2.1. Site of the Experiment
 The experiment was conducted at the paramo site of Gavidia (8°35′N–8°45′N, 70°52′W–70°57′W) in the Andes of Mérida (Mérida State, Venezuela) at an altitude of 3400 m. The mean annual precipitation is 1329 mm, with a dry season between November and March and a rainy season between April and October. The mean annual temperature is 8.5°C differing only by 1.5°C between the coldest and the warmest months but with a mean daily thermal amplitude of 10.5°C. The experiment was set up in (1) a 2-year-old fallow plot (F2y data series) with an estimated soil cover = 0.85 of mainly perennial herbs and (2) in a 7-year-old fallow plot (F7y data series) covered by the characteristic paramo giant rosettes and by shrubs (height = 1 to 1.5 m, estimated soil cover = 0.9, differing markedly from grassland). The soil (humitropepts, USA Soil Taxonomy) is loamy and well drained. In the 0- to 10-cm layer, sand = 54%, silt = 31%, clay = 15%, pH(H2O) = 4.5, water-holding capacity (v/v) = 0.52 (mean values of the two experimental plots), C = 9.4% (plot F2y) and 8.8% (plot F7y), and N = 0.55% (F2y) and 0.56% (F7y). The high organic matter content explains the high water-holding capacity. The cultivation system is based on a long fallow period used for extensive grazing (generally lasting from 5 to 10 years) alternating with a short (1 to 3 years) potato and cereal cropping period.
2.2. 14C and 15N Labeled Plant Material
 A low N-requiring old cultivar of spring wheat (Florence Aurore) was grown from seed to maturity in a labeling chamber with controlled 14CO2 atmosphere (0.03% v/v, 0.86 kBq mg−1 C), temperature, radiation, and alternate lighting conditions. The plants, which were cultivated in pure sand, were periodically flooded with a complete nutrient solution containing Ca(15NO3)2 (10% atomic ratio) as the sole N source. At ear emergence the wheat was dried at 40°C. Only the stems and leaves were used in the experiment. They were ground into particles between 2 and 7 mm long and mixed to obtain a homogeneous material. The C content of the material was 43.0 ± 0.39% (0.821 ± 0.022 kBq mg−1 C), the N content was 1.60 ± 0.05% (15N isotopic ratio = 9.250 ± 0.451%), and the C/N ratio was 26.9 ± 0.9. The biochemical fractions of the straw [van Soest et al., 1991] were as follows: neutral detergent soluble = 0.36, hemicelluloses = 0.25, cellulose = 0.26, lignin = 0.03, and ashes = 0.10. The N content of the straw used in the present part of the experiment was relatively high, but the behavior of the model from a litter with low N content will be discussed elsewhere (work in preparation).
2.4. Data Acquisition
 At sampling, the wet sample was homogenized and 3 × 5 g wet soil was dried at 105°C for the measurement of the moisture content. The remaining wet soil was subsampled for analyses of (1) microbial biomass-14C and -15N (four field replicates × two analysis replicates for MB-14C, four field replicates for MB-15N), and (2) total-14C, (four × eight replicates) and -15N (four × two replicates). Microbial biomass was measured according to the fumigation-extraction method of Brookes et al. : 20 g soil, 150 mL 1 mol(K2SO4)L−1 extractant, 14C measurement on the extracts by liquid scintillation counting (Tricarb 1500, Packard), measurement of N and 15N by Kjeldahl procedure and isotope mass spectrometry (Finnigan delta S), keC (the microbial biomass-C correcting factor) = 0.45 [Joergensen, 1996], and kEN (N correcting factor) = 0.54 [Joergensen and Mueller, 1996]. Total C and 14C were measured simultaneously using Carmograph 12A (Wösthoff, Bochum, Germany), according to Bottner and Warembourg . Total N and 15N were measured using coupled CHN/isotope mass spectrometry.
 Climatic parameters (daily precipitation, mean air temperature, and total radiation) were recorded using an automatic Campbell weather station at the site throughout the experiment period.
