Stronger compensatory thermal adaptation of soil microbial respiration with higher substrate availability

Abstract Ongoing global warming is expected to augment soil respiration by increasing the microbial activity, driving self-reinforcing feedback to climate change. However, the compensatory thermal adaptation of soil microorganisms and substrate depletion may weaken the effects of rising temperature on soil respiration. To test this hypothesis, we collected soils along a large-scale forest transect in eastern China spanning a natural temperature gradient, and we incubated the soils at different temperatures with or without substrate addition. We combined the exponential thermal response function and a data-driven model to study the interaction effect of thermal adaptation and substrate availability on microbial respiration and compared our results to those from two additional continental and global independent datasets. Modeled results suggested that the effect of thermal adaptation on microbial respiration was greater in areas with higher mean annual temperatures, which is consistent with the compensatory response to warming. In addition, the effect of thermal adaptation on microbial respiration was greater under substrate addition than under substrate depletion, which was also true for the independent datasets reanalyzed using our approach. Our results indicate that thermal adaptation in warmer regions could exert a more pronounced negative impact on microbial respiration when the substrate availability is abundant. These findings improve the body of knowledge on how substrate availability influences the soil microbial community–temperature interactions, which could improve estimates of projected soil carbon losses to the atmosphere through respiration.

Table S1.Geographical information, ecosystem types, climate and soil properties of the sampling sites.
Table S2.Unstandardized coefficients (mean ± s.d.), significance and R 2 values of predictive models used to assess the effect of temperature and pedoclimatic conditions on soil microbial respiration without substrate addition.
Table S3.Unstandardized coefficients (mean ± s.d.), significance and R 2 values of predictive models used to assess the effect of temperature and pedoclimatic conditions on soil microbial respiration with substrate addition.Table S4.Standardized coefficients (mean ± s.d.), significance and R 2 values of predictive models used to assess the effect of temperature and pedoclimatic conditions on soil microbial respiration without substrate addition.Table S5.Standardized coefficients (mean ± s.d.), significance and R 2 values of predictive models used to assess the effect of temperature and pedoclimatic conditions on soil microbial respiration with substrate addition.

