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These authors contributed equally: Andrew J. Bennett, Adrian C. Paskey, Arnt Ebinger

Department of Pathobiological Sciences, University of Wisconsin-Madison, Madison, WI, USA
Andrew J. Bennett & Tony L. Goldberg

Department of Microbiology and Immunology, Uniformed Services University of the Health Sciences, Bethesda, MD, USA
Adrian C. Paskey & Kimberly A. Bishop-Lilly

Leidos, Reston, VA, USA
Adrian C. Paskey

Genomics and Bioinformatics Department, Biological Defense Research Directorate, Naval Medical Research Center–Frederick, Fort Detrick, Frederick, MD, USA
Adrian C. Paskey & Kimberly A. Bishop-Lilly

Institute of Diagnostic Virology, Friedrich-Loeffler-Institut, Greifswald-Insel Riems, Germany
Arnt Ebinger, Florian Pfaff, Dirk Höper & Martin Beer

State Office for Agriculture, Food Safety and Fisheries, Rostock, Germany
Grit Priemer

Department of Experimental Animal Facilities and Biorisk Management, Friedrich-Loeffler-Institut, Greifswald-Insel Riems, Germany
Angele Breithaupt

Institute of Novel and Emerging Infectious Diseases, Friedrich-Loeffler-Institut, Greifswald-Insel Riems, Germany
Elisa Heuser & Rainer G. Ulrich

German Center for Infection Research (DZIF), Hamburg-Lübeck-Borstel-Insel Riems, Greifswald-Insel Riems, Germany
Elisa Heuser & Rainer G. Ulrich

Integrated Research Facility at Fort Detrick, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Fort Detrick, Frederick, MD, USA
Jens H. Kuhn

Global Health Institute, University of Wisconsin-Madison, Madison, WI, USA
Tony L. Goldberg More

Consistent with best practices for homoscedastic stationary series using small data sets, we used the ADF, PP, KPSS, and DF-GLS tests to confirm model validation (Table 1). Maximum temperature and wind speed were stationary I(0) at a 1% level of significance while other variables were integrated to order one I(1) indicating stationarity at first difference. According to the DF-GLS test, the mean minimum monthly temperature was also stationary I(0). The absence of integration to order two I(2) for any of the variables indicated the suitability of the ARDL approach.
Table 1 Unit root test results of climatic variables for Augmented Dickey–Fuller (ADF), Phillips–Perron (PP), Kwiatkowski, Phillips, Schmidt, Shin (KPSS), and modified Dickey-Fuller generalized least squares (DF-GLS).
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Published studies on fire-climate relationship23,32 generally do not resolve the non-stationarity issue that often arises in time series data that measures climate variables during recent years. Particularly, for explaining the variability of grassland area burned, ignoring the non-stationarity of the series leads to bad specified models that invalidate some of the results and generate high prediction error. In addition, modeling the series as if they were stationary may produce spurious relations that, although perceived as statistically significant, are not real and do not have a correct interpretation33,34. These potential problems generated by non-stationarity provide possible explanations for the large errors we observed in predictions and estimated relationships between area burned and climate. Cointegration is therefore a solution to model the complex dynamics of multivariate ecological time series when some of them are non-stationary. However, even under cointegration, all model parameters, including the lags of independent variables and the error correction term must be correctly specified. Moreover, the error term should not be serially dependent, in order to prevent spurious relationships arising from temporal correlations33,35. Implementation of statistical tests for stationarity of time series, known as unit root tests, is then a fundamental tool for the ecologist to analyze longitudinal data.
The ADF is among the most used and powerful unit root tests under constant variance and if the lag p is correctly selected. Alternatively, PP unit root tests differ mainly in how they address serial correlation and heteroskedasticity in the errors. ADF tests use a parametric autoregression to approximate the autoregressive moving averages structure of the errors in the test regression, whereas the PP tests ignore any serial correlation in the test regression. Unlike ADF tests, PP tests are robust to general forms of heteroskedasticity and do not require a specified lag length for the test regression23. The ADF and PP tests are asymptotically equivalent but may differ substantially in finite samples due to differences in correcting serial correlation in the test regression. In contrast, DF-GLS is a sensitive test that may increase the power of the previous, especially near stationarity and for small samples. Another recommendation, especially for short time series, is the simultaneous use of the KPSS test.
The lag selection criteria of log-likelihood36 (LR), the final prediction error37 (FPE), Akaike information criterion38 (AIC), Schwarz Bayesian criterion39 (SBC), and Hannan-Quinn information criterion40 (HQ) were used to select the optimal lag on all variables prior to testing for cointegration (see Supplementary Information Table S1). All these criteria are based on the minus maximized value of the respective likelihood function including a penalization term that increases with the number of estimated parameters to favor a more parsimonious model. Balancing out these two terms creates a metric that can be used as a model selection criterion. Both SBC and HQ are harsher in the selection than AIC, tending to choose a more parsimonious model. Therefore, we preferentially select the lag(1) as the optimal lag for subsequent model estimation in order to keep the model more compact and interpretable. The final prediction error, Schwarz Bayesian criterion, and Hannan-Quinn information criterion were used to confirm lag(1) as the optimal lag for subsequent model estimation.
The ARDL bounds testing approach is advantageous over traditional cointegration methods because it can examine a mixed order of integrations. We used the F-statistic to test for the null hypothesis of no-level relationship41 (SI Table S2). The bounds test for cointegration that the F-statistic was above both lower [1(0)] and upper [1(1)] bounds critical values, thus, all the models presented reject the null hypothesis of no cointegration. To validate the cointegration test, we further examined the null hypothesis following42 in the light of response surface regressions that report critical p-value approximations43. The p-values strongly rejected the null hypothesis at a 1% significance level, confirming a level relationship in the proposed models.
We implemented a graphical representation of the ARDL model simulation to provide an easily understandable representation of an instantaneous change (i.e., a shock) in one independent variable on the response in posterior observations (Fig. 3). This contrasts with the more elaborate interpretation of estimated coefficients, given their separation in long and short-run effects. For example, the dynamic plot shows that a positive shock (one standard deviation increase) at time t = 10 in wind speed produces a rapid positive short-run increase in burned grassland area.
Figure 3

