Soil carbon sensitivity to temperature and carbon use efficiency compared across microbial-ecosystem models of varying complexity

Abstract

Global ecosystem models may require microbial components to accurately predict feedbacks between climate warming and soil decomposition, but it is unclear what parameters and levels of complexity are ideal for scaling up to the globe. Here we conducted a model comparison using a conventional model with first-order decay and three microbial models of increasing complexity that simulate short- to long-term soil carbon dynamics. We focused on soil carbon responses to microbial carbon use efficiency (CUE) and temperature. Three scenarios were implemented in all models: constant CUE (held at 0.31), varied CUE (−0.016 °C⁻¹), and 50 % acclimated CUE (−0.008 °C⁻¹). Whereas the conventional model always showed soil carbon losses with increasing temperature, the microbial models each predicted a temperature threshold above which warming led to soil carbon gain. The location of this threshold depended on CUE scenario, with higher temperature thresholds under the acclimated and constant scenarios. This result suggests that the temperature sensitivity of CUE and the structure of the soil carbon model together regulate the long-term soil carbon response to warming. Equilibrium soil carbon stocks predicted by the microbial models were much less sensitive to changing inputs compared to the conventional model. Although many soil carbon dynamics were similar across microbial models, the most complex model showed less pronounced oscillations. Thus, adding model complexity (i.e. including enzyme pools) could improve the mechanistic representation of soil carbon dynamics during the transient phase in certain ecosystems. This study suggests that model structure and CUE parameterization should be carefully evaluated when scaling up microbial models to ecosystems and the globe.

Appendix 1

Conventional model (CON)

The conventional model is representative of first-order models of soil organic carbon (SOC) dynamics. This model includes SOC, dissolved organic C (DOC), and microbial biomass C (MBC) pools with the decomposition rate of each pool represented as a first-order process. The decay constant k _i increases exponentially with temperature T according to the Arrhenius relationship:

$$ k_{i} (T) = k_{i,ref} *\exp \left[ { - \frac{{Ea_{i} }}{R}*\left( {\frac{1}{T} - \frac{1}{{T_{ref} }}} \right)} \right] $$

(4)

where k _i,ref is the decay constant at the reference temperature T _ref (K), and E _ai is the activation energy with i = D, S, or B representing DOC, SOC, and MBC pools, respectively. R is the ideal gas constant, 8.314 J mol⁻¹ K⁻¹. Decomposition of each pool is represented as:

$$ F_{S} = k_{S} *S $$

(5)

$$ F_{D} = k_{D} *D $$

(6)

$$ F_{B} = k_{B} *B $$

(7)

The change in the SOC pool is proportional to external inputs (I _S ), transfers from the other pools, and losses due to first-order decomposition:

$$ \frac{dS}{dt} = I_{S} + a_{DS} *F_{D} + a_{B} *a_{BS} *F_{B} - F_{S} $$

(8)

where a _DS is the transfer coefficient from the DOC to the SOC pool, a _B is the transfer coefficient from the MBC to the DOC and SOC pools, and a _BS is the partition coefficient for dead microbial biomass between the SOC and DOC pools. Transfer coefficients can range from 0.0 to 1.0, with lower values indicating a larger fraction of C respired as CO₂. The change in the DOC pool is represented similarly, but includes a transfer from SOC to DOC in proportion to a _SD and a loss due to microbial uptake, u * D:

$$ \frac{dD}{dt} = I_{D} + a_{SD} *F_{S} + a_{B} *\left( {1 - a_{BS} } \right)*F_{B} - u*D - F_{D} $$

(9)

The change in the microbial biomass pool is the difference between uptake and turnover, where u represents the fraction h⁻¹ of the DOC pool taken up by microbial biomass:

$$ \frac{dB}{dt} = u*D - F_{B} $$

(10)

The CO₂ respiration rate is the sum of the proportion of fluxes that do not enter soil pools:

$$ C_{R} = F_{S} *\left( {1 - a_{SD} } \right) + F_{D} *\left( {1 - a_{DS} } \right) + F_{B} *(1 - a_{B} ) .$$

(11)

Steady state analytical solution

The steady state analytical solutions for the DOC, SOC, and MBC pools in CON are:

$$ D = \frac{{I_{D} + I_{S} *a_{SD} }}{{u + k_{D} + u*a_{B} *(a_{BS} - 1 - a_{BS} *a_{SD} ) - a_{DS} *k_{D} *a_{SD} }} $$

