The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals

Inter-specific body mass allometries can evolve from the natural selection of mass, with {+/-}1/4 and {+/-}3/4 exponents following from the geometry of intra-specific interactions when density dependent foraging occurs in two spatial dimensions (2D, Witting, 1995). The corresponding values for three dimensional interactions (3D) are {+/-}1/6 and {+/-}5/6.\n\nBut the allometric exponents in mobile organisms are more diverse than the prediction. The exponent for mass specific metabolism tends to cluster around -1/4 and -1/6 in terrestrial and pelagic vertebrates, but it is strongly positive in prokaryotes with an apparent value around 5/6 (DeLong et al., 2010). And a value around zero has been reported in protozoa, and on the macro evolutionary scale from prokaryotes over larger unicells to multicellular vertebrates (Makarieva et al., 2005, 2008).\n\nI show that mass specific metabolism can be selected as the pace of the resource handling that generates net energy for self-replication and the selection of mass, and that this selection of metabolism and mass is sufficient to explain metabolic exponents that decline from 5/6 over zero to -1/6 in 3D, and from 3/4 over zero to -1/4 in 2D. The decline follows from a decline in the importance of mass specific metabolism for the selection of mass, and it suggests i) that the body mass variation in prokaryotes is selected from primary variation in mass specific metabolism, ii) that the variation in multicellular animals are selected from primary variation in the handling and/or densities of the underlying resources, iii) that protozoa are selected as an intermediate lifeform between prokaryotes and multicellular animals, and iv) that macro evolution proceeds along an upper bound on mass specific metabolism.