Resource-processing flux
Resource-processing fluxes connect consumer-resource simulations to measured functions such as carbon retention, respiration, resource depletion, and cross-feeding.
Flux definitions
At consumer biomass $C_i$ and resource state $R_\alpha$, gross uptake is:
\[F^{\mathrm{uptake}}_{i\alpha}=C_i u_{i\alpha}R_\alpha.\]With retained fraction $\eta_{i\alpha}=1-\sum_\beta l_{i\alpha\beta}$, retained and leaked fluxes are:
\[F^{\mathrm{retained}}_{i\alpha} =C_i u_{i\alpha}R_\alpha\eta_{i\alpha},\] \[F^{\mathrm{leak}}_{i\alpha\beta} =C_i u_{i\alpha}R_\alpha l_{i\alpha\beta}.\]Maintenance loss is $F_i^{\mathrm{maintenance}}=m_iC_i$.
Resource and community balance
For constant supply $\rho_\alpha$ and linear loss $\omega_\alpha R_\alpha$:
\[\frac{dR_\alpha}{dt}=\rho_\alpha-\omega_\alpha R_\alpha -\sum_iF^{\mathrm{uptake}}_{i\alpha} +\sum_i\sum_\beta F^{\mathrm{leak}}_{i\beta\alpha}.\]At a numerical equilibrium, the residual of this balance should be small. Large residuals indicate that the endpoint is not stationary or that the flux calculation does not match the model’s supply and loss conventions.
Community totals are obtained by summing the relevant consumer and resource axes. A direct flux-based efficiency is:
\[E_{\mathrm{direct}}= \frac{F^{\mathrm{retained}}_{\mathrm{comm}}} {F^{\mathrm{uptake}}_{\mathrm{comm}}}.\]For comparisons across communities, use the same declared reference resource state and the carbon-use-efficiency workflow.
Report total uptake, retained flux, leakage, maintenance or net growth, resource drawdown, the evaluation state, and the model’s resource-supply form.
Implementation status
DigiMicPy exposes the state and parameter arrays needed to calculate these quantities explicitly. See its resource-flux recipe.