Are experiment sample sizes adequate to detect biologically important interactions between multiple stressors?

Abstract

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.

Keywords: additive null model; critical effect size; ecosystem drivers; experimental design; minimum biological effect of interest; multiplicative null model; replicates; statistical power.