The Natural Selection of Metabolism Bends Body Mass Evolution in Time
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bioRxiv preprint doi: https://doi.org/10.1101/088997; this version posted November 28, 2016. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC-ND 4.0 International license. ι∗∗=7=3 bioRxiv (2016) 088997 mrLife.org doi:10.1101/088997 a Malthusian Relativity paper The natural selection of metabolism bends body mass evolution in time Lars Witting Greenland Institute of Natural Resources, Box 570, DK-3900 Nuuk, Greenland Abstract I predict a metabolic time bending of body mass clear fusion that emits energy. And energy driven self- evolution in the fossil record. I show that self-replication replication in replicating molecules selects for an in- generates population dynamic feed-back selection for a body creased use of energy in metabolism (Witting 2016a); a mass that increases exponentially on the per generation use that generates net energy for self-replication and ac- time-scale of natural selection, and that this increase is tivates a population dynamic feed-back that selects for driven partly, or fully, by unconstrained selection for an the evolution of large multicellular animals with sexual exponential increase in mass specific metabolism. The in- reproduction (Witting 2016b). In other words, where it crease in metabolism contracts natural selection time; but, mass specific metabolism evolves also by a mass-rescaling is a mass driven force that forms the mass of stars and that generates a partial decline, and time dilation, with an their release of energy; it is suggested that it is energy increase in mass. The overall contraction or dilation of nat- driven self-replication that selects the energy use and ural selection time is bending evolution in physical time, mass of natural organisms. ^ and this is described by an allometry dw=dt wdt for the Although astronomy and evolutionary biology are / rate of evolution in mass (w) in physical time (t). rather unrelated branches of science, the scientific The bending exponent (dt^ ) is shown to evolve from the methods that were used to reveal this ordering of matter relative importance of metabolism for the evolution of mass, and energy in physics and biology were somewhat sim- and from the spatial dimensions of interactive competition ilar. Where gravity enabled Newton (1687) to explain (1D, 2D, 3D); a prediction that is shown to hold across the 3/2 exponent for the Kepler laws of planetary mo- four scale dependent bending exponents in the fossil record. tion around the Sun, the population dynamic feed-back The exponents are i) 3/2 for 2D and 5/3 for 3D evolution selection of energy driven self-replication enabled Wit- within a niche; as observed for horses over 57 million years of evolution. ii) 5/4 (2D) and 9/8 (3D) for the evolution of ting (2016a,b) to explain the evolution of body mass maximum mass across niches; as found in four mammalian allometries in biology; including a shift in the expo- clades across 30 to 64 million years of evolution. iii) 3/4 nent for mass specific metabolism from a positive 5=6 (2D) and 5/6 (3D) for fast body mass evolution; found for in prokaryotes (DeLong et al. 2010) to a negative 1=4 the maximum mass of trunked, and all terrestrial, mam- for Kleiber (1932) scaling in multicellular animals. mals. And iv) 1 for 2D and 3D evolution along a metabolic This ordering of biology is predicted to spring from bound, as observed across 3.5 billion years of evolution of self-replication selection for a mass specific metabolism the maximum mass in non-sessile organisms. that generates net energy for self-replication. This is Keywords: Evolution, metabolism, body mass, time- done by a net resource assimilation that is selected as a bending, life history, allometry, fossil record biochemical/mechanical handling of resource assimila- tion and the speed, or pace, of this process; with pace 1 Introduction being selected as the mass specific work of metabolism. The unconstrained natural selection that follows gen- The aggregation of inert matter in stars and planets, of erate an acceleration of biotic processes, and a steady organic matter in large organisms, and the associated state selection attractor where interactive competition release of energy from stars and use of energy by or- in multicellular animals selects the increase in net en- ganisms, are some of the most striking features of our ergy into an exponentially increasing mass (Witting universe. An understanding of the formation and en- 1997, 2003). ergetics of these bodies is of immense importance for The importance of the metabolic acceleration for this science. evolution of biotic mass is reflected in the body mass al- It is a pull from gravity that first creates stars from lometries, where the exponents are predicted to evolve interstellar molecular clouds and then activates the nu- as a function of the relative importance of the metabolic 1 bioRxiv preprint doi: https://doi.org/10.1101/088997; this version posted November 28, 2016. