Quality or decomposer efficiency which is most important for the temperature response of litter decomposition ? A modelling study using the GLUE methodology

Effects of temperature history on litter decomposition was evaluated with the Q-model calibrated to a needle litter incubation experiment and using the GLUE modelling framework. The needle litter incubation was a full factorial design with initial and final temperatures 5, 15 and 25oC. Samples going to a different second temperature were moved when approximately 12% carbon had respired. We used four variations of the Q-model; the combination of one or two initial litter quality values and fixed or temperaturedependent decomposer efficiency. The model was calibrated to the constant temperature subset of the data. Evaluated against the subset containing temperature shifts, gave good results, except just after the change in temperature where the model predicted less than measured. Using one or two initial litter quality values and fixed decomposer efficiency had little effect on litter quality and respiration during the final incubation temperature. When the decomposer efficiency was allowed to vary with temperature, the best predictions had decomposer efficiency values that decreased between 5 to 15oC and did not change between 15 and 25oC. Having flexible decomposer efficiency resulted in substantial differences in litter quality between the three temperatures at the end of the initial incubation. This resulted in that samples at the same final temperature, subjected to different initial temperatures, decomposed at significantly different rates. The result suggests that it might be important to consider other factors than the variation in temperature sensitivity with quality when evaluating effects of temperature changes on soil organic matter stability.


Introduction
In view of the expected future climatic change (Solomon, 2007) the temperature dependence of decomposition of litters and soil organic matter (SOM) has since long attracted much interest because a strong positive temperature dependence would create a strong positive climatic feedback.However, both in laboratory incubations and field studies, temperature history and not only current temperature have been shown to affect respiration rates, such that SOM with different temperature histories will have different decomposition rates at the same temperature.These effects can be short term or long term, and be a result of factors like substrate depletion, changes in decomposer community composition and abundance, and changes in quality composition (Kirschbaum, 2006).Quality changes have been challenged as a major factor because the temperature dependence of the rate of utilisation might not respond strongly enough to explain observations as there are several processes involved with sometimes counteracting temperature responses (Davidson and Janssens, 2006;Ågren and Wetterstedt, 2007).It is thus necessary to also consider the temperature dependence of the other factors regulating decomposition.Decomposer community composition and decomposer biomass are two important factors that may be affected by temperature.For example, it has been demonstrated (Devêvre and Horwáth, 2000;Steinweg et al., 2008) that the carbon use efficiency of decomposers decreases with Published by Copernicus Publications on behalf of the European Geosciences Union.
temperature, probably as a result of higher maintenance costs.Allison et al. (2010) suggest that the decomposer biomass should go down with increasing maintenance cost and as a result less extracellular enzymes are produced and decomposition slows down.
Most models, e.g.Century (Parton et al., 1987), G'Day (Comins and McMurtrie, 1993), RothC (Coleman and Jenkinson, 1995), Q ( Ågren and Bosatta, 1998) dealing with soil organic carbon (SOC) conform to the same generic structure.SOC is described as consisting of carbon of different pools or qualities with three main processes driving the changes in SOC quantity and quality: (i) a decomposer community feeding on SOC at some rate (growth rate); (ii) when doing so, part of the carbon it uses is respired as carbon dioxide and part remains as SOC; we call the fraction remaining efficiency (decomposer efficiency); (iii) the fraction remaining undergoes changes in quality.We call this transfer between qualities (pools) dispersion, on average SOC increases in recalcitrance/decreases in quality with time.
To investigate how the factors quality and decomposer efficiency affect respiration at different temperatures (temperature response) we tested the Q-model (Bosatta and Ågren, 2003;Ågren and Bosatta, 1998) against an incubation experiment with needle litter (Wetterstedt et al., 2010).The Q-model was chosen because the fate of carbon and the decomposition processes are relatively easy to follow in it.The factors quality and decomposer efficiency are explored by modifying the model to have one or two initial litter qualities in combination with fixed or flexible (with regard to temperature) decomposer efficiency.
We have chosen to use the GLUE (Generalised Likelihood Uncertainty Estimation, Beven, 2006) framework for model calibration and evaluation.GLUE can be used as a modelling protocol and is well suited to give uncertainty estimations in model output.It also provides criteria for complete model rejection, i.e. the model structure needs to be changed if the model fails to predict empirical data well enough.
The main reason for choosing GLUE as opposed to a formal Bayesian approach was because it allowed us more freedom in specifying a likelihood function.The measurements are known to contain equipment-related errors, there is biological variation within the replicates, the Q-model is nonlinear, and the ever-present model structural error makes the identification of a formal error model to be used in a formal Bayesian approach problematic.Moreover, our main purpose is not to establish the value of the parameters to the best precision possible, but rather to explore qualitative effects of the parameters and the model.Using GLUE, it is often the case that quite different parameter sets give more or less equal good fits (equifinality).Within the framework it is easy and straightforward to use those sets in ensemble modeling.Even though the likelihood function is subjectively chosen it is easy to understand and communicate to a wider audience.The likelihood function is of lesser importance as long as it will help us find parameters that make the model predict measurements well.See also the discussion of the use of the GLUE methodology versus other formal Bayesian approaches (Mantovan and Todini, 2006;Beven et al., 2008).

