Evaluating the robustness of generalized additive models as a tool for threshold detection in variable environments

Abstract

As global climate change and anthropogenic activities amplify widespread environmental variability, there is a strong need for management strategies that incorporate relationships between ecosystem components. This need is especially apparent when changes in environmental drivers cause threshold responses (abrupt, nonlinear changes) in ecosystems. Such ecological thresholds can provide useful reference points for management decisions. However, methods for detecting thresholds in empirical datasets may fail to find an existing threshold, find one that does not exist, or be biased in their estimates of threshold locations. These types of threshold misspecifications can result in high conservation and socioeconomic costs. Simulation studies can mitigate these risks by providing information about method performance across different scenarios. Here, we constructed a series of simulations to evaluate the robustness of threshold detection with generalized additive models (GAMs) when exposed to a variety of common, real-world data characteristics. GAMs generally performed best when time series were long, observation error was low, thresholds were crossed fairly frequently, and covariates were accounted for. Over realistic ranges of values, observation error and frequency of threshold crossing had stronger effects on threshold detectability than time series length. Importantly, detectability was found to depend on both the shape of the threshold relationship and the statistical definition of the threshold location. As a case study, we applied this threshold detection method to an empirical dataset relating ocean temperature and the spatial distribution of Pacific hake (Merluccius productus), the largest volume fishery on the US West Coast. While the data suggest no statistical evidence for a threshold relationship, our simulations indicated approximately equal chances of true and false threshold detection given currently available data. Our results provide general guidelines for where threshold detection with GAMs is likely to be robust and are useful in the context of indicator development for ecosystem-based management in a variable world.