Fig. 1.

The impact of a temperature-dependent allocation efficiency $\epsilon \left(T\right)$ on the TPC of growth rates in a population of photosynthetic cells. (A) Real TPCs for photosynthesis $P$, respiration $R$, and resulting net flux $F$ for Cladophora glomerata (a green alga). (B) Allocation efficiency $\epsilon \left(T\right)$ expressed as a Boltzmann–Arrhenius function (Eq. 4 and SI Appendix, section S1.2) with a range of different temperature dependences (set by the activation energy $E_{\epsilon }$). (C) The result is a range of different potential growth TPCs. (D and E) $\mathrm{\Delta }{E}_r$ (Eq. 5) (D) and $\mathrm{\Delta }{T}_{\text{pk,}r}$ (Eq. 6) (E) as functions of the temperature dependence of $\epsilon \left(T\right)$. (F) Relationships between potential growth and net flux (blues represent colder and reds warmer temperatures). A temperature-dependent $\epsilon \left(T\right)$ affects the shape of the growth TPC and as a result how growth responds to temperature. The growth–net flux relationship can be highly nonlinear in this scenario, with the direction of the nonlinearity (blue-to-red trajectory) depending upon whether $\epsilon \left(T\right)$ increases or decreases with $T$ (B). Temperature-independent $\epsilon \left(\kappa \right)$ (solid black line in B) produces growth TPCs that are qualitatively equal to those of net flux (solid blue line in C) and that are unaffected by $\epsilon \left(T\right)$. In B, C, and F the dotted lines are for $E_{\epsilon }=-0.7$ and the dashed lines are for $E_{\epsilon }=0.7$. Note that in D and E, larger values of $\left|E_{\epsilon }\right|$ produce curves that do not peak within the experimental temperature range (C).