Deriving population scaling rules from individual-level metabolism and life history traits

Individual metabolism generally scales with body mass with an exponent around 3/4. From dimensional arguments it follows that maximum population growth rate (r_max) scales with a −1/4 exponent. However, the dimensional argument implicitly assumes that offspring size is proportional to adult size. Here we calculate r_max from metabolic scaling at the level of individuals within size-structured populations while explicitly accounting for offspring size. We identify four general patterns of how r_max scales with adult mass based on four empirical life-history patterns employed by groups of species. These life-history patterns are determined by how traits of somatic growth rate and/or offspring mass relate to adult mass. One life-history pattern – constant adult:offspring mass ratio and somatic growth rate independent of adult mass – leads to the classic −1/4 scaling of r_max. The other three life-history patterns lead either to non-metabolic population growth scaling with adult mass or do not follow a power-law relationship at all. Using life-history data of five marine taxa and terrestrial mammals, we identify species groups that belong to one of each case. We predict that elasmobranchs, copepods, and mammals follow standard −1/4 power-law scaling, whereas teleost fish and bivalves do not have a pure power-law scaling. Our work highlights how taxa may deviate from the classic −1/4 metabolic scaling pattern of maximum population growth. The approach is generic and can be applied to any taxa.