^{**}=7/3ψ

# Evolution within a niche – the accelerating mass

Body mass evolution in niches; with metabolic acceleration, maximum time contraction, and upward bend trajectories

An infinite r_{ββ}/r_{α}-ratio generates body mass evolution with a dw/dt exponent of

x = (2d-1)/d , [3/2 in 2D, and 5/3 in 3D; Witting, 2016]

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

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

A r_{ββ}/r_{α}-ratio that approaches infinity can be expected for evolutionary lineages that evolve by unconstrained selection within a stable ecological niche. The handling of the resource is then optimised by natural selection, and when handling is at the selection optimum it follows that r_{α} → 0. Net energy and mass may then continue to increase by the natural selection increase in the pre-mass component of mass specific metabolism, generating an infinitely large r_{ββ}/r_{α}-ratio.

This fascinating increase in mass is driven entirely by a constant acceleration of the biochemical and behavioural processes; an acceleration that is generating a strong contraction of the generation time and other time periods of the organism. By speeding up the rate of net resource assimilation by increased metabolism, the individual is burning significantly more energy per unit time, but it is also generating more net energy that is first selected into population growth and then into mass by the interactive competition between the individuals in the population.

### References

- Witting, L. 2016. The natural selection of metabolism bends body mass evolution in time. bioRxiv http://dx.doi.org/10.1101/088997.