Bounding the number of calling animals with passive acoustics and reliable locations

When n animal calls are passively detected at n different times, the number of animals producing the sounds is anywhere between one and n unless more information is available. When extremely reliable confidence intervals of location are also available for each call, the upper bound is still n, but a lower bound can be derived. The lower bound exceeds one when it is physically impossible for an animal to travel quickly enough to go from one reliable location to another within the temporal call interval. When many calls are detected, it may be too complicated or numerically prohibitive to determine the minimum number of animals responsible for the calls in space and time by inspection or brute force methods. Instead, it is advantageous to use graph theory. The lower bound for the number of calling animals can be derived using 100% confidence intervals of each call's location. Mathematical theorems guarantee the lower bound is correct: a lesser value is impossible to obtain. Guaranteed bounds for the abundance of calling animals are useful for conservation in the presence of environmental stress and studying behavior.