Inter-specific allometries are bend by time

Fig. 1 Left: The span of a simulated body mass (w) distribution for placental mammals over time (curves), with dots being the global maximum estimates from Smith et al. (2010). The dashed colour lines mark the time of the simulated allometries in the right plot. Right: The simulated (coloured curves) and observed (dots) relationship between the basal metabolic rate (BMR) and body mass (w). Red curve: 50 million years ago (MA); Green: 30MA; Blue: 0MA. From Witting (2016); data from McNab (2008).

The natural selection of metabolism and mass predicts linear inter-specific allometries from invariant selection responses in clades of animals that diversity with speciation into different ecological niches. But the most well studied allometry, i.e., the relationship between basal metabolism and mass in mammals, is curved (Kolokotrones et al., 2010); with the smaller species hawing a larger metabolism than expected by a linear allometry.

Does this curvature reflect a bug in the allometric theory, or does it follow from a more detailed calculation of the natural selection of inter-specific allometries? This is examined in a new paper on bioRxiv, where I simulate the evolution of the species distributions of placental and marsupial mammals over 65 million years.

Following the extinction of the dinosaurs at the Cretaceous-Paleogene boundary 65 million years ago, I let both clades diversity across ecological niches with a body mass distribution that is constrained by the maximum mass of the clade over time and the current minimum mass. This allows me to calculate the inter-specific allometry as it evolves over time.

The predicted allometries are linear shortly after the diversification where the majority of the body mass variation is selected by the evolution of diverse resource handling across ecological niches. But this evolution stops when the species become fully adapted to their niches, with a body mass distribution that evolves over time to be more and more affected by the background selection of mass specific metabolism.

While this background selection is expected to be invariant of mass on the per generation time-scale of natural selection, the relative increase in physical time is largest in the smaller species that evolve over a larger number of generations. And as the net energy that is generated by the metabolic increase is selected into mass, it follows that the left-hand side of the allometry is bending upward over time with respect to both metabolism and mass.

The bend, from an exponential rate of increase in mass specific metabolism of 9.3x10^-9 on the per generation time-scale, explains the curvature of the metabolic allometry in placental mammals. A rate of increase that is about an order of magnitude smaller explains the smaller curvature in marsupials; predicting placentals with a higher metabolism than marsupials. This agrees with an average metabolism that is 30% larger in placentals relative to marsupials of similar size (McNab, 2008).

References

• Kolokotrones, T., V.Savage, E.J. Deeds and W.Fontana 2010. Curvature in metabolic scaling. Nature 464:753--756.
• McNab, B.K. 2008. An analysis of the factors that influence the level and scaling of mammalian BMR. Comparative Biochemical Physiology A 151:5--28.
• Smith, F.A., A.G. Boyer, J.H. Brown, D.P. Costa, T.Dayan, S.K.M. Ernest, A.R. Evans, M.Fortelius, J.L. Gittleman, M.J. Hamilton, L.E. Harding, K.Lintulaakso, S.K. Lyons, C.McCain, J.G. Okie, J.J. Saarinen, R.M. Sibly, P.R. Stephens, J.Theodor and M.D. Uhen 2010. The evolution of maximum body size of terrestrial mammals. Science 330:1216--1219.
• Witting, L. 2016. The natural selection of metabolism explains curvature in allometric scaling. Preprint at bioRxiv https://dx.doi.org/10.1101/090191.