The Q-model
The Q-model describes litter or SOC as consisting of a continuous spectrum of carbon qualities or decomposabilities instead of being partitioned into a small number of discrete pools.The Q-model has certain advantages over discrete models.Firstly, there are analytical solutions, making it easier to understand and explain model behaviour.Approximate solutions, which are similar in their behaviour, are also available (Bosatta and Ågren, 2003).The approximate solutions are much less computationally demanding and are therefore preferred when doing large model runs, for example during calibration.They substitute the complete distribution of litter qualities in the exact solution with one average quality.Secondly, there are also fewer parameters in a continuous formulation, as opposed to pool models, and the model formulation enforces consistency between them (Bruun et al., 2010).Parameters estimated with the approximate solutions can also be used in the exact solution, possibly with some slight recalibration.
In the Q-model the growth rate (u) of the decomposers depends on carbon quality (q) and temperature (T ) as well as the base rate parameter (u 0 ).The temperature response of the growth rate couples temperature and quality through an Arrhenius function with activation energy G 0 giving u(q,T ) = u 0 e − G 0 qRT where R is the gas constant (Bosatta and Ågren, 1999); we will for convenience allow q > 1 in contrast to the restriction 0 < q < 1 in the original derivation.Decomposer efficiency (e) is set to be either temperature independent (fixed) or allowed to vary with temperature (flexible).In the latter case no specific temperature function has been assumed; the intention is instead to investigate the existence of a temperature dependence.Transfer of carbon to lower qualities, dispersion, is expressed through the parameter η 12 , which is assumed to be temperature independent.Table 1 lists the parameters used in the model.When running the model with two initial litter qualities, the two q 0 's will be selected from behavioural models (see below) where the qualities are somewhat separated.The reason we are using two initial q 0 's in this experiment is to explore the effect of how the different temperature sensitivity of different q 0 's translates into a differential quality evolution.Besides answering the question of which variations of the Q-model that can reproduce the observations, it is necessary to look at the consequences for the distribution of carbon qualities; when extrapolating Table 1.List of parameters.Parameter values are those corresponding to the highest LM.Range is the range used in the calibration procedure.Sampling was done uniformly for all parameters but u 0 which was sampled from a log-distribution.With two initial qualities the q 0 's (q 0−1 and q 0−2 ) were fixed from values obtained with one initial quality (q 0 ).Fixed and Flex. in the table heading refer to fixed or flexible e 0 .Initial parameter range was greater to find suitable parameter space.
One q 0 Two q 0 Parameter Range Fixed Flex.Fixed Flex.Comment from this short-term experiment to long-term carbon storage differences in quality distributions become important.
Four versions of the model were run with combinations of one or two initial qualities combined with fixed or flexible decomposer efficiencies.When using two initial qualities, one quality was chosen as the best one found when using only one quality and the other one was set to a lower value estimated to give a reasonable difference; the sensitivity to this choice was also tested.The initial amount of carbon was partitioned equally between the two qualities.When estimating parameters within GLUE we have used the approximate version of Model III as defined in Bosatta and Ågren (2003).The best parameter set has then been used in the exact solution to calculate quality distributions.