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC-ND 4.0 International license. 2 bioRxiv (2016) 088997 pace for net resource assimilation. Witting (2016a,b) time, and it is larger than one when evolution is bend- describes the natural selection of these allometric cor- ing upward by a contraction of natural selection time. relations across species, and I extend the theory to de- From the −1=4 exponent of Kleiber scaling, where scribe the natural selection conversion of energy into elephants live much longer the mice, we expect biotic organic mass over evolutionary time, by studying body time dilation and a downward bend trajectory (Okie mass allometries as they unfold in time with an evolving et al. 2013). Yet the body mass trajectory of fossil mass. This will provide a base case for the evolution of horses over the past 57 million years is strongly upward metabolism, mass, and major life history and ecological bend with a dt^ exponent of 1.50 (Witting 1997). This traits in multicellular animals over time, and I test the indicates somewhat surprisingly that the lifespan of the theory by predicting body mass trajectories in the fossil horse has declined quite a bit while its mass increased record from first principles. This implies that I will use from about 25 kg to 500 kg over 57 million years of a predicted time-bend of the body mass trajectories to evolution. I will show not only that a 3=2 exponent test for the relative importance of metabolism for the for the horse is likely to have emerged from a body evolution of biotic masses. mass selection that was driven entirely by metabolic acceleration; but more generally that mass evolution 1.1 Time-bend evolution over time can be described as a continuum across four modes of selection, with each mode being supported by The proposed selection predicts an exponential increase a unique bend of the relevant body mass trajectories in in mass on the per generation time-scale of uncon- the fossil record. strained natural selection in a stable environment (Wit- ting 1997, 2003), given evolutionary rates that are in- 1.2 Empirical test of theory variant on the logarithmic scale of metabolism and mass (Witting 2016a,b). This is in agreement with fossil data The basic idea behind my allometric model is popu- where the maximum size of a clade tends to increase lation dynamic feed-back selection that unfolds from in a near-exponential manner during periods of phylo- pre-mass selection for an exponential increase in re- genetic radiation (e.g., Hayami 1978; Trammer 2005; source handling and metabolic pace (Witting 2016a,b). Smith et al. 2010; Okie et al. 2013). And the correla- The resulting increase in resource assimilation gener- tion of evolutionary rates with the per generation time ates population growth with sustained interactive se- scale of natural selection is well documented both for lection for an exponential increase in mass. The in- morphological (Lynch 1990; Gingerich 1993; Okie et al. crease in mass is then imposing selection for a mass- 2013) and molecular traits (Martin and Palumbi 1993; rescaling, where life history traits (x) evolve allometric x^ Gillooly et al. 2005; Nabholz et al. 2008; Galtier et al. correlations with mass xw = w w , wherex ^w is the expo- 2009; Broham 2011). nent and subscript w denotes mass-rescaling. Yet, the The exponential increase generates a log-linear in- evolution of allometries is more complex because the crease of mass over time, but the log-linearity is bend- pre-mass selection for increased metabolism imposes ing in physical time whenever the time-scale of natural a metabolic-rescaling of the life history. This rescal- selection is evolving with the evolutionary changes in ing is transformed into metabolic-rescaling allometries x^ mass (Witting 1997; Okie et al. 2013). A downward (xβ = w β ) by the dependence of body mass evolu- bending is induced when natural selection time is di- tion on the energy that is generated from the pre- lated by a generation time that increases with mass, mass acceleration of metabolic pace (subscript β de- and an upward bending when natural selection time is notes metabolic-rescaling). The final post-mass allome- x^ contracting from a generation time that declines with tries x = w are then products xβxw with exponents mass. x^ =x ^β +x ^w that depend on the relative importance These potential bends are described by an allometry of metabolic acceleration for the evolution of the net energy of the organism.