waveforms of dogs and horses (left panel). In horses, the second daily cycle in the oscillation of body temperature is very similar to the first cycle; in dogs, the second cycle differs considerably from the first one — that is, the rhythm of horses is quite consistent (almost stationary), while the rhythm of dogs is rather variable (hardly stationary).

The idea of quantifying rhythm robustness by means of the QP statistic of the chi square periodogram was introduced informally more than 20 years ago.77 The QP statistic is Sokolove and Bushell's version of the index of rhythmicity of the Enright periodogram, as explained earlier. The relationship between QP and the subjective impression of the "neatness" of a rhythm can be easily comprehended in Figure 3.33. The "neat" rhythm of body temperature of the fat-tailed gerbil (a small nocturnal rodent) yields a periodogram with a large 24-hour QP (90% of the maximal possible QP), while the "crummy" rhythm of the degu (a diurnal rodent) yields a periodogram with a much smaller 24-hour QP (56% of the maximal possible QP). The QP value is not a perfect index of sta-tionarity because it is sensitive to noise in the data set, but it becomes a very close approximation of a perfect index if the noise is filtered out prior to analysis,76 as exemplified in Figure 3.34. One can always question whether biological noise is true noise (i.e., stochastic variation) or some form of deterministic chaos,78 79 but resolution of this issue is not necessary to analyze rhythm robustness in the cir-cadian range.

A final note on the use of the QP statistic as an index of rhythm robustness is necessary: when QP values are computed for a data set, the more days (or circadian cycles) available for analysis, the more confident one can be about the nature of the data. This means that QP values increase as the number of days used increases. Consequently,




Compressed a

Compressed c c


21 23 25 27 Period (hours)

2 3 4 Days

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