Observational data
We have chosen to use the spruce (Picea abies) needle litter data from the temperature experiment by Wetterstedt et al. (2010) (see Figs. 1 and 2).The data consists of time series (four replicates) of litter respiration rates at different temperatures.In some time series the samples have been shifted from one temperature to another when approximately 12% of the initial carbon had been respired.We will denote temperature combinations as initial temperature + final temperature, e.g. 5 + 15 • C, meaning that the sample was first exposed to 5 • C and then 15 • C. The data used for calibration were from needles stored at three temperatures without shifts in temperature (5 + 5 • C, 19 data points; 15 + 15 • C, 14 data points; and 25 + 25 • C, 16 data points).To reduce the variability in data between measurement points, we used a running mean of three consecutive points to smooth the curve (the first and last points were averaged from two points).We also normalised the variance at each measurement point by averaging over the whole measurement period for each temperature, i.e. the variances used when calibrating the model are where O i is the observation at point i and n is the number of points in the measurement series.These steps were taken to obtain a more robust calibration process.However, when the calibrated models are evaluated using the least square method, R 2 are calculated with respect to non-smoothed data (Figs. 1 and 2).

GLUE
The GLUE methodology introduced by Beven and Binley (1992) is a framework for calibrating and using models in predictions.It includes criteria and methods for model rejection and sensitivity analysis of model parameters.A "model" in GLUE terminology is the combination of the "model structure", e.g. the Q-model as opposed to some other model, and the parameter values used to run the model.A "behavioural model" is a model that can simulate real data "good enough".It follows that a non-behavioural model should not be used to forecast data; instead, it would need better parameterisation or a change in model structure.In this text we will, however, use the term "model" with the meaning "model structure".
The GLUE methodology is particularly useful in the field of environmental modelling in which the errors involved in measurement data may be unclear and where the response surface of the "goal function" or likelihood measure (LM) is flat and likely to contain many local optima (cf.Hyvönen et al., 2005).The GLUE methodology also acknowledges that more optima will be found with a more extensive search in the parameter space.Since it is likely that these optima would move with already small differences in measurement data (measurement errors), it is not meaningful to only search for a global optimum.
The use of GLUE includes the following steps (Beven, 2009): 1. Likelihood measure: decide on an informal (or formal) likelihood measure or measures (LM) for use in evaluating each model run, including the rejection criteria, which for a non-behavioural model run will be given a likelihood of zero.Ideally this should be done before running the model, taking into account possible input and observational errors: since calibration data contain means as well as standard deviations, we used a triangular shaped likelihood measure:  stands for the parameter set used.This choice of likelihood measure gives equal weight to the different temperature series.It takes also advantage of the variability in the observed data and is less influenced than the least square method by outliers.Ideally, the model with the parameters in question, should predict all observed data points within their 95% error bounds; i.e. for all LM(M,O min ,O mean ,O max ) observations.How-ever, this turned out not to be feasible, why have chosen LM > 0 as criteria for a behavioural model.

