title: A stochastic model for ecological systems with strong nonlinear response to environmental drivers: application to two water-borne diseases.
abstract: Ecological systems with threshold behaviour show drastic shifts in population abundance or species diversity in response to small variation in critical parameters. 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.
authors: Oswaldo Cruz Foundation, Avenida Brasil, 4365, Residência Oficial, Rio de Janeiro, RJ 21045-900, Brazil. codeco@fiocruz.br
authors: Claudia Torres
authors: CT
authors: Codeço
authors: Subhash
authors: S
authors: Lele
authors: Mercedes
authors: M
authors: Pascual
authors: Menno
authors: M
authors: Bouma
authors: Albert I
authors: AI
authors: Ko
mesh_terms: D000818:Animals; D002771:Cholera / Q000453:epidemiology / Q000635:transmission*; D004196:Disease Outbreaks / Q000706:statistics & numerical data; D017753:Ecosystem; D006801:Humans; D007922:Leptospirosis / Q000453:epidemiology / Q000635:transmission*; D008954:Models, Biological; D011891:Rain; D012377:Rodentia; D012621:Seasons; D013269:Stochastic Processes; D013997:Time Factors; D014871:Water Microbiology
references: BMC Ecol. 2004 Mar 31;4:2
references: 15056394
references: Science. 1983 Aug 12;221(4611):669-71
references: 17787737
references: Vestn Ross Akad Med Nauk. 2006;(2):25-9
references: 16544901
references: Bull Math Biol. 2001 Nov;63(6):1005-23
references: 11732173
references: Wkly Epidemiol Rec. 2005 Jan 21;80(3):21-8
references: 15715138
references: Lancet. 1982 May 29;1(8283):1216-8
references: 6122976
references: Proc Natl Acad Sci U S A. 2005 Feb 1;102(5):1702-7
references: 15653771
references: Trends Ecol Evol. 2005 Sep;20(9):511-9
references: 16701428
references: Am J Trop Med Hyg. 2002 May;66(5):605-10
references: 12201599
references: BMC Infect Dis. 2001;1:1
references: 11208258
references: Proc Natl Acad Sci U S A. 2006 Dec 5;103(49):18438-43
references: 17121996
references: J Toxicol Environ Health A. 2004 Oct 22-Nov 26;67(20-22):1667-77
references: 15371208
references: Proc Natl Acad Sci U S A. 2000 Feb 15;97(4):1438-43
references: 10677480
references: Proc Biol Sci. 2004 Oct 7;271(1552):1985-93
references: 15451687
references: Malar J. 2005 Jan 21;4:6
references: 15663795
references: Arch Dis Child. 2003 Dec;88(12):1070-5
references: 14670771
references: Microbes Infect. 2002 Feb;4(2):237-45
references: 11880057
references: Am J Public Health. 2001 Aug;91(8):1194-9
references: 11499103
references: Am J Trop Med Hyg. 2001 Nov;65(5):657-63
references: 11716133
references: Appl Environ Microbiol. 1984 Aug;48(2):420-4
references: 6486784
references: Nature. 2005 Aug 4;436(7051):696-700
references: 16079845