The consequences of null model selection for predicting mortality from multiple stressors

Many ecological systems are now exposed to multiple stressors, and ecosystem management increasingly requires consideration of the joint effects of multiple stressors on focal populations, communities and ecosystems. In the absence of empirical data, ecosystem managers could use null models based on the combination of independently acting stressors to estimate the joint effects of multiple stressors. Here, we used a simulation study and a meta-analysis to explore the consequences of null model selection for the prediction of mortality resulting from exposure to two stressors. Comparing five existing null models, we show that some null models systematically predict lower mortality rates than others, with predicted mortality rates up to 67.5% higher or 50% lower than the commonly used Simple Addition model. However, the null model predicting the highest mortality rate differed across parameter sets, and therefore there is no general 'precautionary null model' for multiple stressors. Using a multi-model framework, we re-analysed data from two earlier meta-analyses and found that 54% of the observed joint effects fell within the range of predictions from the suite of null models. Furthermore, we found that most null models systematically underestimated the observed joint effects, with only the Stressor Addition model showing a bias for overestimation. Finally, we found that the intensity of individual stressors was the strongest predictor of the magnitude of the joint effect across all null models. As a result, studies characterizing the effects of individuals stressors are still required for accurate prediction of mortality resulting from multiple stressors.