Philippa Kaur

To the Editor — Araújo et al. have published a response to our piece ‘Species distribution models are inappropriate for COVID-19’1 entitled ‘Ecological and epidemiological models are both useful for SARS-CoV-2’2, in which they defend the idea that ecological models are likely to identify the signature of climate drivers in the R0 of COVID-19 transmission.

Nevertheless, we are disappointed to see no attempt to provide any evidence supporting such a perspective. Araújo et al. state that “the point made by Carlson et al. was that top-down correlative models are inappropriate, whereas bottom-up epidemiological models are fine.”2 This framing moves the goalposts and fully misrepresents our piece. We wrote that one highly specialized correlative tool of many (species distribution modelling) is inappropriate for one specific use case (forecasting a directly transmitted virus), with the aim of preventing incorrect work from being published and negatively impacting policy. We stand by that warning, as no new evidence about SARS-CoV-2 changes the limitations we identified.

Unfortunately, the authors’ response includes no explicit discussion of species distribution models, any actual evidence of a climate–transmission link for SARS-CoV-2, or any direct engagement with the microbiological evidence previously outlined. Instead, the authors have proposed a number of new immunological and ecological hypotheses about how climate could drive COVID-19 transmission, some with tenuous mechanisms not currently supported by medical science (for example, perhaps climate creates geographic differences in innate immune responses to a novel pathogen, or changes the duration of infection?). None are testable by broad, correlative ecological methods; although COVID-19 seems to have spread globally unencumbered by climate3, ecological modelling efforts that continue to try and dig up a climate ‘signal’ (heavily confounded by testing, reporting and outbreak timing) will rely on and further perpetuate these unsubstantiated claims.

At such a fragile moment for scientific accuracy and transparency, we are disappointed to see ecologists meet virological data with speculation that could easily gain a life of its own and inform sensitive policy decisions4. In their response, the authors explain that ecologists and epidemiologists should work in tandem, drawing on different lines of evidence and reasoning to form opinions that can best guide policy. As a team doing exactly that, including several experts on species distribution modelling and an eco-epidemiologist working on the COVID-19 response, we suggest that they stop speculating and start listening.

References

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Affiliations

Center for Global Health Science and Security, Georgetown University Medical Center, Washington, DC, USA
Colin J. Carlson

Norwegian Institute for Nature Research, Bergen, Norway
Joseph D. Chipperfield

Department of Ecology & Multidisciplinary Institute for Environment Studies “Ramon Margalef”, University of Alicante, Alicante, Spain
Blas M. Benito

Department of Biological Sciences, University of Bergen and Bjerknes Centre for Climate Research, Bergen, Norway
Richard J. Telford

Department of Mathematical Sciences and Centre for Biodiversity Dynamics, Norwegian University of Science and Technology, Trondheim, Norway
Robert B. O’Hara

Authors
Colin J. Carlson

Joseph D. Chipperfield

Blas M. Benito

Richard J. Telford

Robert B. O’Hara

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Correspondence to Colin J. Carlson.

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Carlson, C.J., Chipperfield, J.D., Benito, B.M. et al. Don’t gamble the COVID-19 response on ecological hypotheses. Nat Ecol Evol (2020). https://doi.org/10.1038/s41559-020-1279-2
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Global cement cycle in 2014
Figure 1 illustrates the 2014 global cement cycle and the associated net CO2 emissions balance (see “Methods”). Driven by the expansion and turnover of in-use stocks, 4.2 Gt of cement and 0.2 Gt of cement kiln dust (CKD) were produced in 2014. Cement stocks in 2014 amounts to ~75 Gt in total, nearly equally split between residential, non-residential, and civil engineering sectors with ~25 Gt each. The longevity of cement stocks means that only 0.5 Gt of demolition waste was generated in 2014. The challenges faced in recycling cement-based products lead to nearly all (99.1%) demolition waste being buried in landfills, or as part of backfills and aggregates in road base (see Supplementary Table 1). We calculate that the global cement cycle gave rise to 3.0 Gt of CO2 emissions and 0.6 Gt of CO2 uptake in 2014, offering a net balance of 2.4 Gt CO2 emissions. Of the total CO2 emissions released from cement production and upstream processes in 2014, 58.4% were released from carbonate calcination, 32.9% from fuel combustion, and 8.6% from indirect emissions for electricity generation. Our result indicates that most of the CO2 uptake (~80%) in 2014 occurred in buildings and infrastructures (in-use stocks), with CKD, construction waste, and demolition waste, together, contributing only ~20% to the total CO2 uptake.
Fig. 1: Global cement cycle in 2014.

