On the origin of biological similarity

The principles of biological similarity have not been adequately defined. Previous studies have not been fully successful, mainly because the search for such principles centered around the idea that a few of them would apply to all animals, just as Newton's principles of mechanical similarity apply to all inanimate objects. However, this is not possible, so that the search has led up a number of blind alleys, ending with a failure to provide a fundamental and unified explanation—as contrasted with empirical justification—for the scaling of basal metabolic rate of many kinds of animals (e.g. mammals, birds, fish, certain small metazoa) according to a 34-power of body mass, M, rather than as M23 (“surface law”) or M1·0; moreover, none of the previous theories can account for the fact that other kinds of animals (e.g. insects, snakes, hibernating mammals) do not obey the M34-rule. Two basic characteristics of all animals are that in the water they are on “the verge of floating” and that movement is interwoven with the nature of animal life itself. These observations lead to the principle of constancy of body density (ρ ⋍ 1) and to the principle of similarity in some defined sense of the muscular apparatus—the universal generator of movement—across species, but only within classes of animals that have evolved similar methods of locomotion. Because muscle tissues are subject to elastic (“spring-type”) contraction forces, a general elastic similarity principle holds for muscle diameter, d, vs. a linear body dimension, L, i.e., d2 ∝ L3 (Galileo-Rashevsky principle; this principle is valid also for the dimensions of the trunk of animals without exoskeleton subject to a gravitational load, e.g. for land mammals but not for sea mammals). A final principle which, combined with the above, leads to the M34-rule for muscle-power generation, is that time is scaled as the linear dimension, T ∝ L (in contrast to Newton's second principle of mechanical similarity for physical objects, T ∝ L12). This principle was introduced in the past either as an arbitrary assumption (Lambert & Teissier) or based on the empirical finding of constancy of muscle shortening velocity (∝ LT across mammalian species (Hill-McMahon). However, this principle cannot be valid for the classes of animals which do not obey the M34-rule. This principle is derived here from the more fundamental principle of constancy, across similar species, of mechanical stress (force over cross-section) endured by contracting muscles. In species such as snakes, however, in which locomotion is generated in a different way, friction forces assume an important role and scaling of time as with mechanical similarity, T ∝ L12, is obtained by assuming a similar velocity of the animals along their axis as size increases; using this scaling, the deviation of snakes from the M34-rule is explained. Interestingly, though, such scaling may have limited the maximal body size of snakes. A yet different principle seems to be operating in insects, leading to the scaling: T ∝ L−13 and a faster than body mass increase of basal metabolic rate. Finally, neither heat loss nor surface-related transport appear to be limiting and setting factors for metabolic rate—indeed “surface arguments” are entirely unbased. Only in some situations where the M34-rule is not obeyed because of heat loss considerations (e.g. dogs adapted to the tropics or to the arctic cold) is a surface argument relevant.