Separating acoustic signal into underlying behaviors with self-exciting point process models

In animal communication, signals can arise endogenously or in response to cues, such as signals by conspecifics. When one signal serves dual functions, such as in birds that use the same song for mate attraction and territorial defense, the underlying reason for a vocalization cannot be determined without direct observations, and even then, may be hard to discern. We present an inhomogeneous, self-exciting point process model to estimate the underlying reasons for why an individual initiates a signal. In our application of these models, endogenous signals are assumed to arise at a constant rate, but each signal can also instigate (“self-excite”) additional signals by conspecific individuals. When applied to bullfrog (Rana catesbeiana) calls and ovenbird (Seiurus aurocapilla) songs, our model performs as well as a homogeneous point process model typically used to describe count data, while providing additional detail on the underlying motivations for signals. Although we apply the models to acoustic signals, our model can be applied to any self-exciting process and can be extended to include spatiotemporal dynamics in signals.