Using SiZer to detect thresholds in ecological data

Ecological systems can change substantially in response to small shifts in environmental conditions. Such changes are characterized by a non‐linear relationship between the value of the response variable and one or more explanatory variables. Documenting the magnitude of change and the environmental conditions that give rise to these threshold responses is important for both the scientific community and the agencies charged with ecosystem management. A threshold is defined as a substantial change in a response variable, given a marginal change in environmental conditions. Here, we demonstrate the usefulness of a derivative‐based method for detecting ecological thresholds along a single explanatory variable. The “significant zero crossings” (SiZer) approach uses a non‐parametric method to approximate the response function and its derivatives and then examines how those functions change across the range of the explanatory variable. SiZer makes fewer assumptions than conventional threshold models and explores a full range of smoothing functions. We believe SiZer is a useful technique for the exploratory analysis of many ecological datasets.