Plots of the dynamic simulated ARDL model showing the effect of: (a,b) positive and negative one standard deviation change in predicted wind speed on burned grasslands (c,d) positive and negative one standard deviation change in predicted maximum temperature on burned grasslands (e,f) positive and negative one standard deviation change in predicted carbon emission on burned grasslands (g,h) positive and negative one standard deviation change in predicted sunlight on burned grasslands. Dots represent average predicted value while dark blue to light blue lines denote 75, 90 and 95% confidence intervals. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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At t = 15 this effect vanishes and the response value stabilizes thereafter (Fig. 3a). The confidence intervals (blue lines) indicate that the long-run change in burned grassland area is statistically significant using 75% confidence intervals, rather than significant with 90% confidence intervals. In contrast, the resulting plot of negative shock wind speed at time t = 10 decreased the mean response over several periods, resulting in a statistically significant equilibrium shift over four periods (Fig. 3b).
To validate the model, we used diagnostic tests to examine the residual independence (Table 2). The coefficient of determination (R-squared) resulted in a goodness of fit of ~ 78.3%. The diagnostic tests showed that functional misspecification error, first-order serial correlation, heteroskedasticity, and non-normality assumptions are adequately controlled in the estimated model. To corroborate the independence of the residuals, we further employed the recursive cumulative sum (CUSUM) plots to examine the stability of the data series over the sampled period (Fig. 4).
Table 2 Short-run and long-run coefficients of dynamic ARDL.
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Figure 4

Recursive CUSUM plot of (a) maximum temperature, (b) minimum temperature, (c) sunlight, (d) wind speed, (e) vapor pressure deficit, (f) relative humidity, (g) precipitation, (h) carbon emission with 95% confidence bands around the null. For all variables, residuals fall between the limits, validating the ARDL bounds testing model and showing stability of the variances of coefficients over time.

