Using SiZer to detect thresholds in ecological data

Abstract

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.

Experimental and environmental factors affect spurious detection of ecological thresholds

“…For example, Evans-White et al (2009) applied NCPA for analysis of macroinvertebrate community-level responses to water-quality gradients. A hybrid approach incorporating model-fitting and datapartitioning was developed by Chaudhuri and Marron (1999) based on the second derivative of polynomial regressions (significant zero crossings, SiZer) and this method has been recently applied for ecological threshold detection in stream benthic macroinvertebrate communities (Sonderegger et al 2009. Each of these methods estimate a change point that ecologists often interpret as an ecological threshold (Evans-White et al 2009) and we use terms ''change point'' and ''threshold'' interchangeably throughout this paper.…”

Considerations for analyzing ecological community thresholds in response to anthropogenic environmental gradients

“…Threshold estimation depends on the selection of response variable, assumed shape of the response, and appropriateness of the corresponding statistical model, any of which can contribute to different interpretations regarding the location of a threshold or whether a threshold exists (e.g., Walsh et al 2005b, Moore and Palmer 2005, Dodds et al 2010. Compounding this problem is the wide array of statistical approaches available for identifying ecological thresholds (e.g., Toms and Lesperance 2003, Qian et al 2003, 2004, Paul and McDonald 2005, Brenden et al 2008, Andersen et al 2009, Sonderegger et al 2009, Baker and King 2010. Selection of an appropriate technique for a specific application from this increasingly lengthy list might not be obvious even to experienced analysts.…”

An analysis on the energy consumption of circulating pumps of residential swimming pools for peak load management

“…(12) cannot be solved by general optimization methods such as least squares, as R p X À r  R n X vs. out temperature changes with r. In this paper, the interior-point algorithm [39] is used to search the optimum of r, meanwhile Sizer [40] is used to obtain parameters of the change-point in the two-phase piecewise regression. Results are shown in Table 1 and Fig.…”