In classical life-history theory with no competitive interactions large body masses are set to evolve from the assumption that reproduction is approximately proportional to body mass (e.g., Roff, 1981, 1992). The proportional relationship is documented in many species, and it seems that it has evolved by natural selection.

On the scale of long-term evolution there is no reason to expect that the proportional relationship can act as constraint on body mass. The proportional relationship is clearly not an absolute constraint because lifetime reproduction is independent of body mass at the scale of between-species comparison. And at the theoretical level there seems to be no physical law that will explain the relationship from constraints intrinsic to the individual. From absolute intrinsic constraints we can instead expect an inverse relation between body mass and lifetime reproduction. This is because the number of offspring that can be produced from a given amount of resource is inversely related to the body mass of the offspring. Given this energetic constraint the classical models of r- and k-selection predict the evolution of only negligible body masses.

The paradox of a body mass that is evolutionarily unstable at the time scale of long-term evolution is avoided by Malthusian Relativity (Witting, 2002). With the energetic constraint of an inverse relationship between lifetime reproduction and body mass it follows that density dependent competitive interactions selects for non-negligible body masses in high-energy organisms. This is because larger individuals can be selected to dominate smaller individuals during competitive interactions, and because the level of interactive competition is so high that the interactive advantage of a large body mass can outbalance the reproductive disadvantage. And at the evolutionary steady state with an exponentially increasing body mass the bias in resource distribution over body mass caused by competitive interactions is exactly so large that lifetime reproduction is proportional to body mass (Witting, 1997).

References

• Roff, D. A. (1981). On being the right size. The American Naturalist 118, 405--422.
• Roff, D. A. (1992). The evolution of life histories. Theory and analysis. New York: University of Chicago Press.
• Witting, L. (1997). A general theory of evolution. By means of selection by density dependent competitive interactions. URL http://www.peregrine.dk, Århus, 330 pp: Peregrine Publisher.
• Witting, L. (2002). From asexual to eusocial reproduction by multilevel selection by density dependent competitive interactions. Theoretical Population Biology 61, 171--195.