The renowned Australian entomologist Alexander J. Nicholson carried out a series of experiments in the 1950s with the intent of learning more about a sheep pest, the blowfly. The results presented here are driven by analyses of the data that Nicholson collected. The situation is of special interest because it involves a system that is nonlinear, has time lags and might be described as non-stationary. There are other complicating aspects including that: the data are aggregate referring to a sum of interacting cohorts, age effects exist, the data are measured at discrete times yet the phenomenon exists in continuous time and a structural change may be taking place. In the work, the spectrogram and complex demodulation prove to be useful tools since the phenomenon is varying, depending on both time and period (or frequency). These tools have in common the notion of an evolutionary spectrum. The goals are to explore some of Nicholson’s data and to illustrate how the tools of complex demodulation and the spectrogram and subject matter can elicit information from time-series data.