Updated: May 26, 2022
Unfortunately there is no single answer to this, because it depends on how loud the animal call is that you're listening to. Obviously you will be able to hear a Screaming Phia (Lipaugus vociferans) from further away than a hummingbird. So it's helpful to think about it in terms of what animal you are trying to record or what is the quietest sound you want to record.
Once you have a rough idea of the how loud your animal of interest is, you can work out the volume of detection, or acoustic footprint of your recorder for that animal, which is defined by the maximum distance from a recorder that you can still detect a call.
Note that we call it a volume of detection, not area. That is because it extends in all 3 dimensions, above the recorder as well as to the sides.
If your animal of interest is inside this volume of detection, you will be able to hear it in the recordings. However if the recorder gain is set too high, or the animal is too close to the recorder then the recoding will clip (exceed the maximum levels), and you can lose information. We call this space the volume of clipping.
In many cases you can still identify an animal if the sound is clipped, although computer algorithms may have a harder time, and you can also lose quieter calls that were happening at the same time. If you are trying to detect a quiet or rare call event, then it is often worth having a higher gain to increase your overall volume of detection even if it means you may get occasional clipping of a nearby call. However if the ambient noises are also loud then increasing the gain might not be the best option because the ambient sounds might clip the signal more often and reduce the overall likelihood of detecting your call event.
Selecting the right gain level is all about optimising your volume of detection and volume of clipping. Most people are happy to put up with some clipping if it means they can have a larger volume of detection. If in doubt, we recommend gain settings of 40-50dB to get started with however we highly recommend conducting a gain trial wherever possible.
If you happen to know the loudness (in dB SPL) of an animal call then you can work out roughly how far away you can detect it by:
r = 10 ^ ((As - 14)/ 20 )
where As is the call volume in dB SPL of the animal as measured from 1m away.
E.g. Given an animal with a 70dB call (when measured from 1m away), the maximum distance that the microphone can detect that call from is:
r = 10 ^ ((70 - 14)/ 20 )
r = 630 m
But that doesn't mean you will have a very intelligible recording. Let's say you want 5dB of signal gain above the noise floor to be able to reasonably identify the call over the noise. Then the equation becomes:
r = 10 ^ ((70 - 5 - 14)/ 20 )
r = 355 m
Note this equation only takes into consideration the spreading loss, as the sound waves expands out volumetrically through the air away from the source. Attenuation, or absorption through the air as the sound waves loose energy to the air molecules, is another factor that reduces the strength of a call over distance however this matters more in the ultrasound band than the audible band and hence has been omitted from the above equation.
For more information about how sound propagates and attenuates through air, see Sound attenuation through the air.