Using dose-response functions to improve calculations of the impact of anthropogenic noise

Estimating the number of animals impacted by a stressor typically involves combining a dose-response function with information about the distribution of animals and of the stressor. Regulators often prefer a single threshold to a full dose-response function, but much of the variability observed in the threshold at which different individuals respond to a stressor is an inherent characteristic of populations that needs to be taken into account to predict the effects of stressors. When selecting an exposure threshold, regulators need information on the proportion of the population that will be protected. Regulatory processes that calculate the number of animals impacted must draw from the dose-response function, the actual distribution of the animals, and a model mapping how the stressor intensity declines with distance from the source. Ignoring any of these factors can lead to significant errors in estimates of the area and numbers of animals affected. This paper focuses on behavioural responses of marine mammals to anthropogenic sound and demonstrates that a common approach of selecting the threshold at which half of the animals respond (RLp50) grossly underestimates the number of animals affected. We present an example, using a published dose-response function, where the number affected is underestimated by a factor of 280. Results would be similar for any stressor whose strength decreases following an inverse-square function as it dilutes into the environment. This paper presents a method to use a dose-response function to derive a more accurate estimate of animals affected and to set a threshold (the Effective Response Level) that corrects the problem with the RLp50 estimate. Estimates of effects of stressors should include estimates of uncertainty, which can be used to adapt thresholds to different policy contexts and conservation problems.