The principle of similitude in biology: From allometry to the formulation of dimensionally homogenous ‘Laws’

Abstract

© 2019, Springer Nature B.V. Meaningful laws of nature must be independent of the units employed to measure the variables. The principle of similitude (Rayleigh, Nature 95:66–68, 1915) or dimensional homogeneity, states that only commensurable quantities (ones having the same dimension) may be compared, therefore, meaningful laws of nature must be homogeneous equations in their various units of measurement, a result which was formalized in the π theorem (Vaschy, Ann Tél 19:25–28, 1892 ; Buckingham, Phys Rev 4:345–376, 1914). However, most relations in allometry do not satisfy this basic requirement, including the “3/4 Law” (Kleiber, Hilgardia 6:315–351, 1932) that relates the basal metabolic rate and body mass, besides it is sometimes claimed to be the most fundamental biological rate (Brown et al., Ecol 85:1771–1789, 2004) and the closest to a law in life sciences (West and Brown, Phys Today 57:36–42, 2004). Using the π theorem, here we show that it is possible to construct an unique