Evolution across niches – the symmetrical case

A r_ββ/r_α-ratio around unity generates body mass evolution with a dw/dt exponent of

x = 3(2d-1)/4d , [9/8 in 2D, and 5/4 in 3D; Witting, 2020]

As illustrated by the green curves in Fig. 1, the resulting trajectory is bend upward in physical time due a natural selection time that contracts as

∂ ln τ / ∂ ln w = (3-2d)/4d , [-1/8 in 2D, and -1/4 in 3D]

Fig. 1 Lifespan (τ, left) and body mass (w, middle) evolution in physical time given intra-specific interactions in 3D. Unconstrained evolution across niches follow the green curve, and it is characterised by a dw/dt-exponent of 5/4 (right). From Witting (2020).

For this selection we have a generation time that is declining with mass with a -1/8 exponent in 2D (-1/4 in 3D), instead of increasing with the familiar 1/4 exponent (1/6 in 3D). This change of sign in the evolutionary direction of time is induced by the selected acceleration of mass specific metabolism that is generating half of the energy for the selection increase in mass.

A r_ββ/r_α-ratio around unity is given by symmetrical unconstrained evolution in resource handling and metabolic pace. This is the expected base case for the evolution of maximum size in a taxonomic group that is diversifying with speciation across ecological niches. This evolution includes selection on the handling of new resources, and it allows larger species to evolve as lineages diversity into new niches where an increased resource exploitation is possible. Representing this form of diversifying evolution, a r_ββ/r_α-ratios around unity is expected for the evolution of maximum body mass in phylogenetic clades.

Evidence

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 r_ββ/r_α-ratio and the rate of change in mass (dw/dt, Table 1, from Witting, 2020). In agreement with unconstrained natural selection across ecological niches, the exponents of the estimated r_ββ/r_α-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 r_ββ/r_α-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, r_ββ/r_α-ratios, and spatial dimensionality (d) for the evolution of the maximum mass in five mammalian clades. From Witting (2020), 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 r_ββ/r_α-ratio around one as predicted for across niche evolution with unconstrained symmetrical selection on resource handling and metabolic pace. From Witting (2020).

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References

• 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. εm Proceedings of the Royal Society B 280:20131007.
• Witting, L. 2020. The natural selection of metabolism explains curvature in fossil body mass evolution. Evolutionary Biology 47:56--75, https://dx.doi.org/10.1007/s11692--020--09493--y.