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.

中文翻译：

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使用被动声学和可靠位置限制呼叫动物的数量

当在n 个不同时间被动检测到n个动物叫声时，除非有更多信息可用，否则发出声音的动物数量介于 1 和n之间。当每个调用也可以获得极其可靠的位置置信区间时，上限仍然是n，但可以推导出下界。当动物在物理上不可能足够快地移动以在时间呼叫间隔内从一个可靠位置移动到另一个位置时，下限超过 1。当检测到许多呼叫时，通过检查或蛮力方法确定在空间和时间上负责呼叫的最小动物数量可能太复杂或在数值上令人望而却步。相反，使用图论是有利的。可以使用每个呼叫位置的 100% 置信区间推导出呼叫动物数量的下限。数学定理保证下界是正确的：不可能获得较小的值。在存在环境压力和研究行为的情况下，保证呼叫动物数量的界限对于保护是有用的。