinear response to environmental drivers: application to two water-borne diseases"],"prefix":"10.1098","volume":"5","author":[{"given":"Claudia Torres","family":"Code\u00e7o","sequence":"first","affiliation":[{"name":"Oswaldo Cruz Foundation, Avenida Brasil4365, Resid\u00eancia Oficial, Rio de Janeiro, RJ 21045-900, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Subhash","family":"Lele","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Statistical Sciences, University of Alberta, EdmontonAlberta, Canada T6G 2G1"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mercedes","family":"Pascual","sequence":"additional","affiliation":[{"name":"Department of Ecology and Evolutionary Biology, University of MichiganAnn Arbor, MI 48104, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Menno","family":"Bouma","sequence":"additional","affiliation":[{"name":"Department of Infectious and Tropical Diseases, London School of Hygiene and Tropical MedicineKeppel Street, London WC1E 7HT, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Albert I","family":"Ko","sequence":"additional","affiliation":[{"name":"Gon\u00e7alo Muniz Research Center, Rua Waldemar Falc\u00e3o 121, Brotas Salvador, BA, 40295-001Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"175","published-online":{"date-parts":[[2007,8,14]]},"reference":[{"key":"e_1_3_2_2_1","unstructured":"Anderson R& May RInfectious diseases of humans: dynamics and control1992 Oxford UK:Oxford University Press."},{"key":"e_1_3_2_3_1","doi-asserted-by":"publisher","DOI":"10.1080\/15287390490492313"},{"key":"e_1_3_2_4_1","doi-asserted-by":"publisher","DOI":"10.1186\/1471-2334-1-1"},{"key":"e_1_3_2_5_1","doi-asserted-by":"publisher","DOI":"10.2105\/AJPH.91.8.1194"},{"key":"e_1_3_2_6_1","doi-asserted-by":"crossref","unstructured":"Efron B& Tibshirani R.J. 1993 An introduction to the bootstrap. 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