Many current paradigms for acoustic event detection (AED) are not adapted to the organic variability of natural sounds, and/or they assume a limit on the number of simultaneous sources: often only one source, or one source of each type, may be active. These aspects are highly undesirable for applications such as bird population monitoring. We introduce a simple method modelling the onsets, durations and offsets of acoustic events to avoid intrinsic limits on polyphony or on inter-event temporal patterns. We evaluate the method in a case study with over 3000 zebra finch calls. In comparison against a HMM-based method we find it more accurate at recovering acoustic events, and more robust for estimating calling rates.