Model parameters: decide which model parameters and
input variables are to be considered uncertain: all model parameters were considered uncertain (Table 1).
3. Parameter distributions: decide on prior distributions from which the uncertain parameters and variables can be sampled: we have chosen uniform initial distributions for all parameters except u 0 , for which a logarithmic one was used (Table 1).To further narrow the sampling space, initial sample runs were made to localise parts of the parameter space that were more likely to generate good fits.with the assumptions in steps 1 and 2: twenty thousand parameter sets were drawn from uniform distributions for all parameters except u 0 , which was drawn from a log-distribution, (Table 1) and used as initial points in the Simulated annealing algorithm (Mathematica 7.0.0Ubuntu/Linux).This procedure results in only one "optimum" set of parameters.The procedure was therefore repeated 28 000 times and the optimum sets together with their resulting likelihood values were stored.Calibration was made simultaneously against samples that had been kept at 5 + 5 • C, 15 + 15 • C and 25 + 25 • C.

Dotty plots
There exist a number of methods to assess sensitivity in nonlinear models.The method most often used within the GLUE framework is to make a scatter-plot/dotty plot of each parameter (on the x-axis) versus the likelihood measure (y-axis) obtained during the calibration/conditioning process.From the resulting swarm of points, one can find trends showing for example that certain parameters are present in only a short interval of the initially sampled points, whereas others have a uniform density along the x-axis.If only a small segment of the initially sampled parameter space is found among the behavioural model runs, restricting that parameter to a smaller range will probably improve the number of behavioural model runs.On the contrary, if behavioural runs are equally distributed along the parameter axis, extending the parameter range might disclose/unravel areas of the parameter space which are more likely to prove behavioural.

Using the model
Behavioural parameter sets are used in ensemble runs to generate a mean output value and likely error bounds.An ensemble run is obtained when running the same model with many parameter sets (as is the case in this article) or run-ning different models to obtain a distribution of results.The likelihood measure, LM, or any other performance measure, can then be used to weigh the different outputs to create a weighted mean.Error bounds can be generated from the max and min from the model runs, or at any preferred significance level obtained from a cumulative density curve.In this article we will simply use max and min of the selected models as bounds.

One initial quality, fixed decomposer efficiency
With one initial quality (q 0 ) and fixed decomposer efficiency (e 0 ) the dotty plots (data not shown) showed more or less evenly distributed LM's, except for u 0 for which fits tended to be better with increasing u 0 .This indicates that the upper boundary for u 0 might have been too small.The generally even distribution of all parameters means that, within the used ranges, different parameters compensate for each other, making the model rather insensitive to changes in single parameters.We got 257 parameter sets that were behavioural.The best fit yielded a LM of 0.243, and was within boundaries at 37 out of 48 data points in the calibration set (Fig. 1).
When validated against experiments with shifts in temperature, the model follows the data well during the initial temperature phase; this is not surprising because it was calibrated on similar data (Fig. 1).During the final incubation after a temperature increase, the model underestimates the increase in respiration during the first days when going from 5 • C to 15 • C or 25 • C. When shifting downwards in temperature the model predicts initially slightly higher values than observed.
With fixed decomposer efficiency, temperature history has negligible effect on future respiration rates.The respiration at the final temperature after the shift for the 5 + 25  the 25 + 25 • C treatment (Fig. 3a).The same holds for the 25 + 5 • C and 5 + 5 • C treatment.

One initial quality, flexible decomposer efficiency
With one initial quality (q 0 ) and flexible decomposer efficiency (e 0 ) there are few points in the dotty plots at the extremes of the x-axis for q 0 , meaning that high and low q 0 were unlikely to give good fits.u 0 , G 0 and e 0 's are fairly evenly distributed.η 12 is skewed towards the lower end of the spectrum (Fig. 4).The best fit yielded a LM of 0.284, and was within boundaries at 37 out of 48 points (Fig. 2).33 sets were found behavioural.
The model with flexible decomposer efficiency fits the data slightly better than the fixed decomposer efficiency version when validated against the experiment with temperature shifts, as well as bracketing more of the data points due to the wider uncertainty bounds (Fig. 2).When going down in temperature, the model seems to over-shoot slightly, at least initially (15 + 5 • C, 25 + 5 • C) and when going up (5 + 25 • C and possibly 15+25 • C) the model misses the initial respiratory peak.
To search for trends in how e 0 varied with temperature we reran the simulations with the one q 0 flexible e 0 model to obtain a larger number (160) of behavioural parameter sets (LM > 0).Decomposer efficiencies were plotted in pairs, i.e.With temperature dependent decomposer efficiency, respiration responded strongly to temperature history.For example, the sample initially at 25 • C respired substantially more than the one initially at 5 • C when both were at 25 • C. Similarly, the sample initially at 25 • C respired more than the one initially at 5 • C when both are at 5 • C (Fig. 3b).