The term cement most commonly refers to hydraulic (chiefly Portland) cement56. All stocks and flows of cement-related materials are herein expressed in un-hydrated cement equivalent and excluding inert materials that are used as aggregate in concrete and mortar. Percentages may not add up to 100% due to rounding. RES residential buildings, NONR non-residential buildings, CIV civil engineering, CKD cement kiln dust.

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Decarbonization storylines and scenario narratives
To understand how the cycle depicted in Fig. 1 could develop in the future, we used a top-down stock-flow approach driven by data on cement production, trade, sectoral use, and lifetime1, to estimate the historical and contemporary cement stocks. We observed that the per capita cement stocks in all ten regions have increased since 1930 (see Supplementary Figs. 1–10). Global average cement stocks per capita reached 10.2 tonnes per capita in 2014, with industrialized and transitioning regions ranging from 12.7 to 23.7 tonnes per capita, developing regions ranging from 2.7 to 7.5 tonnes per capita, and several mature economies approaching 35 tonnes per capita. However, regional cement stocks are not equally distributed across sectors. Post-industrial regions (especially the Commonwealth of Independent States; CIS) typically have higher levels of per capita cement stocks in the civil engineering sector. In contrast, China has a lower level of per capita cement stocks in the civil engineering sector, but a considerably higher level in buildings. We speculated that these variations could be explained by multiple factors, such as the development stage, patterns of urban expansion, architectural specification, as well as availability and choice of construction materials1. Earlier studies have shown a saturation phenomenon for per capita in-use stock development of bulk materials, such as iron25,26 and copper27 in industrialized countries, but not for aluminum, due to its relatively short history of use28. Likewise, the development patterns of per capita cement stocks generally comply with an S-shaped curve, and saturation is evident in several highly developed countries1. The saturation of per capita cement stocks implies that the growth rate of buildings and infrastructures in use (where cement stocks reside) will decrease marginally and eventually reach a plateau, as services provided by cement stocks become saturated17,29,30,31,32. Furthermore, as evidenced in several highly developed economies1, decreasing trends of per capita cement stocks have become manifest, reflecting that material efficiency strategies have come to play a significant role in these economies. We therefore envisage three scenario storylines with varying levels of cement stocks similar to the Resource Efficiency-Climate Change Nexus (RECC) scenario modeling framework33, which is built upon the Shared Socioeconomic Pathway (SSP) scenarios and the Low Energy Demand (LED) scenario34; the first scenario storyline (S1–3) is characterized by a low cement stock level, the second scenario storyline (S4–6) by a medium cement stock level, and the third scenario storyline (S7–9) by a high cement stock level. The saturation level of per capita cement stocks is regarded as a tangible indicator for various human needs in mature societies, including shelter, transport networks, factories, offices, as well as commercial, educational, healthcare, and governmental facilities. It is the level of service provided by per capita cement stocks that are expected to saturate, not just the quantity of material involved; the two are linked by the material intensity of the in-use product stocks. Concurrent with the development of cement stocks, demand for cement will slow down, decline, and ultimately stabilize, given that the dynamics of cement stocks, to a large degree, determine the demolition rate and reconstruction rate for cement-related materials, according to the mass-balance principle21,35.
In light of the observed historical patterns of cement stocks and the essential role of in-use stock dynamics to the cement cycle, we simulate the future cement cycle in ten regions using a stock-driven approach17 based on the historical patterns of per capita cement stocks identified in our previous work1, three storyline-consistent target values of per capita cement stocks (i.e., saturation levels), and a moderately growing population obtained from the medium scenario of United Nations World Population Prospects36. We deem the level of in-use cement stocks as an explicit physical representation of service provision to society, thereby constructing nine stock-driven scenarios (created from three saturation levels and three saturation times) to explore the evolution of cement-related materials until 2100 due to the longevity of buildings