(12)

$$ S = \frac{{I_{S} + D*\left( {a_{DS} *k_{D} + u*a_{B} *a_{BS} } \right)}}{{k_{S} }} $$

(13)

$$ B = \frac{u*D}{{k_{B} }} $$

(14)

GER

The GER microbial model represents SOC change as a function of input rate I _S , microbial turnover r _B , MBC, and extracellular enzyme V _max and K _m :

$$ \frac{dS}{dt} = I_{S} + r_{B} \cdot B - B \cdot \frac{V \cdot S}{K + S} $$

(15)

C inputs and dead biomass enter the SOC pool, and SOC is lost through decomposition, which is assumed to be a Michaelis–Menten process represented by the last term in Eq. 15. MBC change is a function of microbial turnover and assimilation of decomposed soil organic C, which occurs with C use efficiency E _C :

$$ \frac{dB}{dt} = E_{C} \cdot B \cdot \frac{V \cdot S}{K + S} - \tau_{B} \cdot B $$

(16)

where E _C is a linear function of temperature with slope m:

$$ E_{C} \left( T \right) = E_{C,ref} + m*(T - T_{ref} ) $$

(17)

The CO₂ respiration rate (C _R ) is then the fraction of decomposition not assimilated by microbial biomass:

$$ C_{R} = (1 - E_{C} ) \cdot B \cdot \frac{V \cdot S}{K + S} $$

(18)

V _max and K _m (Y) have an Arrhenius dependence on temperature, similar to Eq. 4 in the conventional model:

$$ Y(T) = Y_{ref} *\exp \left[ { - \frac{{Ea_{Y} }}{R}*\left( {\frac{1}{T} - \frac{1}{{T_{ref} }}} \right)} \right] $$

(19)

Steady state analytical solution

The steady state analytical solutions for the SOC and MBC pools in GER are:

$$ S = \frac{{r_{B} \cdot K}}{{E_{C} \cdot V - r_{B} }}; \quad \frac{{r_{B} }}{V} < E_{C} < 1 $$

(20)

$$ B = \frac{{I_{S} \cdot E_{C} }}{{r_{B} \cdot (1 - E_{C} )}} $$

(21)

where E _C must be larger than r _B /V, otherwise microbes cannot assimilate enough C to compensate for microbial turnover; if E _C  = 1, then microbes respire no C, all C is assimilated, and biomass grows indefinitely.

AWB

AWB is a more complex version of GER that includes explicit DOC and ENZC pools. Microbial biomass increases with DOC uptake (F _U ) times C use efficiency and declines with death (F _B ) and enzyme production (F _E ):

$$ \frac{dB}{dt} = F_{U} *E_{C} - F_{B} - F_{E} $$

(22)

where assimilation is a Michaelis–Menten function scaled to the size of the microbial biomass pool:

$$ F_{U} = \frac{{V_{U} *B*D}}{{K_{U} + D}} $$

(23)

Microbial biomass death is modeled as a first-order process with a rate constant r _B :

$$ F_{B} = r_{B} *B $$

(24)

Enzyme production is modeled as a constant fraction (r _E ) of microbial biomass:

$$ F_{E} = r_{E} *B $$

(25)

Temperature sensitivities for V, V _U , K, and K _U follow the Arrhenius relationship as in Eq. 19. Note that this relationship differs from the published version of AWB that used a linear relationship for K and K _U temperature sensitivity. We used the Arrhenius relationship here to facilitate comparison with the other models and used the parameter values from the linear relationship at 20 °C as the reference values in Eq. 19. CO₂ respiration is the fraction of DOC uptake that is not assimilated into MBC:

$$ C_{R} = F_{U} *\left( {1 - E_{C} } \right) $$

(26)

The enzyme pool increases with enzyme production and decreases with enzyme turnover:

$$ \frac{dE}{dt} = F_{E} - F_{L} $$

(27)

where enzyme turnover is modeled as a first-order process with a rate constant r _L :

$$ F_{L} = r_{L} *E $$

(28)

The SOC pool increases with external inputs and a fraction (a _BS ) of microbial biomass death and decreases due to decomposition losses:

$$ \frac{dS}{dt} = I_{S} + F_{B} *a_{BS} - F_{S} $$

(29)

where decomposition of SOC is catalyzed according to Michaelis–Menten kinetics by the enzyme pool:

$$ F_{S} = \frac{V*E*S}{K + S} $$

(30)