Two initial qualities, fixed and flexible decomposer efficiency
In the model runs with two initial qualities, the contribution (both at time 0 and at 12% carbon loss) of the lower quality (q 0−1 ) to respiration is much lower (1/4700 and 1/2700 at 5 • C and 25 • C, respectively) than the respiration of the higher quality (q 0−2 ).Therefore the respiration from the high quality totally dominated the respiration and the model behaved qualitatively the same as with a single initial quality but with different "optimal" parameters.

Model behaviour
The calibration data showed considerable variation in the variability between days.Also, the respiration did not always decrease monotonically as expected.We do not know whether this variability in input data comes from short-time biological variation or from measurement errors.We had, therefore, to relax the condition that, for each behavioural parameter set, predictions should be within error bounds for all points in each temperature series.Despite that, calibration to the constant temperature subsets worked well with R 2 values in the range of 0.83-0.96.However, even though the ensemble runs mostly covered all calibration points, at 5

Choice of likelihood measure (LM)
Our choice of likelihood measure, LM, is subjective.Ultimately, the objective should be to acquire parameters "useful in model prediction" (Beven, 2009, p. 124), and the LM should be chosen to help in doing so.One way of interpreting "useful in model prediction" is that the model should be able to bracket our observations, which it did in most of the cases (Figs. 1 and 2).Since the primary objective of this paper is not to model decomposition in general, but rather to highlight the effects on quality composition and respiration rates of a temperature-dependent efficiency and the coupling of quality with temperature, the likelihood measure used is of lesser importance; see Beven (2009, p. 165) for further discussion of choice of likelihood measure.

One or several initial qualities
We have considered two main ways in which temperature history can affect current respiration rates.The first is that different qualities have different temperature dependencies, which should lead to a difference in quality composition at different temperatures and equal carbon loss (for a more detailed discussion, see Wetterstedt et al., 2010).However, with our choice of two different initial qualities (q 0−1 = 1.80, q 0−2 = 2.50), the lower quality decomposed at only about 1/4700 at 5 • C respectively 1/2700 at 25 • C of the rate of the higher one.Together with the relatively small difference in temperature sensitivity between the two q 0 's (fixed e 0 , two q 0 model: Q 10−1 = 2.9, Q 10−2 = 2.1; flexible e 0 , two q 0 model: 3) this did not in this short-term experiment translate into a sufficiently large quality evolution between the temperatures; it is essentially only the highest quality that decomposes.Choosing a larger q 0−1 resulted in more use also of the lower quality, but at the expense of a smaller difference in Q 10 between the two qualities.However, whatever q 0−1 is chosen, the effect on the temperature response is small.