and infrastructures. Our scenarios build upon three key assumptions: first, per capita cement stocks in the ten regions follow a development path that is consistent with S-shaped curves or inverted S-shaped curves toward a global convergence of per capita cement stocks, and therefore, regions or end-use sectors that have a per capita cement stock below the saturation level will see a continuing growth, while those with a per capita cement stock over the saturation level will see a decline (see Supplementary Fig. 11); second, the formulated pathways of per capita cement stocks do not entail abrupt changes in resulting cement demand, and therefore, the development pathways of per capita cement stocks in a few regions or end-use sectors are adjusted to smoothen the trends in cement demand; third, technological development for optimizing cement use in buildings and infrastructure proceeds, but without fundamental breakthroughs (e.g., new materials that replace cement to a full extent), because cement is a ubiquitous, relatively cheap building material of good workability.
In all of the nine scenarios, we parameterize two boundary conditions, saturation level and saturation time, to reflect the varying patterns of cement stocks and varying levels of future demand-side material efficiency in different regions. By considering a range of saturation levels, we cover both a range of service levels provided by the in-use cement stocks and a range of material efficiencies in their delivery. The saturation time reflects the speed of stock growth (parameterized by the time when the per capita cement stocks reach 98% of the saturation level). Given the regional heterogeneity of socioeconomic and geographic circumstances, we set varying saturation levels and times for different regions to fit the historical development of per capita cement stocks (see Supplementary Table 2). A modified Gompertz model is used for simulating the growth curves of per capita stocks based on assumed saturation levels and times (see Supplementary Note 2.2).
Under the nine stock-driven scenarios, we further characterize the sponge effect and its resulting net CO2 emissions balance for the cement cycle and explore future decarbonization pathways. This includes both demand-side mitigation options to increase material efficiency, reflected in the chosen saturation levels for in-use stocks, and supply-side mitigation options, represented by changes in the CO2 emissions intensity of cement production. We extract five supply-side CO2 emissions mitigation measures from the global cement technology roadmap4,9 (see Table 1): thermal efficiency (E-M1), electric efficiency (E-M2), alternative fuel (E-M3), clinker substitution (E-M4), and carbon capture and storage (E-M5). Each measure represents an effort beyond what would occur under a no-action scenario; therefore, the remaining CO2 balance is quantified by subtracting the CO2 emissions reduction potentials of the five measures (when they are rolled out simultaneously) from the no-action scenario. The CO2 uptake is explicitly simulated in a physicochemical carbonation model5 by applying Fick’s diffusion law (see “Methods”).
Table 1 Supply-side mitigation measures and their implementation.
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Decarbonization pathways of global cement cycle
The gradual rise and then saturation of in-use stocks lead to cyclical variations in global cement demand over the next decades (see Supplementary Figs. 12–22), while the global demolition waste generation continues to rise due to the delay between demand and demolition caused by the longevity of in-use cement stocks (see Supplementary Figs. 23–33). Our estimates of cement demand in the year 2050 (4.3–6.7 Gt yr−1) are more wide-ranging than those estimated by the International Energy Agency technology roadmap for the global cement industry (4.7–5.1 Gt yr−1)2,9.
Figure 2a shows CO2 emissions under the no-action scenario and the effects of the mitigation measures. In 2050, the no-action CO2 emissions under low-, medium-, and high-saturation levels reach 3.0–3.4 Gt yr−1, 3.4–4.0 Gt yr−1, and 3.8–4.7 Gt yr−1, respectively. In parallel, the CO2 uptake (effects of U-M4 subtracted, the same hereinafter) rises to 0.9–1.0 Gt yr−1 (low-saturation levels), 1.0–1.1 Gt yr−1 (medium-saturation levels), and 1.1–1.3 Gt yr−1 (high-saturation levels) by 2050. The no-action CO2 emissions balance (when CO2 uptake is considered) in 2050 increases to 2.1–2.3 Gt yr−1 (low-saturation levels), 2.4–2.9 Gt yr−1 (medium-saturation levels), and 2.7–3.4 Gt yr−1 (high-saturation levels), respectively. By 2100, the balance is at slightly lower levels, ranging from 1.5 Gt yr−1 to 3.1 Gt yr−1.
Fig. 2: Decarbonization pathways and supply-side mitigation measures of the global cement cycle across the nine stock dynamic scenarios.

