Biology Reference
In-Depth Information
values indicative of varying degrees of rhythmic determination. Thus,
the lower the RAE value, the more statistically significant the respective
rhythmic component is. This method is specifically designed to
process data sets that are relatively short and/or noisy and is generally
capable of extracting relatively weak rhythms. In addition, it extracts
meaningful periods despite mean and variance nonstationarities
that may exist in the data.
Results for the data sets from Figures 11-14 and 11-15 are presented in
Figures 11-22 and 11-23, respectively. In the first data set, only one
significant periodic component was determined with an oscillatory
amplitude of 99.63
0.88 y-axis units. The RAE for this component
was calculated to be 0.009, an extremely low RAE value—indicative
of an extremely well-determined rhythm. The estimated period is
23.997
0.011 hours.
The analysis of the second data set is more interesting, as the data were
confounded with mean and variance nonstationarity in addition to
noise. As seen from the output, shown in the right panel of Figure 11-23,
four periodic components were identified with the respective average
estimates for the periods and nonsymmetric 95% confidence intervals
shown in Table 11-1.
The RAE associated with the periodic component of 23.4 is the smallest,
with a value of 0.183 (not shown on printout). In addition, we point out
the first period listed in the first column appears to be the effect of an
attempt to fit the data trend as a periodic component.
B. A Model-Independent Algorithm: PHASEREF
The last method we introduce for assessing period, oscillatory
amplitude, and phase information from a rhythmic data series is
referred to as PHASEREF. This is a maximally assumption-free strategy
in which no model form for any rhythms is assumed. However, the
interpretation of results does require the assumption that there exists in
the data series being analyzed one dominant, primary rhythmic
component, the period of which is (approximately) known a priori.
PHASEREF is a modification of a method presented by Meerlo et al.
(1997). It requires the user to provide two period values with which to
calculate two sets of smoothed running average values of the data series
to be analyzed.
One smoothing filter should have a period value close to that
expected for the dominant rhythm being expressed in the data
series. For a circadian time series, this value would be approximately
24 hours. The result of smoothing the data with this period filter is
an appropriately smoothed baseline series in which the dominant-period
rhythm is nearly completely removed. Only long-term trends
