  Metabolism and evolution are closely connected: if a mutation incurs extra
energetic costs for an organism, there is a baseline selective disadvantage
that may or may not be compensated for by other adaptive effects. A
long-standing, but to date unproven, hypothesis is that this disadvantage is
equal to the fractional cost relative to the total resting metabolic
expenditure. This hypothesis has found a recent resurgence as a powerful tool
for quantitatively understanding the strength of selection among different
classes of organisms. Our work explores the validity of the hypothesis from
first principles through a generalized metabolic growth model, versions of
which have been successful in describing organismal growth from single cells to
higher animals. We build a mathematical framework to calculate how
perturbations in maintenance and synthesis costs translate into contributions
to the selection coefficient. This allows us to show that the hypothesis is an
approximation to the actual baseline selection coefficient. Moreover we can
derive the correct prefactor in its functional form, as well as analytical
bounds on its accuracy for any given realization of the model. We illustrate
our general framework using a special case of the growth model, which we show
provides a quantitative description of metabolic expenditures in data collected
from a wide array of unicellular organisms (both prokaryotes and eukaryotes).
In all these cases we demonstrate that the hypothesis is an excellent
approximation, allowing estimates of baseline selection coefficients to within
15% of their actual values. Even in a broader biological parameter range,
covering growth data from multicellular organisms, the hypothesis continues to
work well, always within an order of magnitude of the correct result. Our work
thus justifies its use as a versatile tool, setting the stage for its wider
deployment.
