Mass specific metabolism

The net energy (ε) of an individual is a product

ε = α v

between a physiological mechanical/biochemical handling (α) of resource assimilation and the speed (v), or pace, of this process. Handling speed reflects energy that is used for handling per unit mass, with energy being provided by metabolism, e.g., as a fraction (c) of mass specific metabolism (β). This makes handling speed a function of mass specific metabolism [ v = c β ], with the metabolic fraction (c) that is used for handling being determined by natural selection.

The net energy for self-replication is also gross energy [ ε_g = α_g v = α_g c β ] minus the total metabolism

ε = α_g c β - w β

where w is the mass of the individual. With the partial derivative ∂ ε / ∂ c = α_g β > 0 being positive, it follows, from the selection of net energy for self-replication, that the metabolic fraction is selected to unity [ c^**=1 ]. This implies a mass specific metabolism that is selected as the pace of the biological processes that generate net energy for self-replication

ε = α β

And with the net energy of the organism being a product of resource handling and pace, it follows that the selection for increased net energy is realised through an exponential increase in handling and mass specific metabolism

r_ε = r_α + r_ββ

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