810 



PERIODIC FUNCTIONS IN MAMMALS 



o 



o 

 d. 



E 



o 



E 



Q. 



< 



1. 01 



0.8 



0.6 



0.4 



0.2 



Individual ZRD-mice 



/ a- 



Mean for ZRD-mice 



_L 



22 23 24 25 26 



T 



Estimate of period (hojrs) 



Fig. 5. Circadian periods in rectal temperature of ZRD mice, born 

 blind for several generations. The decrease in amplitude of mean again 

 indicates desynchronization among animals constituting the group (cf. 

 Fig. 4). 



equality, dealing with the case when nuisance parameters are present 

 (Lehman, 1950), M. Rao, in our department, has worked out a lower 

 bound for the variance of the estimated period, thereby enhancing the 

 value of periodograms for analyses of time series to which a periodic 

 model does not strictly apply. For these cases, the use of correlograms 

 (Kendall, 1948) and of other computational procedures (cf. Parzen, 

 1957a,b) also is pertinent. Probably existing models will have to be 

 "dressed up" with a few stochastic processes, an endeavor started at 

 the University of Minnesota by M. Rao, under the guidance of Pro- 

 fessor I. R. Savage. Such mathematical operations, in themselves not 

 a biologist's goal, are tools which can contribute substantially to the 

 reliability and reproducibility of studies on rhythms, particularly in 

 clinical research, for which the degree of standardization achieved in 

 work on experimental animals is not easily attainable. We shall allude 

 again to periodograms of physiologic data, while, at this point, we 



