Climate change is rapidly increasing the frequency of extreme events. Sea surface temperature anomalies, heat waves, and droughts have become more frequent, with potentially disastrous consequences for ecosystem structure and function. Yet ecosystems exhibit remarkable spatial variation in their sensitivity to climate change. Identifying why sensitivity to climate extremes varies among ecosystems remains challenging, in part because there is no standardized method for quantifying ecosystem sensitivity. Sensitivity can be decomposed into four inter-related components: resistance, resilience, recovery, and lag effects. The methods for estimating these components differ among ecosystems and among studies within an ecosystem. For example, drought resistance in grasslands is calculated as the change in aboveground net primary production (ANPP) per mm change in rainfall (i.e. the slope of the ANPP-precipitation regression), the percent decline in ANPP during disturbance from previous years, the percent reduction from mean ANPP during disturbance, the log-response ratio of disturbance to previous years, etc. Methods for estimating lag effects are no less variable and suffer from the difficulty of making statistical inferences from one point in time. Thus, there is a pressing need for a theoretical and quantitative framework for estimating resistance, resilience, recovery, and lag effects to extreme events that can be applied across many disparate ecosystems and stress events to enable rigorous comparisons.
Results/Conclusions
Here, I provide such a framework by coupling ARIMAX time series models with Impulse Response Functions common to economics. Economists use Impulse Response Functions to quantify how resistant commodities and markets are to sudden shocks, how long it takes for markets to recover after the stress event, and whether markets exhibit stability or lag effects after a stress event. Adapting Impulse Response Functions to ecosystems allows can help ecologists identify resistant ecosystems are to stress under standardized conditions (i.e. a two standard deviation decline in rainfall) for standardized responses. Importantly, Impulse Response Functions integrate all components of ecosystem sensitivity (resistance, resilience, recovery, and lag effects) into one quantitative framework, allowing ecologists to easily calculate all four metrics of sensitivity in a standardized format that allows for comparisons both within and among ecosystems. I demonstrate this method by calculating resistance, resilience, and lag effects for fifteen grassland sites. My results support the long-held conclusion that arid ecosystems are the least resistance to drought, but also suggest that lag effects might be much less common than previously thought.