Divergent carbon use efficiency-growth rate tradeoff in popular biological growth models

Abstract. Carbon use efficiency (CUE) is an important trait emerging from processes regulating biological growth. CUE can be computed either based on the growth of structural biomass or total biomass divided by substrate uptake rate. Nonequilibrium thermodynamics and observations suggest that, for an exponentially growing population, structural biomass CUE should first increase, then peak, and finally decrease with specific growth rate; meanwhile, total biomass CUE increases asymptotically with specific growth rate. We compared predictions from six popular models that are often used for plant and microbial growth in existing ecosystem models. We found that, for an exponentially growing population of biological cells, (1) the Pirt model and Compromise model predict that structural biomass CUE increase asymptotically with growth rate; (2) the modified Droop model predicts that structural biomass CUE decreases with growth rate; and (3) the variable internal storage model and two dynamic energy budget models predict that structural biomass CUE first increases, then peaks, and finally decreases with growth rate. Moreover, the modified Droop model predicts that total biomass CUE is constant with growth rate, while all other five models predict that total biomass CUE increases with growth rate asymptotically. For non-exponential biological growth, we show that there is no deterministic relationship between total biomass CUE or structural biomass CUE with respect to either growth rate or temperature. Therefore, we contend that biological growth models should explicitly represent interactions between substrate acquisition, substate transformation, and maintenance respiration to better capture observed CUE dynamics and thereby ecosystem biogeochemistry.