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Simulation and analysis of ARDL dynamics
The grassland ecosystems of Xilingol are characterized by highly dynamic and complex interactions among climate, human settlement patterns, ignition, and vegetation cover. Increased grazing constrains grassland burning leading to an “area burned deficit”. Otherwise, the system is highly responsive to high-speed seasonal winds with low relative humidity, quickly drying fuel, and increasing the potential for extensive grassland fires across the region28.
The long-run and short-run dynamics illustrated in Table 2 show that wind speed represents the dominant variable that extensively increases grassland area burned over both the long and short run. Arithmetically, a 1% increase in mean monthly wind speed increases the burned grassland area by 6.9% (different from zero in a 99% confidence interval (99% CI)) in the long run, and 2.2% (99% CI) in the short run, while holding other variables constant. Besides the direct impact of wind speed on the grassland area burned, it is likely to affect other environmental conditions which also influence fire behavior throughout the Xilingol region. That is, the dynamics of the whole system show complex causal relations that may not be completely explicit on single equation coefficients. For example, our data suggest that wind speed increased following the burning of grasslands (see Supplementary Information Fig. S1). This is consistent with the observation of more extensive burned grasslands over the study period also associated with a dramatic increase in wind speed, an indicator of potential positive feedback not considered in previous studies23. Importantly, high wind speeds were measured in May–August accompanied by the dry land surface conditions and atmospheric aridity, contributing to the influence of burning grasslands feeding back to further promote pyrogenic conditions. Above the threshold, each incremental increase in wind speed on a monthly scale leads to larger burned grasslands across the Xilingol region, overriding other ecological properties, and grassland functions.
Threshold maximum temperature causes uncertainty in ecological change
The maximum temperature is also an important predictor of the increasing extent of burned grasslands. The estimated elasticity of maximum temperature in the long-run indicates that a 1% increase in maximum temperature results in a 2.4% increase in burned grassland extent (99% CI) while holding other variables constant (Table 2). The short-run estimated elasticity of maximum temperature is similar to the long-run response, as a 1% increase in maximum temperature leads to a 2.3% (99% CI) increase in burned grasslands. The results corroborate similar studies13,14,15,22.
The effect of maximum temperature could have more uncertainty because significant relationships between it and burned grasslands occur only when the regional summer maximum temperature exceeded a threshold level, producing a nonlinear relationship22. That is, slight changes in maximum temperature are unlikely to change the ecosystem except when a threshold is crossed, above which effects can be dramatic.
A more meaningful understanding of the effect of maximum temperature on burned grassland areas can be achieved by the use of the simulations of the ARDL model, given that all the relationships among variables are considered. At time t = 10, a small increase in maximum temperature in the short run is not statistically significant, but becomes statistically significant in the long run. Following a negative shock on the temperature at t = 10, the maximum temperature decreases, stabilizing three periods later. The equilibrium temperature shift over the long-run scenario time is statistically significant (95% CI). Discrepancies between burned grassland area and maximum temperature trends in Xilingol may be rooted in urbanization, vegetation type transitions, and/or natural variability to climate response. Additionally, the frequency of human ignitions, along with other anthropogenic disturbances, strongly supported the abrupt impact of maximum temperature overpowering the influence of other environmental variables (SI Fig. S2).
Influence of sunlight on burned grasslands and ecological change
The amount of sunlight exacerbates changes in burned grassland area both directly via the drying effect of radiant heat on fuel and indirectly by influencing other climatic parameters such as temperature and humidity. A 1% increase in sunlight resulted in a 1.98% and 0.24% (99% CI) increase in burned grasslands in the long and short-runs, respectively (Table 2). A negative shock in ln(sunlight) at time (t = 10), insignificantly impacted burned grassland area over the next several periods (Fig. 3). This rapid response is explained by the inclusion of sunlight with a lagged-difference as a dependent variable. Conversely, a positive shock to ln(sunlight) at time (t = 10) increases area burned, which, in turn, shifts the equilibrium and predicts the ecological change just beyond t = 10.
Impacts of burned grasslands to carbon emissions and ecological change
