^{**}=7/3ψ

# Net energy

Natural selection for an exponential increase in the net energy of organisms

When other things are equal there is natural selection for an increase in the net energy that is available for self-replication. With fitness r = ln λ ∝ ln [p ε τ / w] being given by the exponential increase in numbers on a per generation time-scale, the selection gradient on the net energetic state (ε) is unity on logarithmic scale

∂ r / ∂ ln ε = 1

[λ:per generation multiplication factor; p:probability to survive to reproduce; τ:reproductive period; w:body mass]. The secondary theorem of natural selection (Robertson, 1968; Taylor, 1996) is then predicting an exponential increase

r_{ε} = d ln ε / d τ = σ^{2} ∂ r / ∂ ln ε = σ^{2}

given an invariant resource and additive heritable variance (σ^{2}).

Competitive exclusion by inter-specific competition can exclude smaller species from essential resources. This can create a cascade of species that differ in net energy; from a possible minimum to a maximum, with an exponential increase in the maximum reflecting unconstrained selection in the species that dominate inter-specific interactions.

### References

- Robertson, A. 1968. The spectrum of genetic variation. pp. 5--16, In: R. C. Lewontin (ed.) Population Biology and Evolution. Syracuse University Press, New York.
- Taylor, P.D. 1996. The selection differential in quantitative genetics and ESS models. Evolution 50:2106--2110.