2.5. Predictive Models
 The five models tested with Vensim software (Ventana Systems, Inc., Harvard, Massachusetts) are presented in Figure 1. Three compartments are present in all the models: labile (VL), stable (VS) fractions of necromass (NC = VL + VL) and microbial biomass (MB). MOMOS-3, -4, and -5 contain a compartment for humified compounds (H). MOMOS-2 and -6 contain compartments for labile (HL) and stable (HS) humified compounds. MOMOS-2 is the model already presented by Sallih and Pansu  using data from a labeling experiment performed under laboratory conditions, with measurements of total 14C, microbial biomass 14C and not yet decomposed plant fragments 14C. MOMOS-3 results from the simplification of MOMOS-2, with an equation system analogous to the Roth-C model [Jenkinson, 1990], but without the inert organic matter compartment of Roth-C (not necessary for this short-term 14C and 15N experiment). MOMOS-4 offers a further simplification of MOMOS-3: The recycling part of H and MB compartments are removed. MOMOS-5 explores two new modifications: (1) the whole outputs from plant material (VL+VS) and humus (H) compartments are the inputs of MB, and (2) the outputs of MB are defined by a respiration quotient (qCO2) and a microbial mortality rate (kMB). The equation system of MOMOS-5 is similar to that of the CANDY model [Franko et al., 1995] and to that used by Saggar et al.  to calculate 14C turnover and residence times in soils. However, MOMOS-5 differs from the former models in the following aspects: (1) fractionation of NC inputs into VL and VS, (2) change of kinetic calculation of the microbial respiration (see below, equations (9) and (10)), and (3) elimination of the flow fractionation between necromass and MB used in CANDY (in MOMOS-5 the whole flow from the NC substrate enters into MB). MOMOS-6 attempts to improve MOMOS-5 by introducing a stable humus compartment (HS) that results from the slow maturation of HL and supplies the dormant MB with maintenance energy, when the fresh C input is exhausted. MOMOS-5 and -6 are only regulated by first-order kinetic constants (k parameters, dimension t−1), without the dimensionless parameters (efficiency factors) often used in SOM models to fractionate the flows between the compartments (P parameters in MOMOS-2 to -4, or, e.g., Jenkinson and Rayner , Parton et al. , or Franko et al. ).
Figure 1. Flow diagram's of the five versions of the MOMOS model compared. NC, total necromass; VL, labile necromass; VS, stable necromass; MB, microbial biomass; H, humified compounds (humus); HL, labile humus; HS, stable humus.
Download figure to PowerPoint
 For each model, the initial necromass (NC) was partitioned over VL and VR on the basis of its biochemical characteristics using the equations proposed by Thuriès et al. [2001, 2002], which give for this labeled straw the stable fraction of NC: fs = 0.107.
 The general equation of the models is
where x is the vector of the state variables (compartments), is the vector of the rates variables, and A is the parameter matrix of each model. A and x are written, for MOMOS-2,
and for MOMOS-6,
For the labeling experiment described in this paper (one single initial input of dead matter and an initial amount C0 of 14C with a stable fraction fS), the initial conditions are given by
 At each incubation time, the total 14C evolution from the n compartments (n = 4 for MOMOS-3, -4, -5; n = 5 for MOMOS-2, -6) is given by
 In the case of MOMOS-5 and -6, equation (8) becomes particularly simple,
where qCO2 is the metabolic quotient of the microbial biomass [Anderson and Domsch, 1993]. Another condition is necessary to ensure correct performance of MOMOS-5 and -6: qCO2 must be controlled by the amount of MB. The qCO2 increases when MB is growing (particularly in response to the initial high supply from VL) and decreases when MB decreases or becomes inactive (dormant MB). Then is linked to MB by a second-order kinetics. In order to allow use of MOMOS-5 or -6 in different situations, we suggest (1) the introduction of a respiratory coefficient kresp (dimension t−1) and (2) the weighting of the kresp values by the ratio of the actual level of MB in the studied soil and its equilibrium value (CMB0 measured in biologically stable soil, i.e., a long time after the former inputs of substrate). For the present labeling experiment, CMB0 = 0.15 g kg−1, the level of MB-14C measured at the end of the experiment. The qCO2 is given by
 The N calculation of MOMOS-2 to -6 is simplified compared to the initial MOMOS-N model (MOMOS-1 [Pansu et al., 1998]). Ammonia and nitrate pools are combined in a single pool of inorganic-N. For each of the five models, the N state variables are derived from the C model, using the C-to-N ratios of the compartments. If η is the vector of the C-to-N ratios and y is the vector of N contents, the simulation of organic N status at a given incubation time is governed by
If η0 is the initial 14C-to-15N ratio of the plant material, the inorganic 15N (iN) is
In this labeling experiment, the values η0, ηt (remaining total 14C-to- remaining total 15N), and ηMB (14C-to-15N of microbial biomass) were measured. The ηVL value is linked to η0 and ηVS by
The ηH or ηHL values are linked to the other data by
Thus the only η values that have to be estimated are ηVS (14C-to-15N of the stable fraction of NC) in MOMOS-3 to -5 or ηVS and ηHS (14C-to-15N of the stable fraction of humus) in MOMOS-2 and -6. In order to avoid irregularities in predictions, the values calculated for ηH or ηHL are smoothed in the interval [ηMB, (η0 + ηMB)] with ηHS = 6 ηMB/5 for MOMOS-6.