a The no-action CO2 emissions and uptake pathways from 2015 to 2100 coupled with the results of the five supply-side mitigation measures. b The 2015–2100 accumulated mitigation potential by the five supply-side mitigation measures and uptake. CO2 emissions (1.5 °C): the red line represents the calculated CO2 emissions pathway that is consistent with the 1.5 °C budgets (a 66.7% probability) in the IPCC’s special report (see “Methods”). CO2 balance (no-action): the black line represents the no-action CO2 balance, that is, no-action CO2 emissions minus no-action CO2 uptake. Net CO2 balance: the brown line represents the net CO2 balance when the five supply-side mitigation measures are implemented. U-M4: clinker substitution marginally reduces CO2 uptake in cement-related materials. Acc. accumulated, Low low stock saturation level, Medium medium stock saturation level, High high stock saturation level, Slow slow stock saturation time, Moderate moderate stock saturation time, Fast fast stock saturation time.

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By implementing a full portfolio of mitigation measures, CO2 uptake begins to overtake the remaining CO2 emissions from cement production by the late 2090s, bending the net CO2 emissions balance below zero (Fig. 2a). However, in the medium term, the 2050 net CO2 emissions balance of the global cement cycle will reach 1.0–1.2 Gt yr−1 (low-saturation levels), 1.2–1.5 Gt yr−1 (medium-saturation levels), and 1.4–1.8 Gt yr−1 (high-saturation levels), respectively. Of the nine stock-driven scenarios, none generates a trajectory of net CO2 emissions balance that follows, or is below, the 1.5 °C-consistent pathway, meaning excessive CO2 is emitted along all trajectories. If the cement industry is to contribute to the 1.5 °C limit in proportion with other industrial sectors, achieving the CO2 emissions reduction target by employing mitigation measures in the production stage alone is extremely challenging, because net CO2 emissions balance largely hinges on in-use stock dynamics, and concomitant demand and demolition.
Long-term accounting for CO2 uptake along the cement cycle, which could be regarded as passive CO2 sequestration, greatly changes the net CO2 emissions balance of the global cement cycle. Across the stock-driven scenarios, the cumulative CO2 uptake from 2015 to 2100 amounts to 81.1–117.2 Gt (Fig. 2b). These values correspond to roughly 30% of the no-action CO2 emissions arising from the global cement cycle over the same period. All decarbonization pathways are characterized by widespread deployment of CCS technologies (E-M5) in the production stage. From 2015 to 2100, cumulative CO2 emissions mitigated by CCS technologies, which could be regarded as active CO2 sequestration, are 56.7–94.2 Gt, accounting for ~25% of no-action CO2 emissions from cement production (Fig. 2b). We therefore conclude that deep decarbonization of the global cement cycle calls for both passive CO2 sequestration and active CO2 sequestration, but also that these measures are likely not enough to reach the 1.5 °C climate goal—more innovative or drastic approaches are needed.
Regional disparities of decarbonization potential
Figure 3 shows that the regional patterns of the sponge effect shift along with the stock dynamics and population trends, resulting in varying cumulative no-action CO2 emissions and mitigation strategies. The population boom and gradual rise of in-use stocks are major factors that drive CO2 emissions in emerging regions, as massive improvements in the provision of shelters and infrastructures in these regions take place. For example, Africa’s no-action cumulative CO2 emissions from 2015 to 2100 are 53.9–108.5 Gt. Although China’s per capita cement stocks had already peaked in 2014, its cumulative no-action CO2 emissions during 2015–2100 will still reach 61.7–75.6 Gt, due to the shorter lifetimes of in-use cement stocks in China. Meanwhile, the cumulative no-action CO2 emissions that will occur in industrialized regions (NA, EU, CIS, and DAO regions altogether) from 2015 to 2100 are lower, ranging from 22.0 to 47.9 Gt. Compared with other regions, the active CO2 sequestration (E-M5) plays a more dominant role in emerging regions (e.g., ~30% in both Africa and India). This indicates that CCS implementation should take place in the emerging regions where new demand for cement and production facilities increases rapidly. However, CCS is still at the demonstration stage, and their large-scale market deployment is hindered by high estimated costs37, which is a significant issue for investment constrained emerging economies, suggesting that effective policies, intensified research to reduce CCS costs, and/or international financial support for CCS in cement production are urgently needed. Active CO2 sequestration by CCS can be further utilized (carbon capture and utilization; CCU) as a feedstock to produce chemicals and fuels; however, the development of CCU technologies is still in its infancy and limited to the laboratory scale37.
Fig. 3: Regional patterns of cumulative non-action CO2 emissions (2015–2100) and relative contribution of the five supply-side CO2 emissions mitigation measures, CO2 uptake, and CO2 balance.

