Deriving Population Scaling Rules from Individual-Level Metabolism and Life History Traits

AbstractIndividual 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-to-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 either lead to nonmetabolic population growth scaling with adult mass or do not follow a power-law relationship at all. Using life history data on 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.