Rescuing rhythms from noise: A new method of analysis

The analysis of a temporal series usually begins with a visual inspection of the raw data, from which a proper method for the detection of periodicities is chosen. Some of the methods currently used, as circular statistics, Cosinor, or spectral analyses, are useful when it comes to ascertain the existence of some periods, expected ‘a priori’ or to detect unknown frequencies. Even though some of the methods allow a wide scanning of possibilities, difficulties arise when signals are weak and concealed in larger amplitude noise. The register of the activity of a cave cricket, Strinatia brevipennis, under constant conditions, showed an intricate pattern of small peaks, interspersed with rare ones of much higher amplitudes. Attempts to analyse these data with the usual methods gave inconsistent results and sometimes did not detect rhythms. The results are mostly biased by the large amplitude components which hamper the detection of rhythms from weak signals. Schimmel and Paulssen (1997) proposed a noise-reduction method, which detects weak but coherent signals. This new tool was developed for the analysis of seismic data, being afterwards adapted to the analysis of temporal series of biological data. The method is called phase weighted stack (PWS) and per-forms a weighted summation of temporal series according to their coherence. The results are stacked time series which are cleaned up from incoherent noise, allowing the detection of weak signals that otherwise would be undistinguishable from noises. The method also enables the identification of the time (hour) of every periodic signal. The use of PWS in the analysis of crickets ’ activity data cleared out frequencies, exposing a circadian component in all records