The five supply-side measures refer to those listed in Table 1. The red-yellow-green palette represents the 2015–2100 cumulative (no-action) CO2 emissions. The column chart represents the relative contribution of the five supply-side CO2 emissions mitigation measures, CO2 uptake, and the remaining CO2 balance. NA North America, LAC Latin America & Caribbean, EU Europe, CIS Commonwealth of Independent States, AF Africa, ME Middle East, IN India, CN China, DAO Developed Asia & Oceania, DA Developing Asia. S1: low–fast; S2: low–moderate; S3: low–slow; S4: medium–fast; S5: medium–moderate; S6: medium–slow; S7: high–fast; S8: high–moderate; S9: high–slow.

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Experimental design
We measured the responses of plant community biomass, nitrogen mineralization rate, soil decomposition potential and litter decomposability, to the three treatments nitrogen (N) addition and above- and belowground insect herbivory in a fully factorial block experiment. Each treatment was replicated once within each block, giving a total of 64 experimental enclosed one by one m plots (Fig. 1). The experiment was established in the spring of 2013 in an organic agricultural field (59° 44′ 27.9″ N, 17° 41′ 02.9″ E) near Uppsala, Sweden, with sandy soil, low soil carbon content and a total N content of 0.08%. In each of the plots, we established plant communities of nine common grassland species: four grasses (Agrostis capillaris L., Dactylis glomerata L., Festuca rubra L., Lolium perenne L.), three non-leguminous forbs (Achillea millefolium L., Leucanthemum vulgare Lam., Plantago lanceolata L.), and two leguminous forbs (Lotus corniculatus L., Trifolium pratense L.). The plant communities were established in late May 2013 from seedlings from seeds (Herbiseed, Twyford, United Kingdom) that were sown in the greenhouse 6–8 weeks prior to planting. All plant communities had the same species composition and all species were planted at equal starting densities in a 1 × 1 m plot of soil. Plants were spaced 10 cm apart in a 9 × 9 grid formation. The position of individual plants within enclosures was randomized for each enclosure, i.e. the planting scheme was not the same in any two enclosures. We manually weeded all enclosures (i.e. removed all plants emerging from the soil’s seed bank) on one occasion during the month that followed planting. In addition, we removed all weeds that we encountered during the subsequent harvests (see “Plant community biomass” section).
Figure 1

Part of the enclosures (sized 1 × 1 × 2 m) used in the experiment at the initiation of the experiment in 2013 (a), and the plat community inside one of the enclosures in 2015 (b).