The DOC pool receives external inputs, the remaining fraction of microbial biomass death, the decomposition flux, and dead enzymes, while assimilation of DOC by microbial biomass is subtracted:

$$ \frac{dD}{dt} = I_{D} + F_{B} *\left( {1 - a_{BS} } \right) + F_{S} + F_{L} {-} F_{U} $$

(31)

Steady state analytical solution

The steady state analytical solutions for SOC, DOC, MBC, and ENZC in AWB are:

$$ S = \frac{{ - r_{L} *K*\left( {I_{S} *\left( {r_{B} *\left( {1 + E_{C} *\left( {a_{BS} - 1} \right)} \right) + r_{E} *\left( {1 - E_{C} } \right)} \right) + E_{C} *I_{D} *a_{BS} *r_{B} } \right)}}{{I_{S} *\left( {r_{B} *\left( {r_{L} *\left( {1 + E_{C} *\left( {a_{BS} - 1} \right)} \right)} \right) + r_{E} *\left( {r_{L} *\left( {1 - E_{C} } \right) - E_{C} *V} \right)} \right) + E_{C} *I_{D} *\left( {a_{BS} *r_{B} *r_{L} - r_{E} *V} \right)}} $$

(32)

which simplifies to the following if I _D  = I _S :

$$ S = \frac{{ - r_{L} *K*\left( {r_{B} + r_{E} } \right)*\left( {1 - E_{C} } \right) + 2*E_{C} *a_{BS} *r_{B} }}{{r_{L} *\left( {r_{B} + r_{E} } \right)*\left( {1 - E_{C} } \right) + 2*E_{C} *\left( {a_{BS} *r_{B} *r_{L} - r_{E} *V} \right)}} $$

(33)

$$ D = \frac{{-K_{U} *(r_{B} + r_{E} )}}{{r_{B} + r_{E} - E_{C} *V_{U} }} $$

(34)

$$ B = \frac{{E_{C} *(I_{D} + I_{S} )}}{{\left( {1 - E_{C} } \right)*(r_{B} + r_{E} )}} $$

(35)

$$ E = \frac{{B*r_{E} }}{{r_{L} }} $$

(36)

MEND

Five C pools are considered in MEND: (1) particulate organic carbon (POC, represented by the variable P in model equations), (2) mineral-associated organic carbon (MOC, M), (3) active layer of MOC (Q) interacting with dissolved organic carbon through adsorption and desorption, (4) dissolved organic carbon (DOC, D), (5) microbial biomass carbon (MBC, B), and (6) extracellular enzymes (EP and EM). The component fluxes are DOC uptake by microbes (denoted by the flux F ₁), POC decomposition (F ₂), MOC decomposition (F ₃), microbial growth respiration (F ₄) and maintenance respiration (F ₅), adsorption (F ₆) and desorption (F ₇), microbial mortality (F ₈), enzyme production (F ₉), and enzyme turnover (F ₁₀). Model equations for each component are listed as follows:

$$ F_{1} = \frac{{\left( {V_{D} + m_{R} } \right)*B*D}}{{E_{C} *\left( {K_{D} + D} \right)}} $$

(37)

$$ F_{2} = \frac{{V_{P} *E_{P} *P}}{{K_{P} + P}} $$

(38)

$$ F_{3} = \frac{{V_{M} *E_{M} *M}}{{K_{M} + M}} $$

(39)

$$ F_{4} = \left( {\frac{1}{{E_{C} }} - 1} \right)*\frac{{V_{D} *B*D}}{{K_{D} + D}} $$

(40)

$$ F_{5} = \left( {\frac{1}{{E_{C} }} - 1} \right)*\frac{{m_{R} *B*D}}{{K_{D} + D}} $$

