Critical windows: A method for detecting lagged variables in ecological time series

Many developmental processes in the life sciences, ecology and even economics depend strongly on environmental conditions occurring a bounded time interval, results often far later. Examples are as diverse plant phenology, grapewine maturation, diapause induction so on. The method proposed here, aims at detecting quickly such effects. basic idea is to regress recorded of series replications process against function an independent series. This variable defined set periods time, systematically scanned by varying their lower upper bounds. In simple cases when this integral effect strictly limited window, response model, under form correlation coefficients, tractable its shape predictable. It same window bell-shaped can be fitted with other weighting functions Beta polynomials. null hypothesis absence influence any past interval tested Monte-Carlo simulation. most likely determined maximum coefficient, bivariate confidence estimated bootstrap. period found rectangular shaped used starting point for more specific windows. technique has advantage avoiding split climatic into arbitrary slices, thus multiplying predictors complicating models selection. closely linked continuous lag distributed simplification that interest not explicitly dependent. given prediction aphids population dynamics, male morphs aphids, phenology ash tree.