The consequence of carbon emissions from burned grasslands was found to be an important relationship in the long run. Carbon emissions, whether from these fires or other sources in Xilingol may influence the extent of burning in this region by contributing to the forcing of atmospheric temperature. More directly, grassland fires resets succession, potentially increasing ecosystem flammability (SI Fig. S3). The estimated elasticity of carbon emission, in the long run, is 0.91, hence, a 1% increase in carbon emissions is related to a 0.86% increase in burned grasslands (95% CI) in the long run and 0.91% (99% CI) in the short run (Table 2).
The graphical representation of Fig. 3 shows that a change in predicted carbon emissions on burned grasslands and ecological change. The positive shock of carbon emission on burned grasslands and ecological change was associated with a small increase in carbon emission in the short run that is statistically significant at time t = 10. Consistent with other modeled changes, carbon emissions also increase significantly over the predicted value in the long run.
Ecological properties under threshold-governed ecosystems
The mechanism underpinning ecological properties can vary widely with significant uncertainty where threshold relationships among different biophysical processes occur22. The model suggests significant changes in the frequency of climatic variations prior to and in response to, the increased areal extent of burned grasslands (SI Figs. S1–S3). Our results highlight the importance of varying patterns in dominant burned grassland climatic factors (e.g., SI Figs. S1–S3) may also hint at broader implications, suggesting that sudden ecosystem state changes, fire-related or otherwise, may naturally exhibit significant variability across space and time22. The results strongly suggest that area burned increases mainly due to increases in wind speeds during the summer season when characteristically warm temperatures and low humidity facilitate fuel drying and fire spread (see SI Fig. S2) and not due to concurrent changes in anthropogenic activities such as fire suppression practices, land management, and human ignitions. This is not to say that anthropogenic activities are negligible in dictating the modern extent of annually burned grasslands. Rather, increased human ignition is associated with increased burned grassland extent, further confounding a modeling effort based solely on physical ecosystem drivers.
Our long-run analyses suggested that predicted burned grassland extent is insensitive to change in maximum temperature, vapor pressure deficit, precipitation, or relative humidity. These findings contrast with studies that predict increased fire impacts in north-eastern China in response to higher maximum temperature, decreased precipitation, greater vapor pressure deficit, and lower humidity28,44,45,46,47. We posit four potential explanations for this divergence: First, although inter-annual precipitation outside the fire season varies significantly in Xilingol grasslands, little precipitation arrives during the fire season itself. Therefore, inter-annual variation in fire season precipitation is insufficient to impact burned grassland extent. Second, grassland soil field capacity in this region is quite high. Therefore, fire season fuel moisture levels are accordingly unresponsive to precipitation variation. Third, the vast majority of fires in Xilingol originate from human activities23,28. These ignitions, and wind speeds and temperatures coincident with them, rather than fuel conditioning, may explain burned grassland extent. Finally, it is also possible that our statistical approach is insufficiently sensitive to detect a precipitation response under the conditions experienced across the 18-year time series used in this study.
Model estimation
Our empirical strategy for estimating the proposed models follows a series of tests required before the application of the novel dynamic simulations of ARDL27. First, the dynamic ARDL simulations require that the series are integrated below order two, I(2), meaning that the series can be integrated of order one, I(1); integrated of order zero, I(0), or a mixture of both I(1) and I(0). To test the level of integration in the series, we utilized the Augmented Dickey–Fuller (ADF)48, Phillips–Perron (PP)49, Kwiatkowski, Phillips, Schmidt, Shin (KPSS)50, and modified Dickey-Fuller generalized least squares (DF-GLS)51 unit root techniques. While all the unit root techniques are tested based on the null hypothesis of unit root, KPSS is tested based on the null hypothesis of stationarity. Testing for unit root is an important component in the model estimation to prevent a spurious relationship between the series. A simplified version of testing for unit root can be expressed in AR (1) as:

$$y_{t} = a + rho y_{t – 1} + varepsilon_{t} ,quad t = 1 ldots T$$
(1)

where yt is the series to be tested for unit root, εt is the error term. εt is independent and identically distributed, independent of the initial detected value y0, and has a zero-mean if the previous observation of (mathrm{y}) is: (Eleft( {varepsilon_{t} |y_{t – 1} ldots y_{0} } right) = 0). The null hypothesis of the unit root can be tested by H0: ρ = 1 against the alternative H1: ρ  More

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