Biology Reference
In-Depth Information
rhythm is retained, together with any longer-period trends. Next, the
times of occurrence of up-crossings and down-crossings of the short-
period filtered curve with regard to the baseline curve are computed (see
Figure 11-24). The times of maximum and minimum differences
between the two curves are also calculated from the difference of the
short-period smoothed series and the baseline series. Period estimates
for the dominant rhythm can now be obtained from successive
differences between up-crosses, maxima, down-crosses, and minima,
respectively.
A typical implementation of this analytical strategy might entail
calculating a 6-hour and a 24-hour running average of the original data
series. The crossings of these two smoothed lines provide the rising
and falling phase markers for each cycle. The maximum differences
between the smoothed curves for each cycle calculated between the
peak and the trough allow calculating the amplitude of each cycle. The
time of peak provides a third phase marker (assuming that acrophase
is to be used as the phase reference marker of record). More details can
be found in Abe et al. (2002).
Although maximally assumption-free, attempts to apply this method
directly may meet with technical difficulties. For example, the period
estimates presented in Figure 11-25 differ significantly from both those
obtained for the same data sets through the use of FFT-NLLS and the
actual simulated value of 24 hours. The tabulated summary of the
algorithm output presented in Figure 11-26 provides an explanation.
Whereas the expected estimates for TAU(up), TAU(down), and TAU
(max) are in the vicinity of 24 hours, numerous instances appear in which
values for period estimates are considerably shorter than 24 hours. This is
a consequence of noise confounds creeping in, beginning at about 100
hours of x-axis time and manifesting consistently beyond about 200 hours
of x-axis time. In such cases, preprocessing of the data through filtering
may be beneficial. We present such examples in the next section.
VI. PREPROCESSING BEFORE ANALYSIS
We note that, in general, preprocessing of the data may introduce bias
into the analytical results. In some cases, however, preprocessing may be
necessary if the presence of significant confounds hinders the direct
analysis of the time series. Pros and cons should always be carefully
weighed before the use of preprocessing techniques. The next two
exercises illustrate this point.
A. ARFILTER Followed by Rhythms Analysis
Examples are provided here of analyses of the noisy, nonstationary
time series introduced in Figure 11-15, except this time preprocessed
