The detection range of calling animals is commonly described by the passive sonar equations. However, the sonar equations do not account for interactions between source and ambient sound level, i.e., the Lombard effect. This behavior has the potential to introduce non-linearities into the sonar equations and result in incorrectly predicted detection ranges. Here, we investigate the relationship between ambient sound and effective detection ranges for North Atlantic right whales (Eubalaena glacialis) in Cape Cod Bay, MA, USA using a sparse array of acoustic recorders. Generalized estimating equations were used to model the probability that a call was detected as a function of distance between the calling animal and the sensor and the ambient sound level. The model suggests a non-linear relationship between ambient sound levels and the probability of detecting a call. Comparing the non-linear model to the linearized version of the same model resulted in 12 to 25% increases in the effective detection range. We also found evidence of the Lombard effect suggesting that it is the most plausible cause for the non-linearity in the relationship. Finally, we suggest a simple modification to the sonar equation for estimating detection probability for single sensor monitoring applications.
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