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.