^{**}=7/3ψ

# Body mass allometries

Body mass allometries evolve from mass-rescaling and primary selection on metabolism

Given the rescaling of the life history with mass and metabolism, we can calculate the exponents of the final body mass allometries for a variety of situations. These are given as the sum of the exponents for the metabolic-rescaling and mass-rescaling allometries, with the former representing the importance of metabolism for the evolution of mass, and the latter the rescaling of the life history in response to the evolutionary changes in mass.

These exponents are listed in Table 1, where they are denoted by a hat over the trait symbol. Apart from the home range exponent that is always one, the exponents depend on the β_{β}^{•} exponent for the pre-mass component of mass specific metabolism (β_{β}). They are shown for the two extreme cases where all the variation in net energy (ε), and thus also body mass, is caused either by variation in metabolic pace (β_{β}^{•}=1) or by variation in resource handling/availability (β_{β}^{•}=0). The intermediate case with similar importance of handling and pace (β_{β}^{•}=1/2) is also shown, together with cases where post-mass metabolism is independent of mass (b=0). The latter depends on the spatial dimensionality of the interactive behaviour, with b=0 for β_{β}^{•}=1/2d.

The majority of post-mass exponents are given as fractions, where 2d is the common denominator. The most well known set of allometric exponents for multicellular animals, i.e., the set where b=-1/4, is evolving for two dimensional interactions when all of the variation in body mass is caused by variation in the handling and availability of resources across ecological niches.

_{β}:pre-mass component of β; α:resource handling; τ:time periods; p:survival; R:lifetime reproduction; r:population dynamic growth rate; h:home range; n:abundance. From Witting (2016).

### References

- Witting, L. 2016. The natural selection of metabolism and mass selects allometric transitions from prokaryotes to mammals. bioRxiv http://dx.doi.org/10.1101/084624.