The evolution of curved allometries

Fig. 1 A simulated unconstrained relationship between the basal metabolic rate (BMR) and body mass (w) for a mammalian like clade that evolved for 65 million years. A straight allometric line with an exponent of 0.75 is expected only in the absence of primary selection on mass specific metabolism (r_ββ=0). The allometry is bend to an increasing degree when r_ββ increases from zero (red) to 2.4x10^-8 (black). From Witting (2018).

When a clade diversifies from a common ancestor into a multitude of evolutionary lineages across ecological niches, we predict the evolution of linear inter-specific allometries with 1/4 exponents in 2D, and 1/6 exponents in 3D (Witting, 2017a).

This is because the majority of the inter-specific variation in net energy originates from primary variation in the handling and/or densities of the resources in the different niches, with only a small fraction originating from evolutionary differences in the pre-mass component of mass specific metabolism. But what happens when evolution in resource handling comes to a hold as the different lineages become well adapted to their niches?

If there is no metabolic evolution, we may expect a stationary distribution over time. Yet, with primary selection on mass specific metabolism, we expect that most species will show some positive background evolution in mass specific metabolism and mass. And even though this selection on metabolism and mass is expected to be mass invariant, it will affect mainly the smaller species because they evolve through a larger number of generations than the larger species (Witting, 2018). As illustrated in Fig. 1, this creates an upward bend in the lower size range of the allometry over time, with the degree of bending being dependent on the pre-generation rate of increase in the pre-mass component of mass specific metabolism.

Evidence

Fig. 2 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).

Curvature in allometric scaling was documented by Kolokotrones et al. (2010) for the maybe best studied allometry, i.e., the relationship between the basal metabolic rate and body mass in mammals.

The curved allometry is explained by a simulation of body mass selection in placental mammals over the past 65 million years (Witting, 2018). The best fit of the current allometry is given by the blue curve in the left plot in Fig. 2. The upward bend in the metabolism of the smaller species implies an overall exponent that is smaller than 0.75 should a linear allometry be fitted to the data. The overall linear exponent is 0.72 across the entire range of simulated body masses, and it increases to 0.74 for the upper half of the body mass distribution, and declines to 0.67 for the lower half.

The estimated rate of exponential increase in the pre-mass component of mass specific metabolism is 9.3x10^-9 (95% CI: 7.3x10^-9 - 1.1x10^-8) on the per generation timescale. The bend is more apparent in placental than marsupial mammals (MacKay, 2011), and this reflects a per generation rate of increase that is about an order of magnitude larger in placentals (Witting, 2018). From the differences in the curvature of the metabolic allometry we conclude that placentals have evolved a higher metabolism than marsupials; in agreement with an average metabolism that is 30% larger in placentals relative to marsupials of similar size (McNab, 2008).

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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.
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