Carbon-use efficiency
Carbon-use efficiency (CUE) measures how much consumed carbon is retained for biomass production rather than leaked, respired, or otherwise unavailable for growth. A DigiMic analysis should distinguish an individual consumer’s efficiency from a community summary.
Species-level efficiency
For consumer $i$ taking up resource $\alpha$, define the retained fraction:
\[\eta_{i\alpha}=1-\sum_\beta l_{i\alpha\beta}.\]For a declared reference environment $R^0$, potential uptake and retained flux are:
\[U_i^0=\sum_\alpha u_{i\alpha}R_\alpha^0,\qquad G_i^0=\sum_\alpha u_{i\alpha}\eta_{i\alpha}R_\alpha^0.\]Gross and maintenance-adjusted forms are:
\[\epsilon_i^{\mathrm{gross}}=\frac{G_i^0}{U_i^0},\qquad \epsilon_i^{\mathrm{net}}=\frac{G_i^0-m_i}{U_i^0}.\]State which form is used and how zero or negligible uptake is handled.
Community summaries
A biomass-weighted mean describes the efficiency of abundant surviving taxa:
\[E_{\mathrm{biomass}}= \frac{\sum_i C_i^*\epsilon_i}{\sum_i C_i^*}.\]A flux-weighted mean emphasizes consumers that process more resources:
\[E_{\mathrm{flux}}= \frac{\sum_i C_i^*U_i^0\epsilon_i}{\sum_i C_i^*U_i^0}.\]These answer different questions and should not be reported interchangeably. The first is a community-trait summary; the second is closer to retained carbon per unit of potential consumption.
Choose the reference environment
Using a common $R^0$ prevents the efficiency metric from being defined by the post-assembly outcome it is intended to explain. Suitable choices include the initial medium, a chemostat carrying-capacity vector, a mean environment across scenarios, or a measured experimental medium. Use the same reference when comparing communities.
Report the reference resources, gross or net convention, extinction threshold, weighting method, and treatment of near-zero denominators.
Implementation status
DigiMicPy exposes the uptake, leakage, mortality, and equilibrium arrays needed for these calculations but has no dedicated CUE helper. Its package recipe shows the current NumPy calculation.