A common method for censusing calling marine mammals is passive acoustic monitoring where underwater hydrophones record data over large timespans. Several methods exist for estimating the true number of calls emitted in the monitored area, with the most common being distance sampling and mark-recapture. Both rely on fitting tunable parameters to data. The number of animals producing the calls is then derived by using a mean call rate. However, this rate is uncertain, often varying by factors from two to five. John Spiesberger and colleagues developed an algorithm, without any tunable parameters, producing a mathematically-guaranteed value for the minimum number of animals producing the calls. We tested whether this method detects changes in the mean number of calling animals using the Student t-test with 80% power and 5% false-alarm rate between two scenarios. Each scenario has the same number of calls, but first and second scenarios have call rates differing by a factor of three. The change in the number of calling animals is successfully detected, whereas traditional approaches cannot discern any change because both scenarios have the same number of calls. The statistics of the simulated calls for this study resembles sounds from migrating bowhead whales in the Beaufort sea.