Aligning some Nicholson sheep-blowfly data sets with system input periods

During the 1950s the Australian entomologist Alexander Nicholson studied a sheep pest, lucilia cuprina, (L cuprina), the sheep-blowfly. In laboratory experiments blowfly populations were set up in cages. They were supplied with necessary food and water and every other day counts were made of the numbers in their various stages of development. The experiments went on for over a year. Various statistical studies have been carried out on their data. Sadly, the bulk of the data appears to be lost. Recently this author made the discovery of total population counts for ten Nicholson experiments. These data were in a collection of copies of index cards he made during a trip to Australia in 1977. In eight of the experiments the input food was varied cyclically in sawtooth fashion, each experiment having a different period of application. However, and what is the concern of this article, which data set went with which period of application remains unclear. In the present study use is made of periodograms, spectrograms and seasonal adjustment to seek a one-to-one correspondence between series and period. The estimate constructed is consistent under smoothing and limiting conditions. It is time domain based, but confirmed by periodogram and spectrogram computation. Copyright © 2013 John Wiley & Sons Ltd