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This paper is concerned with the design and analysis of delay-tolerant networks (DTNs) deployed for free-roaming animal monitoring, wherein information is either transmitted or carried to static access-points by the animals whose movement is assumed to be random. Specifically, in such mobility-aided applications where routing is performed in a store-carry-and-drop manner, limited buffer capacity of a carrier node plays a critical role, and data loss due to buffer overflow heavily depends on access-point density. Driven by this fact, our focus in this paper is on providing sufficient conditions on access-point density that limit the likelihood of buffer overflow. We first derive sufficient access-point density conditions that ensure that the data loss rates are statistically guaranteed to be below a given threshold. Then, we evaluate and validate the derived theoretical results through comparison with both synthetic and real-world data.