Introduction

The most general allometric equations describe metabolic rate as a linear function of body mass raised to an exponent of approximately ¾ (Hemmingsen 1960; Appendix III). This regularity holds a special fascination for biologists, because its wide applicability suggests that this may be a rare example of a general biological law (Wilkie 1977). Before this claim is accepted, it should be examined as closely as possible.

One could seek confirmation by examining those allometric equations that relate metabolic rate to body size in particular taxa. The equations assembled in Appendix III suggest that the generality holds at these more restricted levels. The mode of the frequency distribution of the slopes (Figure 4.1) lies between 0.725 and 0.750; the median of the distribution is 0.735 and the mean is 0.738 (SD = 0.11; N = 146). There is no great advantage in promoting 0.74 over 0.75, for the two values are not significantly different and the latter is widely accepted and slightly easier to compute (Kleiber 1961). Figure 4.1, therefore, confirms the ¾ law or Kleiber's rule as a valid statistical generalization. This does not imply that ¾ is the “true” value of the slope for all equations, only that ¾ is a reasonable approximation.

Figure 4.1 may overestimate the dispersion in the slopes, because the slope in body size relations is not completely independent of the intercept.