RESUMEN
As most ecosystems are being challenged by multiple, co-occurring stressors, an important challenge is to understand and predict how stressors interact to affect biological responses. A popular approach is to design factorial experiments that measure biological responses to pairs of stressors and compare the observed response to a null model expectation. Unfortunately, we believe experiment sample sizes are inadequate to detect most non-null stressor interaction responses, greatly hindering progress. Using both real and simulated data, we show sample sizes typical of many experiments (<6) can (i) only detect very large deviations from the additive null model, implying many important non-null stressor-pair interactions are being missed, and (ii) potentially lead to mostly statistical outliers being reported. Computer code that simulates data under either additive or multiplicative null models is provided to estimate statistical power for user-defined responses and sample sizes, and we recommend this is used to aid experimental design and interpretation of results. We suspect that most experiments may require 20 or more replicates per treatment to have adequate power to detect nonadditive. However, estimates of power need to be made while considering the smallest interaction of interest, i.e., the lower limit for a biologically important interaction, which is likely to be system-specific, meaning a general guide is unavailable. We discuss ways in which the smallest interaction of interest can be chosen, and how sample sizes can be increased. Our main analyses relate to the additive null model, but we show similar problems occur for the multiplicative null model, and we encourage similar investigations into the statistical power of other null models and inference methods. Without knowledge of the detection abilities of the statistical tools at hand or the definition of the smallest meaningful interaction, we will undoubtedly continue to miss important ecosystem stressor interactions.
RESUMEN
Understanding how multiple co-occurring environmental stressors combine to affect biodiversity and ecosystem services is an on-going grand challenge for ecology. Currently, progress has been made through accumulating large numbers of smaller-scale empirical studies that are then investigated by meta-analyses to detect general patterns. There is particular interest in detecting, understanding and predicting 'ecological surprises' where stressors interact in a non-additive (e.g. antagonistic or synergistic) manner, but so far few general results have emerged. However, the ability of the statistical tools to recover non-additive interactions in the face of data uncertainty is unstudied, so crucially, we do not know how well the empirical results reflect the true stressor interactions. Here, we investigate the performance of the commonly implemented additive null model. A meta-analysis of a large (545 interactions) empirical dataset for the effects of pairs of stressors on freshwater communities reveals additive interactions dominate individual studies, whereas pooling the data leads to an antagonistic summary interaction class. However, analyses of simulated data from food chain models, where the underlying interactions are known, suggest both sets of results may be due to observation error within the data. Specifically, we show that the additive null model is highly sensitive to observation error, with non-additive interactions being reliably detected at only unrealistically low levels of data uncertainty. Similarly, plausible levels of observation error lead to meta-analyses reporting antagonistic summary interaction classifications even when synergies co-dominate. Therefore, while our empirical results broadly agree with those of previous freshwater meta-analyses, we conclude these patterns may be driven by statistical sampling rather than any ecological mechanisms. Further investigation of candidate null models used to define stressor-pair interactions is essential, and once any artefacts are accounted for, the so-called 'ecological surprises' may be more frequent than was previously assumed.