Fixed or flexible decomposer efficiency
The second mechanism, varying decomposer efficiency (e 0 ) with temperature, resulted in a clear effect on quality distributions and thus temperature sensitivity and respiration rates (Figs. 3 and 6).The reason for this is two-fold.Most importantly, with higher efficiency, when carbon is taken from the initial quality, a smaller part is lost by respiration and a larger part is converted to lower qualities.Thus, to obtain the same mass loss more of the initial quality has to be processed.Secondly, the dispersed carbon will for the same reason persist for longer which means that yet more initial carbon needs to be processed before reaching the same cumulative respiration as at the lower decomposer efficiency.As a result at equal mass losses, the higher efficiency produces a lower quality.The flexible model is better fitted to the initial more rapid increase at the beginning of the experiment as well as after the shift in temperature.Having a temperature dependent e 0 also leads to a model that simulates differences in respiration rates at the same final temperature from samples of different initial incubation temperatures (Fig. 3).Surprisingly, having flexible decomposer efficiency resulted in fewer behavioural parameter sets.This is surprising because it adds two extra parameters which should increase the possibility of finding better fits.It seems however that the two extra parameters decreased the probability of finding good parameter sets and because the calibration was run with the same number of trial parameter sets, this resulted in fewer behavioural parameter sets.J. Å.M. Wetterstedt and G. I. Ågren: Quality or decomposer efficiency The behaviour of e 0 points in the direction that decomposer efficiency might decrease with increasing temperature.This could be one of the explanations to why respiration is so strongly correlated to temperature.However, it can be difficult to compare e 0 between different models, between models and experiment, or indeed, between different experiments (cf.Devêvre and Horwáth, 2000;Steinweg et al., 2008).In experiments e 0 is not measured directly and a number of more or less explicit assumptions are introduced when calculating e 0 from measurable quantities such as consumed substrate and respiration; such assumptions may or may not distort the relation between conceptual and observed values.In models, we also simplify the system; simplifications that differ between models.

Other temperature effects
One part where the model has difficulty in reproducing the experiment is directly after temperature shifts, where respiration is underestimated and overestimated after shifts upward and downward, respectively.These deviations between predictions and observations are similar to those observed when extrapolating respiration rates obtained at constant temperatures to temperature shifts in the study by Wetterstedt et al. (2010).We propose that these deviations over a few days represent transient adjustments in decomposer properties to new conditions.A possible interpretation is that these transients result from decomposer adaptation to new temperatures and that previously cold-adapted organisms respond more strongly than previously warm-adopted (Bradford et al., 2008).It remains an open question how important such transients may be under field conditions where temperatures are changing continuously, albeit less rapidly than in most experimental studies.
It should also be born in mind that the temperature response we find in e 0 depends on the assumptions we have made about the temperature dependence of the other factors.For example, we are assuming that the dispersion function is temperature independent although the rate of decomposition is highly sensitive to the strength of dispersion (Hyvönen et al., 2005).This is a simplifying assumption but we are not aware of any experiments demonstrating temperature sensitivity of dispersion.Likewise, although there are theoretical arguments for the effects of quality on the temperature dependence of the rate of carbon utilisation (Bosatta and Ågren, 1999), this has not been tested rigorously experimentally.Allison et al. (2010) point out another complication from temperature dependent decomposer efficiency.If decomposer efficiency goes down with temperature, decomposers assimilating the same amount of carbon will produce less biomass, which in turn should lead to a lower production of extracellular enzymes that can release assimilable carbon.In our terminology this should correspond a positive coupling between e 0 and u 0 .The increased loss of carbon caused by a temperature increase resulting from lowered decomposer ef-ficiency would then be counteracted by a lower use of carbon.Schimel and Weintraub (2003) suggest instead that lowered decomposer efficiency would not occur at the expense of enzyme production but rather lead to decreased microbial biomass.There is a possibility that different microbial populations are active at different temperatures and that cold-adaptation increases maintenance costs, i.e. decreases efficiency, which can lead to a negative coupling between growth rate and efficiency over changing temperatures (Lipson et al., 2009).In the laboratory experiment by Wetterstedt et al. (2010) the scope for changes in microbial populations was limited and the response should more reflect those of a fixed microbial composition although there were indications of changes in the microbial population (E.Bååth, unpublished data).The question of the mechanisms behind the temperature response of decomposition is still far from being solved and it is likely that we need to consider additional couplings between processes.

