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Download paper Released 2018-02-2

Curvature and outliers in allometric scaling

A 2018 release in Oikos shows that the natural selection of metabolism is bending inter-specific allometries over time; explaining curvature and outlier species in metabolic scaling.

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 (2018); data from McNab (2008).

Metabolic outliers have remained an unsolved mystery in evolutionary biology. Why have shrews and the honey possum evolved a higher metabolism than expected from their small size, and why have the bowhead whale and the hairy-nosed wombat a smaller metabolism than expected from their large size?

A more general, yet related unexplained pattern, is the curvature in the metabolic allometry across placental mammals. Here, instead of being a straight line, is the allometry a bend curve with a small upward tilt in the smaller size range (Fig. 1).

My paper in Oikos shows that these systematic deviations from a straight allometric relation can evolve by the same primary selection of metabolism and mass that explains the evolution of straight allometries. The difference is only a matter of scale and time.

A straight allometry is predicted when an evolutionary lineage diversifies into many species across ecological niches. This is a case where size variation evolves primarily from resource variation across niches. But there is also a persistent background selection for increased metabolism, and this is generating a slight bend in the allometry over time.

The primary selection of metabolism generates part of the net energy for the selection of size, with a metabolic increase that is expected to be about the same in all animals on the per-generation time-scale of natural selection. But evolution in physical time is accelerated in the smaller species relative to evolution in the larger, because the former evolves over a larger number of generations. And it is this size dependent distortion in the rates of evolution in physical time that generates an increasing bend in the metabolic allometry over time.

If, in a similar way, a single species is selected to be small, or large, at an early stage relative to the other species in a clade, it will evolve to be an outlier over time because its metabolic increase is selected over a larger, or smaller, number of generations.


  • 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. 2018. The natural selection of metabolism explains curvature in allometric scaling. Oikos 127:991--1000, https://dx.doi.org/10.1111/oik.05041.