Full size image

The plant communities were enclosed above ground by a mesh net cage (mesh size 0.2 × 0.4 mm, anti-aphid net 20/12, Artes Politecnica, Schio, Italy) of 2 m height, and below ground, by a sheet metal frame of 0.5 m depth with a mesh net bottom. The net had a vertical zipper on one side that allowed entry to the cage. Prior to planting, the base frame was re-filled with soil from the field to a depth of 0.5 m. By refilling the enclosures with unsterilized soil we accepted an uncontrolled level of background herbivory, from insects dwelling in or hatching from of the soil. We considered this natural background herbivory to be preferable to the unrealistic conditions of a fully sterile soil.
N additions
The N treatment corresponded to 40 kg N ha−1 year−1, which is in the upper range of current N deposition levels for Western European grasslands2, were applied at three occasions,early July 2013, late June 2014, and early July 2015. We applied the N by dissolving ammonium nitrate in 10 l that was watered in the enclosure. Unfertilized enclosures received the same amount of water. No further watering of the plots was carried out.
Herbivory
The aboveground herbivory treatment consisted of adults of the grasshopper Chorthippus albomarginatus (De Geer), added in mid-July 2013 at a density of 10 individuals per enclosure (5 females and 5 males) and allowed to reproduce in the enclosures in subsequent years. We chose the study species as it is one of the most common grasshoppers in the area, and all specimens were collected within a radius of approximately 5 km from the experimental site. For the belowground herbivory treatment, we added wireworms, a common generalist root herbivores in European grasslands, which are the larval stage of the click beetle genus Agriotes spp, in mid-July 2013 at a density of 10 individuals per cage. In July 2014, we estimated grasshopper density by counting the individuals in each of the enclosures. Statistical analysis showed that differences in emerged number of nymphs among enclosures were unrelated to N addition (F1,21 = 0.095, p = 0.76) and belowground herbivory (F1,21 = 0.24, p = 0.63). Based on the counting, we adjusted grasshopper densities with in each treatment combination. We did this systematically, by dividing the enclosures into quartiles, based on grasshopper density. We did not adjust densities from plots ending up within the two mid-quartiles (19–31 grasshoppers per enclosure), but we transferred grasshoppers from enclosures within the highest quartile to those within the lowest quartile, to give 25 individuals per enclosure. At the time of adjusting the grasshopper densities, we also added 10 extra individuals of the wireworms to each enclosure assigned to this treatment. In 2015, we made no adjustments of herbivore densities. However, we assessed grasshopper densities by visual counting, and grasshopper densities were unaffected by N (F1,21 = 3.2; p = 0.09) and belowground herbivory (F1,21 = 0.7; p = 0.4).
Plant community biomass
Aboveground plant community biomass, henceforth denoted as total shoot biomass, was measured in mid-September 2013, 2014 and 2015, by harvesting the plants. The timing of the harvests corresponded to the peak of standing biomass in the communities. Because all plants renew their aboveground biomass annually, the harvested biomass approximates the annual aboveground production. At harvest, we cut all aboveground plants at 5 cm height above the soil surface. All collected plant material was brought to the lab and oven-dried at 65 °C for 48 h. To simulate the management of a semi-natural grassland, we conducted an additional harvest in mid-June. This harvest was, however, not repeated in 2015 as the plants were left so they could go to seed for a parallel study on plant reproduction.
Belowground plant community biomass, henceforth denoted as total root biomass, was assessed in September 2015 at the end of the 3-year experiment. We collected five soil cores from each enclosure, to a depth of 15 cm, using a cylindrical soil corer (ϕ10 cm). We pooled the five cores into one composite sample (volume of 5.9 dm3). The samples were kept refrigerated at 4 °C for 3 months before sieving, first with a 5 mm mesh and then a 2 mm mesh sieve. Prior to the second sieving the samples were left to dry for 3 days to facilitate the separation of soil and roots. Finally, the root samples were oven-dried at 65 °C for 48 h, and thereafter weighed.
Decomposition potential of the soil
To assess decomposition potential of the soil under the different herbivory and nitrogen treatments, we used the tea bag method that produces standardized decomposition rate estimates26. We used two types of tea, Lipton Rooibos and Lipton Green Tea (Unilever Belgium, Brussels, Belgium). In in mid-June 2015, we buried (depth of c. 8 cm) two bags of rooibos tea (recalcitrant) and two bags of green tea (easily degradable) in the soil of each enclosure. All tea bags were weighed before being buried. After 90 days, we dug up, dried at 70 °C for 48 h, and re-weighed the bags. The mass loss of the tea bag was used as an estimate of decomposition potential of the soil.