Supporting text
Comparison of models describing the relationship between microbial respiration and temperature.
The most common approaches for measuring the response of soil microbial respiration to temperature have been the van's Hoff [1] and Arrhenius functions [2].The former assumes that respiration scales as an exponential function of temperature (and is conceptually the same as the often-used Q10 model), while the later assumes that respiration scales as an exponential function of minus the inverse of temperature.Both the Arrhenius and Q10 models predict a monotonic increase in respiration rates as temperature rises, whereas both in the laboratory and in the field, a clearly identifiable temperature optimum in the unimodal trend of soil microbial respiration has been observed [3].Thus, the Arrhenius model might limit extrapolation outside the optimal temperature range for microorganisms.Although the Q10 model has an advantage in its simplicity, it is not a constant value because it differs depending on the temperature interval used for calculation [4].Hence, these two approaches may limit the scaling of the thermal responses of microbial respiration to warming.Over the past decades, many feasible alternative mathematical models have been used to improve theoretical understanding of thermal adaptation.For example, the square-root model developed by Ratkowsky et al. (Ref. 5) could effectively describe the direct effect of temperature on microbial respiration as well as the thermal adaptation of microorganisms.Subsequently, Lloyd and Taylor (Ref. 1) introduced a parameter into the Arrhenius function to modify the activation energy with temperatures, which has greatly improved the model's prediction.However, the square-root and Lloyd-functions cannot predict the decline in soil respiration above optimum temperatures.In this case, the macromolecular rate theory (MMRT) model, which considers mechanisms that may cause enzymatically driven nonlinearities with temperature, could better predict molecular responses to temperature [6][7][8].Which of these different thermal response models should be selected, and how microbial adaptation would be included as their parameterization remain open questions.
We outline two criteria for evaluating model selection approaches: (1) giving a plausible result thermodynamically speaking and (2) providing a statistically superior fit [9].We estimated the parameters of MMRT, square-root and Lloyd-function models for 11 sampling sites at three incubation temperatures with or without substrate addition, respectively (Supplementary Tables S6-S8).Furthermore, linear mixed-effect models include the most important drivers of microbial respiration to quantify thermal adaptation [10,11].
We found that the MMRT model predicted thermodynamically plausible results for only ten out of 22 combinations (11 sampling sites × 2 substrate treatments, Supplementary Table S6).The square-root model predicted that the parameter a × Tmin had statistically significant effects for only twelve out of 22 combinations, where Tmin allowed for a direct descriptor of the thermal adaptation of microbial respiration (Supplementary Table S7).However, the Lloyd-function predicted statistically significant effects of β for 20 out of 22 combinations, where β was a parameter related to temperature sensitivity of microorganisms (Supplementary Table S8).We also found that results from the above three model approaches had similar R 2 regardless of the sampling sites and substrate treatment combinations.Thus, the Lloyd-function was selected for subsequent analyses due to its successful fits to data under substrate excess and depletion.) at the temperature T (K), T0 is reference temperature (K), kB is Boltzman's constant (i.e., 1.3806 × 10 -26 kJ K -1 ), h is Planck's constant (i.e., 6.6261 × 10 -37 kJ s), R is the universal gas constant (i.e., 8.314 × 10 -3 kJ mol -1 K -1 ), ∆H is the change in enthalpy (kJ mol -1 ), ∆S is the change in entropy between the enzyme-substrate complex and the enzyme bound to the transition state at T0 (kJ mol -1 K -1 ), ∆Cp is the change in the heat capacity of the enzyme (kJ mol -1 K -1 ).Topt corresponds to the temperature at maximum reaction rate (℃), Tmax corresponds to the temperature where the rate of change is greatest (℃).We took the first and second derivative of MMRT to calculate Topt and Tmax, respectively.The T0 value was set to approximately 10 ℃ below average temperature at the maximum rate.Significant (P < 0.05) parameters are shown in bold.The thermodynamically unreasonable results of the MMRT models were presented as ∆Cp > 0 or Topt > 110 ℃. ) measured at the temperature T (℃).Tmin is the minimum temperature for microbial respiration (℃), and a is a slope parameter without any direct biological meaning, but related to the absolute microbial respiration rate.Significant (P < 0.05) parameters are shown in bold.
Fig. S1.Relationships between measured microbial respiration and mean annual temperature (MAT) at three incubation temperatures (T) without (a, c and e) and with substrate addition (b, d and f).(a) and (b) for the dataset from this study, (c) and (d) for the dataset for the dataset from Bradford et al. (Ref.12), (e) and (f) for the dataset from Dacal et al. (Ref.13).

Fig. S1 .
Fig. S1.Relationships between measured microbial respiration and mean annual temperature (MAT) at three incubation temperatures (T) without (a, c and e) and with substrate addition (b, d and f).(a) and (b) for the dataset from this study, (c) and (d) for the dataset for the dataset from Bradford et al. (Ref.12), (e) and (f) for the dataset from Dacal et al. (Ref.13).

Table S6 .
Parameters and R 2 values of the Macromolecular Rate Theory (MMRT) model.

Table S7 .
Parameters and R 2 values of the square-root model.

Table S8 .
Parameters and R 2 values of the Lloyd function.

Table S9 .
Standardized coefficients (mean ± s.d.), significance and R 2 values of predictive models used to assess the effect of temperature and pedoclimatic conditions on soil microbial respiration for datasets in Bradford et al. (Ref.12) and Dacal et al. 13ef.13).

Table S2 .
Unstandardized coefficients (mean ± s.d.), significance and R 2 values of predictive models used to assess the effect of temperature and pedoclimatic conditions on soil microbial respiration without substrate addition.

Table S3 .
Unstandardized coefficients (mean ± s.d.), significance and R 2 values of predictive models used to assess the effect of temperature and pedoclimatic conditions on soil microbial respiration with substrate addition.

Table S4 .
Standardized coefficients (mean ± s.d.), significance and R 2 values of predictive models used to assess the effect of temperature and pedoclimatic conditions on soil microbial respiration without substrate addition.

Table S5 .
Standardized coefficients (mean ± s.d.), significance and R 2 values of predictive models used to assess the effect of temperature and pedoclimatic conditions on soil microbial respiration with substrate addition.

Table S7 .
Parameters and R 2 values of the square-root model [Ref.5].

Table S9 .
Standardized coefficients (mean ± s.d.), significance and R 2 values of predictive models used to assess the effect of temperature and pedoclimatic conditions on soil microbial respiration for datasets in Bradford et al. (Ref.12) and Dacal et al.