Model responses to CO2 and warming are underestimated without explicit representation of Arctic small‐mammal grazing

. 2021 Dec 8;32(1):e02478. doi: 10.1002/eap.2478

Mass‐balance equations

\frac{d B_{C}}{dt} = P_{s} - L_{itC} - R_{a} - G_{C}

\frac{d B_{N}}{dt} = U_{N} - L_{itN} - G_{N}

\frac{d D_{C}}{dt} = L_{itC} + L_{VC} - R_{h} - Q_{CR}

\begin{matrix} \frac{d D_{N}}{dt} = L_{itN} + U_{Nm} + L_{VN} \\ - N_{min} - Q_{NR} \end{matrix}

\begin{matrix} \frac{dN}{dt} = N_{in} + N_{min} + V_{UN} \\ - U_{N} - U_{Nm} - Q_{DIN} \end{matrix}

Allometry and stoichiometry constraints

S = B_{C} \frac{(\propto B_{C} + 1)}{(γ B_{C} + 1)}

Ψ = \frac{B_{C}}{B_{N} q_{B}}

Φ = \frac{D_{C}}{D_{N} q_{D}}

Process equations

Carbon

Nitrogen

P_{s} = \frac{g_{C} S C_{a}}{Ψ (k_{C} + C_{a})} Q_{10 Ps}^{T / 10}

U_{N} = \frac{g_{N} Ψ S N}{k_{N} + N} Q_{10 U}^{T / 10}

L_{itC} = m_{CB} B_{C}

L_{itN} = \frac{m_{NB}}{Ψ} B_{N}

R_{a} = r_{B} B_{C} Ψ Q_{10 Ra}^{T / 10}

U_{Nm} = \frac{g_{Nm} Φ D_{C} N}{k_{Nm} + N} Q_{10 Um}^{T / 10}

G_{C} = (n_{V} + g_{V} - ε_{V} (T - T_{0})) V / 10, 000

G_{N} = G_{C} / q_{V}

R_{V} = r_{V} (G_{C} - n_{V} V / 10, 000)

V_{UN} = m_{NV} V / 10, 000

L_{VC} = G_{C} - R_{V}

L_{VN} = G_{N} - V_{UN}

R_{h} = r_{D} D_{C} Φ Q_{10 Rh}^{T / 10}

N_{min} = \frac{m_{Nm} D_{N}}{Φ} Q_{10 m}^{T / 10}

Q_{CR} = q_{DOM} Q_{NR}

Q_{NR} = β_{NR} D_{N}

Q_{DIN} = β_{N} N