Malthusian Relativityι**=7/3ψ
The bend of evolutionary time

Evolution across niches the symmetrical case

The maximum body mass in mammalian clades evolve from unconstrained selection across ecological niches

Okie et al. (2013) provides estimates of the maximum body mass in several mammalian clades over the past 60 million years of evolution. For five of these I was able to estimate the body mass exponent for the rββ/rα-ratio and the rate of change in mass (dw/dt, Table 1, from Witting, 2016). In agreement with unconstrained natural selection across ecological niches, the exponents of the estimated rββ/rα-ratios were around one in four of the five cases. This was found to hold for both 2D evolution in even-toed ungulates and carnivores (with dw/dt exponents around 9/8) and 3D evolution in whales and primates (dw/dt exponents around 5/4). The last clade (trunked mammals; 2D) had a rββ/rα-ratio exponent around zero; which is expected for a fast body mass evolution where the increase in resource handling/density is outrunning the increase in the pre-mass component of mass specific metabolism.

Table 1 dw/dt-exponents, rββ/rα-ratios, and spatial dimensionality (d) for the evolution of the maximum mass in five mammalian clades. From Witting (2016), with data from Okie et al (2013).

In Fig. 2 I show the estimated trajectory for the maximum mass and lifespan for 3D evolution in whales. Given a 70 year lifespan of a 100 tonne blue whale today, it is estimated that the 410 kg whale ancestor that lived 31 million years ago had a lifespan around 275 years.

Fig. 2 The lifespan (τ, left) and maximum body mass (w, middle) across whales, as estimated for data provided by Okie et al (2013). Fossil whales have a dw/dt-exponent around 1.28 (right), and this coincides with a rββ/rα-ratio around one as predicted for across niche evolution with unconstrained symmetrical selection on resource handling and metabolic pace. From Witting (2016).


  • Okie, J.G., A.G. Boyer, J.H. Brown, D.P. Costa, S.K.M. Ernest, A.R. Evans, M.Fortelius, J.L. Gittleman, M.J. Hamilton, L.E. Harding, K.Lintulaakso, S.K. Lyons, J.J. Saarinen, F.A. Smith, P.R. Stephens, J.Theodor, M.D. Uhen and R.M. Sibly 2013. Effects of allometry, productivity and lifestyle on rates and limits of body size evolution. Proceedings of the Royal Society B 280:20131007.
  • Witting, L. 2016. The natural selection of metabolism bends body mass evolution in time. Preprint at bioRxiv