Decomposition of plant litter
To assess treatment effects on the decomposition of plant litter produced in the enclosures, we used dried plant material from the September 2014 harvest. The decomposition was measured using plant litter harvested from the same enclosure. The material was stored under cool, dry conditions from the harvest in September 2014 until May 2015, when litter for P. lanceolata, T. pratense, and D. glomerata was extracted for litterbag construction. We used these species as they based on the 2014 biomass harvest were dominant species, and as they represent three functional groups, namely grasses (D. glomerata), non-leguminous forbs (P. lanceolata) and leguminous forbs (T. pratense).
The litterbags were manufactured using polyamide mesh (Sefar Nitex 03—50/37, Sintab, Oxie, Sweden) with a pore size of 50 µm, which allows entry of bacteria, fungi and certain microfauna only. Approximately 1 g of dry litter of P. lanceolata, T. pratense, or D. glomerata was enclosed in a right triangular bag with 14 cm sides. After sealing and weighing we placed the bags (one for each plant species), on the soil surface in the enclosure from which the litter originated. We put out the litterbags in mid-June 2015, and collected them after 90 days, when we after dried at 70 °C for 48 h and weighed them. Litter mass loss over the experimental period was then used as an estimate of plant litter decomposability.
Nitrogen mineralization rate
We assessed the amount of inorganic N mineralized over the growing season in the enclosures with the buried bag technique26,27. A soil sample of about 300 g was taken from each enclosure in mid-June 2015 by extracting six evenly spaced cores (ϕ25 mm, 10 cm deep) and mixing them into one composite sample. We spitted the composite sample into two samples and put them in polyethylene bags. One bag was buried c. 8 cm below the soil surface in the middle of the enclosure, and the other was brought back to the lab for storage in a freezer (− 20 °C) until analysis. After 90 days, we recollected the buried bags, brought them to the lab and stored them in a freezer until further analyses. These samples were later analyzed for inorganic N content (g/kg of NO3/NO2 and NH4 respectively) using 2 M KCl extraction (Agrilab AB, Uppsala, Sweden). We estimate soil net N mineralization produced over the 90-day period by was subtracting the amount of nitrate and ammonium in the control bags from that in the buried bags.
Statistical analyses
We used linear mixed effects models28 to test how primary production, soil decomposition potential, N mineralization, and litter decomposability responded to N fertilization and above- and belowground herbivory.
Total shoot biomass was analyzed as a dependent variable of the fixed factors N and above- and belowground herbivory, including all possible interactions between the three factors. Year was included as a fixed factor, to account for variation among the harvests in the different years. Enclosure was nested within block in the random structure of the model. To account for autocorrelation of repeated measures within enclosures, we added a first-order autoregressive correlation structure to the model. Total root biomass was analysed with N and above- and belowground herbivory as fixed factors, with all possible interactions among the factors, and block included as a random factor. We also tested for treatment effects on the ratio between root and shoot production in 2015. Finally, we explored whether herbivory generated effects on aboveground shoot biomass were dependent on differences in soil decomposability (mass loss of read tea) and nitrate production by including these variables as covariates in the analyses.
In the analysis of mass loss of the red and green tea, we first calculated the mean mass loss for each tea type (i.e. the mean for the two bags of each type) in each enclosure. The mean mass losses of each tea type and the litter mass losses of D. glomerata, P. lanceolata and T. pratense were then analyzed in linear mixed effects models with block as random factor. In each model, N and above- and belowground herbivory were included as fixed factors, including all possible interactions between the three. For T. pratense, two enclosures were excluded as there was no T. pratense litter from 2014 to use (i.e. the species had gone extinct in these enclosures). A third enclosure was excluded from the analysis, as its amount of T. pratense litter from 2014 was only 0.1 g and skewed the analysis. All analyses were performed in R version 3.2.3 (2015). More

