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Interceptive eavesdropping on the alarm calls of heterospecifics provides crucial information about predators. Previous research suggests predator discrimination, call relevance, reliability, and reception explain when eavesdropping will evolve. However, there has been no quantitative analysis to scrutinize these principles, or how they interact. We develop a mathematical framework that formalizes the study of the key principles thought to select for eavesdropping. Interceptive eavesdropping appears to be greatly affected by the threat faced by caller and eavesdropper, as well as presence of informational noise affecting the detection of calls and predators. Accordingly, our model uses signal detection theory to examine when selection will favor alarm calling by a sender species and fleeing by an eavesdropping receiver species. We find eavesdropping is most strongly selected when (1) the receiver faces substantial threats, (2) species are ecologically similar, (3) senders often correctly discriminate threats, (4) receivers often correctly perceive calls, and (5) the receiver's personal discrimination of threats is poor. Furthermore, we find (6) that very high predation levels can select against eavesdropping because prey cannot continuously flee and must conserve energy. Reliability of heterospecific calls for identifying threats is thought to be important in selecting for eavesdropping. Consequently, we formally define reliability, showing its connection to specificity and sensitivity, clarifying how these quantities can be measured. We find that high call relevance, due to similar vulnerability to predators between species, strongly favors eavesdropping. This is because senders trade-off false alarms and missed predator detections in a way that is also favorable for the eavesdropper, by producing less of the costlier error. Unexpectedly, highly relevant calls increase the total number of combined errors and so have lower reliability. Expectedly, when noise greatly affects personally gathered cues to threats, but not heterospecific calls or detection of predators, eavesdropping is favored., Competing Interests: None., (© 2023 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd.)