Modeling the Growth of Organisms Validates a General Relation between Metabolic Costs and Natural Selection

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. We validate this result from physical principles through a general growth model and show it holds to excellent approximation for experimental parameters drawn from a wide range of species.

Figure 1

The growth $C_G$ (blue) and maintenance $C_M$ (red) contributions to an organism’s total resting metabolic cost $C_T=C_G+t_r{C}_M$ per generation time $t_r$. The symbols ($\mathrm{circles}=\mathrm{prokaryotes}$, $\mathrm{triangles}=\mathrm{unicellular}\mathrm{eukaryotes}$) represent data tabulated in Ref. [12]. $C_G$ and $C_M$ have units of $10^9\mathrm{P}$ (phosphate bonds hydrolyzed) and $10^9\mathrm{P}/\mathrm{h}$, respectively. The lines represent best fits to the theoretical expressions for $C_G$ and $C_M$ from the allometric growth model.

Figure 2

(a) ${\sigma }_B$ (solid curves) from Eq. (3) and ${\sigma }_B^{\prime }$ (dashed curves) from Eq. (4) versus $\alpha$, for the allometric growth model with $E_m=2600\mathrm{J}/\mathrm{g}$, $B_m=7\times {10}^{-3}\mathrm{W}/\mathrm{g}$, and $\epsilon =2$. At any given $\alpha$, the parameter ${\mathrm{\Pi }}_0$ for each pair of curves (different colors) is chosen to correspond to particular reproductive times $t_r$, indicated in the labels. (b) Contour diagram showing the logarithm of the maximum possible discrepancy ${\log }_{10}|1-{\sigma }_B^{\prime }/{\sigma }_B|$ for any allometric growth model parameters, as a function of $\alpha$ and $\epsilon$. To illustrate biological ranges $\alpha$ and $\epsilon$, the symbols correspond to data for various species ($\mathrm{circles}=\text{unicellular}$, $\mathrm{triangles}=\text{multicellular}$) drawn from the growth trajectories analyzed in Ref. [25] (light blue) and Ref. [23] (dark blue). See the Supplemental Material, Sec. III [33] for a detailed species list.