POPULATION CYCLES IN MAMMALS AND BIRDS : DOES PERIODICITY SCALE WITH BODY SIZE ?

We consider Calder's hypothesis that cycle periods of fluctuating populations of mammalian herbivore scale with the 4th root of body mass. Data adduced by Peterson et al. , in support of this hypothesis are re-examined using techniques from spectral analysis. New herbivore data and population statistics for carnivores are also considered. The following results are obtained: o (1) support for the hypothesis does not depend on the method used to assign a period, provided that one is willing to accept cycle periods which are not statistically significant. (2) The explanatory power of the proposed scaling law depends critically on whether or not populations are treated individually or averaged by species. (3) Adding new herbivore species to the Peterson data set decreases the fit and changes the scaling exponent. (4) As originally predicted by Calder, there is no relationship between body mass and cycle period in carnivores./lt We suggest that Calder's hypothesis represents an expected lower bound when the period is plotted against body mass in the presence of noise and observational errors.

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