Conclusions
When fitting complex models with many adjustable parameters it is a common situation that many different parameter combinations are almost equally good and there is no additional information to be used for discriminating between them (Hyvönen et al., 2005).The strength of the GLUE method in a context like this one is that is does not select just one optimal set of parameters but allows all the possible parameters that match preselected conditions.What we learn in this study is that for almost all parameter combinations, e 0−5 is larger than e 0−15 and e 0−25 .This is a strong suggestion that decomposer efficiency is, indeed, temperature dependent at least in the range 5-15 • C; above that range the results are less clear.This is a key result of this study.
A temperature-sensitive decomposer efficiency was shown to have a much stronger influence on quality differentiation, and thus respiration, than the temperature sensitivity of utilisation of different qualities.The difficulties in capturing changes in respiration rates at rapid temperature changes should caution us about extrapolating short term effects to longer time periods (cf.Wetterstedt et al., 2010); understanding the rate at which a microbial community can adjust requires more investigations.Our results show also that it is necessary to more carefully consider the temperature dependence of other processes than those directly coupled to the rate of substrate utilisation.

Fig. 1 .
Fig. 1.Model predictions of respiration rates for the one initial quality, fixed decomposer efficiency model and observed respiration rates for all combinations of initial (T i ) and final (T f ) temperatures (5 • C, 15 • C, and 25 • C.) Weighted ensemble run predictions (solid black line) with max/min curves (blue dashed lines) for the behavioural parameter sets.The yellow fields show 95% error bounds around measured data points (dots).Least square R 2 -values are shown in top right corner of each sub-graph.

Fig. 2 .
Fig. 2. Model predictions of respiration rates for the one initial quality, flexible decomposer efficiency model and observed respiration rates for all combinations of initial (T i ) and final (T f ) temperatures (5 • C, 15 • C, and 25 • C.) Weighted ensemble run predictions (solid black line) with max/min curves (blue dashed lines) for the behavioural parameter sets.The yellow fields show 95% error bounds around measured data points (dots).Least square R 2 -values are shown in top right corner of each sub-graph.

Fig. 3 .
Fig.3.Respiration rates of samples as a function of time, predicted by the flexible and fixed decomposer efficiency models with constant temperatures (solid lines) and with a switch between 5 • C and 25 • C at 12% respired carbon (broken lines) using the parameter set with the highest LM (Table1).For clarity, the transitions between temperatures are slightly displaced from exactly 12%.(a) Fixed e 0 .(b) Flexible e 0 .Note, this simulation does not give the same result as the weighted ensemble predictions (Figs.2 and 3).

Fig. 4 .
Fig. 4. Dotty plots for the one initial quality, flexible decomposer efficiency.Each dot represents one model run.The likelihood measure, LM, or "goodness of fit", is plotted against parameter values.The x-scales cover the allowed ranges of the parameters.Parameter sets resulting in a LM > 0 where used in ensemble simulation runs.

Fig. 5 .
Fig. 5. Correlations between efficiencies at 5 • C, 15 • C, and 25 • C from behavioural parameter sets in the one initial quality, flexible decomposer efficiency model.Solid line: linear regression of data.Broken line: 1:1 line.
• C and 15 • C the data points might have a more concave pattern than what the model can predict (Figs. 1 and 2 at 5 + 5 • C, 15+15 • C).When the model is validated against the temperature shift experiments, experiments tend to respond more strongly just at the temperature shift than the model.

Fig. 6 .
Fig. 6.Distributions of qualities for combinations of one or two initial qualities and fixed or flexible decomposer efficiency (e 0 ) when 12% carbon has been lost for samples incubated at 5 • C or 25 • C. Solid lines and black bars are for samples at 5 • C. Dashed lines and grey bars are for samples at 25 • C. The bars have been shifted slightly leftwards and rightwards from their value to visually separate them.Bars show the amount of carbon that has not been used by decomposers so far (remaining at the initial qualities).The lines show the distributions of carbon that the decomposers have converted into new qualities.With flexible decomposer efficiency, more carbon has been converted (lines) and less remains at the initial quality (bar) at the higher temperature.With two initial qualities the losses have essentially only occurred from the highest quality.Note that the sums of the bar(s) and the areas under the corresponding temperature curves are all equal, 88% of initial carbon.