 During the simulations, the kinetic constants are daily corrected by two functions, one for temperature f(T) and one for moisture f(w); f(T) is a law with Q10 = 2 for a reference temperature of 20°C assumed to be valid for these mountain soils [Kätterer et al., 1998]; f(w) is a linear function of the actual soil moisture scaled by moisture content at field capacity (f (w) = 0 for w = 0). For the 5- to 10-cm soil layer, the actual moisture was calculated by the SAHEL model [Penning de Vries et al., 1989]. With the corrective factor f(T) × f(w) in [0, 1] interval, the general formulation (equation (1)) of the models becomes
2.6. Comparison of the Predictive Quality and Sensitivity of the Models
 The four vectors of measured data were:
= total 14C (nine sampling occasions (so) during 2 years of incubation), corresponding to the predicted values ,
= total 15N (nine so) corresponding to the predicted values ,
= MB-14C (nine so) corresponding to the predicted values MB,
= MB-15N (nine so) corresponding to the predicted values MB,
For each model, four residual sums of square (RSS) were calculated for the m so,
 The smallest RSS corresponds to the best fit. In addition, the comparison should take the number of model parameters p into account. The best model has the smallest RSS and also the smallest p. MOMOS-5 has five parameters: kVL, kVS, kMB, kHL, and kresp. MOMOS-3 and -4 have six parameters: kVL, kVS, kMB, kH, PMB, and PH. However, the specific parameterization of this experiment takes kVS = kH and reduces MOMOS-3 and -4 to five parameter models. MOMOS-2 has eight parameters: kVL, kVS, kHL, kHS, kMB, PHL, PMB, and PHS. However, again, the parameterization of this experiment takes kVL = kHL, kVS = kHS, and PHL = 0.77 (value found by Sallih and Pansu ) and also reduces MOMOS-2 to a five-parameter model.
 Thus the predictive quality of the models MOMOS-2–-5 can be pairwise compared by the F tests,
(u, t ∈ [2–5], t ≠ u, m sampling occasions, for each of the four models applied to each of the four series total-14C and -15N, MB-14C, and -15N.
 For a given state variable (SV), a scaled dimensionless sensitivity to a parameter (PA) can be defined by
for the SV total-14C, total-15N, MB-14C, and MB-15N from 13 November 1998 to 11 November 2000 at a daily time step. The values of the parameters were randomly sampled (200 simulations) from a normal distribution. For each parameter, the mean of the distribution is presented in Table 1; the relative standard deviation (sd) was 10%.
Table 1. Estimated Values of the Parameters for the Five Tested Modelsa
|MOMOS-2||0.54||0.004||0.01||kVL|| ||kVS|| || ||0.014|| ||0.08||500|| ||10.5|
|MOMOS-3||0.13||0.004||0.01|| ||kVS|| || || ||0.06||0.36|| ||450||10.9|| |
|MOMOS-4||0.13||0.002||0.007|| ||kVS|| || || ||0.06||0.36|| ||500||10.5|| |
|MOMOS-5||0.6||0.003||0.45|| ||0.05|| || ||0.03|| || || ||27||Cal|| |
|MOMOS-6||0.6||0.003||0.45||0.05|| ||5 10−5||3 10−4||0.03|| || || ||46||Cal||9.9|
|SV||Sensitivity Analysis (Ssv, Equation (19)) of MOMOS-4 (Type 1) Model|
|Tot-14C 3 m||0.17||0.17||0.05|| ||0.17|| || || ||0.17||1.5|| || || || |
|Tot-14C 24 m||0.03||1.0||0.14|| ||1.0|| || || ||0.09||1.7|| || || || |
|Tot-15N 3 m||0.04||0.09||0.05|| ||0.09|| || || ||0.27||1.9|| || || || |
|Tot-15N 24 m||0.03||0.9||0.2|| ||0.9|| || || ||0.14||2|| || || || |
|MB-14C 3 m||0.17||0.08||0.3|| ||0.08|| || || ||2.5||0|| || || || |
|MB-14C 24 m||0.07||0.15||3.2|| ||0.15|| || || ||2.4||0|| || || || |
|MB-15N 3 m||0.16||0.07||0.2|| ||0.07|| || || ||2.4||0|| || || || |
|MB-15N 24 m||0.05||0.12||3.8|| ||0.12|| || || ||2.3||0|| || || || |
|SV||Sensitivity Analysis (Ssv, Equation (19)) of MOMOS-6 (type 2) Model|
|Tot-14C 3 m||0.3||0.02||1.2||0.5|| ||<0.01||0.01||0.7|| || || || || || |
|Tot-14C 24 m||0.2||0.16||2.3||2.0|| ||<0.01||0.16||1.1|| || || || || || |
|Tot-15N 3 m||0.4||0.02||1.2||0.5|| ||<0.01||0.01||0.9|| || || || || || |
|Tot-15N 24 m||0.2||0.16||2.2||2.0|| ||<0.01||0.2||1.2|| || || || || || |
|MB-14C 3 m||0.4||0.04||0.20||1.4|| ||<0.01||0.02||1.1|| || || || || || |
|MB-14C 24 m||0.2||0.15||0.43||0.43|| ||<0.01||0.09||1.5|| || || || || || |
|MB-15N 3 m||0.4||0.04||0.35||1.4|| ||<0.01||0.02||1.1|| || || || || || |
|MB-15N 24 m||0.3||0.09||0.56||0.56|| ||<0.01||0.06||1.5|| || || || || || |