To threshold or not to threshold? That's the question

Abstract

The concept of evaluating multiple alternative models to determine ecological response form is over a century old and is ever more relevant as modern computing power allows ever more complicated models to be routinely used but often without a reasonable model verification process, particularly in fields where the ecological conceptual model is still developing. The emphasis for developing a statistical model is to test the validity of the hypothesis represented by the model. We present a framework of model identification and evaluation that includes exploratory data analysis and model diagnostics and evaluation. This framework emphasizes the importance of evaluating multiple alternative models when evaluating the validity of the model. This process is illustrated by using a model-building problem for quantifying the stream ecological response to urbanization using a data set from a large ecological study designed to understand how stream ecosystems respond to urbanization. The paper focuses on the question of whether a threshold model is appropriate, and demonstrates the importance of evaluating multiple alternative models in the detection of ecological thresholds, and illustrates how choosing an inappropriate model can lead to erroneous conclusion regarding the existence of thresholds.