Abstract
We review time-frequency methods that can be useful in quantifying circadian and ultradian patterns in behavioral records. These records typically exhibit details that may not be captured through commonly used measures such as activity onset and so may require alternative approaches. For instance, activity may involve multiple bouts that vary in duration and magnitude within a day, or may exhibit day-to-day changes in period and in ultradian activity patterns. The discrete Fourier transform and other types of periodograms can estimate the period of a circadian rhythm, but we show that they can fail to correctly assess ultradian periods. In addition, such methods cannot detect changes in the period over time. Time-frequency methods that can localize frequency estimates in time are more appropriate for analysis of ultradian periods and of fluctuations in the period. The continuous wavelet transform offers a method for determining instantaneous frequency with good resolution in both time and frequency, capable of detecting changes in circadian period over the course of several days and in ultradian period within a given day. The discrete wavelet transform decomposes a time series into components associated with distinct frequency bands, thereby facilitating the removal of noise and trend or the isolation of a particular frequency band of interest. To demonstrate the wavelet-based analysis, we apply the transforms to a numerically-generated example and also to a variety of hamster behavioral records. When used appropriately, wavelet transforms can reveal patterns that are not easily extracted using other methods of analysis in common use, but they must be applied and interpreted with care.
Highlights
Behavioral rhythms of animals span a wide range of cycle lengths, including circannual rhythms that vary with the seasons, changes in activity due to the estrous cycle in rodents, circadian rhythms that track the daily light-dark cycle, and ultradian rhythms of activity occurring within a single day
The ultradian rhythms emerge as a consequence of multiple physiological processes, not currently well understood, and tend to have greater interindividual variability than circadian rhythms [2]
The discrete wavelet transform provides an alternative method to inverting the discrete Fourier transform (DFT) for identifying the daily pattern of activity bouts, with the flexibility that it does not require bouts be timed each day
Summary
Behavioral rhythms of animals span a wide range of cycle lengths, including circannual rhythms that vary with the seasons (period of 1 year), changes in activity due to the estrous cycle in rodents (cycle length of 4-5 days), circadian rhythms that track the daily light-dark cycle (period of 1 day), and ultradian rhythms of activity occurring within a single day (typically periods of 8 h or less). We briefly describe several methods of time-frequency analysis, the Fourier periodogram and discrete and continuous wavelet transforms, and apply them to a numerically-generated time series with known circadian and ultradian periods to illustrate their use. This approach works best for animals with very predictable timing of activity bouts; the discrete wavelet transform described below offers a more flexible tool for this purpose. The discrete wavelet transform provides an alternative method to inverting the DFT for identifying the daily pattern of activity bouts, with the flexibility that it does not require bouts be timed each day. The AWT can tell us both what periods are present in the times series and
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