Effect of detrending and normalization on the analysis of luciferase-reported rhythms. This example is taken from an antennal pair isolated from a BG-luc; cry+ adult. luc activity was recorded for 8 days in constant darkness and at a constant temperature of 27°C. a) The upper panel in this column shows a plot of the raw data given in counts per second of bioluminescence plotted on the ordinate. Samples were recorded hourly as indicated on the abcissa. The dashed line illustrates a trend line defined by the application of a 72 hour low pass filter (see  for more detail about this use of filters). The lower panel shows the autocorrelation function for the raw data plotted immediately above. We use the autocorrelation function to detect rhythmicity[23, 27]. Correlation coefficients with range from -1 to 1 appear on the ordinate and the lag is plotted on the abscissa. The shaded area centered around 0 defines a 95% confidence interval. In this case, the shape of the function indicates one rhythmic cycle followed by a decrease, a pattern that suggests the signal is not rhythmic, b) The upper panel in this column shows the detrended and normalized signal obtained from the raw data shown in a). The signal was obtained by dividing each data value by the corresponding value on the trend line for a given time point. The values on the ordinate are given in arbitrary units and vary around a mean of 1 (as described in ). The lower panel shows the autocorrelation function for the detrended and normalized signal shown immediately above it. The application of these procedures reveals the presence of significant rhythmicity within the data set shown in a) above. The RI value is the value of the autocorrelation function at the third peak (marked by the asterisk); it indicates the strength of rhythmicity (see Table 1, Materials and Methods and  for more detail). The RS value is obtained from the ratio of the RI value to the 95% confidence line. Thus when RS is ≥ 1, the rhythm is statistically significant (see Materials and Methods for more detail). The absence of an asterisk in the lower panel of a) indicates the absence of a third peak in the autocorrelation function for the raw data set.