(41)

$$ F_{6} = K_{ads} *D*\left( {1 - \frac{Q}{{Q_{max} }}} \right) $$

(42)

$$ F_{7} = \frac{{K_{des} *Q}}{{Q_{max} }} $$

(43)

$$ F_{8} = m_{R} *B*\left( {1 - p_{EP} - p_{EM} } \right) $$

(44)

$$ F_{9,EP} = p_{EP} *m_{R} *B;\,\,F_{9,EM} = p_{EM} *m_{R} *B $$

(45)

$$ F_{10,EP} = r_{EP} *E_{P} ;\,\,\,F_{10,EM} = r_{EM} *E_{M} $$

(46)

where V _i and K _i represent the V _max and K _m for enzymatic degradation of pool i, m _R is the maintenance respiration rate, Q _max is the maximum DOC sorption capacity, K _des and K _ads are the specific adsorption and desorption rates, p _i is the fraction of m _R associated with production of enzyme i, and r _i is the turnover rate of enzyme pool i. V _i , K _i , m _R , K _des , and K _ads follow Arrhenius temperature sensitivity similar to Eq. 19, and E _C is linearly dependent on temperature as in Eq. 17. The differential equations are as follows for the pools:

$$ \frac{dP}{dt} = I_{P} + \left( {1 - g_{D} } \right)*F_{8} {-} F_{2} $$

(47)

$$ \frac{dM}{dt} = \left( {1 - f_{D} } \right)*F_{2} {-} F_{3} $$

(48)

$$ \frac{dQ}{dt} = F_{6} - F_{7} $$

(49)

$$ \frac{dB}{dt} = F_{1} - \left( {F_{4} + F_{5} } \right) - F_{8} - (F_{9,EP} + F_{9,EM} ) $$

(50)

$$ \frac{dD}{dt} = I_{D} + f_{D} *F_{2} + g_{D} *F_{8} + F_{3} + \left( {F_{10,EP} + F_{10,EM} } \right) - F_{1} - (F_{6} + F_{7} ) $$

(51)

$$ \frac{{dE_{P} }}{dt} = F_{9,EP} - F_{10,EP} $$

(52)

$$ \frac{{dE_{M} }}{dt} = F_{9,EM} - F_{10,EM} $$

(53)

and the CO₂ respiration rate is calculated as:

$$ C_{R} = F_{4} + F_{5} $$

(54)

MEND represents microbial respiration as a fraction of assimilation (Eqs. 40, 41) whereas GER and AWB represent respiration as a fraction of microbial uptake (Eqs. 18, 26); note that these representations are algebraically identical with respect to CUE.

Steady state analytical solution

The steady state analytical solutions to the MEND differential equations are as follows:

$$ P = \frac{{K_{P} }}{{V_{P} *p_{EP} *E_{C} *\frac{{(I_{D} /I_{P} ) + 1}}{{r_{EP} *A}} - 1}} $$

(55)

$$ M = \frac{{K_{M} }}{{V_{M} *p_{EM} *\frac{{E_{C} }}{{r_{EM} *\left( {1 - f_{D} } \right)*A}}*\left( {1 + \frac{{I_{D} }}{{I_{P} }}} \right) - 1}} $$

(56)

where

$$ A = 1 - E_{C} + \left( {1 - p_{EP} - p_{EM} } \right)*E_{C} *\left( {1 - g_{D} } \right)*\left( {\frac{{I_{D} }}{{I_{P} }} + 1} \right) $$

(57)

Equations 55–56 simplify to the following if I _D  ≪ I _P :

$$ P = \frac{{K_{P} }}{{V_{P} *p_{EP} *\frac{{E_{C} }}{{r_{EP} *\left( {1 - g_{D} *E_{C} } \right)}} - 1}} $$

(58)

$$ M = \frac{{K_{M} }}{{V_{M} *p_{EM} *\frac{{E_{C} }}{{r_{EM} *\left( {1 - g_{D} *E_{C} } \right)*\left( {1 - f_{D} } \right)}} - 1}} $$

(59)

$$ D = \frac{{m_{R} *K_{D} }}{{V_{D} }} $$

(60)

$$Q = \frac{{Q_{max}}}{\left({1 + \left({\frac{1}{({D}*K_{BA})} }\right)}\right)} $$

(61)

$$ E_{P} = \frac{{\left( {B*m_{R} *p_{EP} } \right)}}{{r_{EP} }} $$

(62)

$$ E_{M} = \frac{{\left( {B*m_{R} *p_{EM} } \right)}}{{r_{EM} }} $$

(63)

$$ B = \frac{{I_{D} + I_{P} }}{{\left( {\frac{1}{{E_{C} }} - 1} \right)*m_{R} }} $$

(64)

See Table 2 for all model parameter values.

Table 2 Parameters used in model comparison