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Spatial distribution of SOC content
Interpolation parameters were obtained based on a geostatistical semi-variance function method, and results of the parameters obtained by Kriging to get a better overall model. The SOC content in Daxing’anling Mountain is transformed from discrete point information to continuous surface information, and the spatial distribution characteristics of SOC content could then be further analyzed. Through this approach, we can use fewer sampling points to predict spatial information of soil properties in the entire Daxing’anling Mountain area, as shown in Fig. 2. Results suggest that prediction accuracy is high. It can be seen in the map of the spatial distribution that SOC content is heterogeneous, lower in the northwest and southeast. SOC content generally ranges from ~ 40–70 g/kg.
Figure 2

Spatial distribution of SOC content in the Daxing’anling Mountain range. Select the ordinary Kriging model and perform Kriging interpolation on the sampling point data to obtain the spatial distribution of SOC content. The figure was generated by ArcGIS 10.1.

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Principal component analysis of SOC and auxiliary environmental variables
To determine the contributions of environmental auxiliary variables to SOC, correlations between SOC and environmental auxiliary variables were analyzed. Auxiliary environmental variables, their abbreviations and results are displayed in Table 1, showing a range of positive and negative correlation coefficients.
Table 1 SOC content correlation with environmental variables in the Daxing’anling Mountain range.
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The SOC content in Daxing’an Mountain is taken as the dependent variable, and ten influential factors such as quantitative normalized difference vegetation index, integrated land use index, slope, aspect, elevation, profile curvature, plan curvature, topographic wetness index, convergence of confluence, and surface temperature are taken as independent variable, using X1 X2……X10 named. Based on ten independent variables and principal component analysis, the eigenvalues, contribution rates and cumulative contribution rates of the ten environmental auxiliary factors in this paper are obtained, and the main influencing factors of SOC content are analyzed and determined. The results are shown in Table 2.
Table 2 Influence factor eigenvalue and principal component contribution rate.
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The cumulative contribution of the first, second, third, fourth, and fifth principal components is 73.5%. The top five principal components met the requirements of the Kaiser criterion, which suggests strong explanatory power for the SOC variation for Daxing’anling Mountain.
The first principal component is NDVI, whose contribution rate is 20.4%. The second principal component is the land use comprehensive index (18.5%), indicating that the change of soil organic carbon content in Daxing’anling Mountain is related to residential land, roads, rivers, and green space. The third principal component is the slope (14.2%), the fourth principal component is the aspect (10.2%), and the fifth is the elevation (10.2%). Indicating that the topographic changes in Daxing’an Mountain range are correlated with the SOC content and will have a certain influence on it.
Evaluation of the geographically weighted regression Kriging model
Using geographically weighted regression (GWR) and multiple linear regression (MLR) models for analysis, the same auxiliary variables were selected to compare the two models. Bandwidth was set according to the modified Akaike-information criterion18 as shown in Table 3. The R2 value of the GWR model (0.47) is higher than that of the MLR model (0.30), which suggests the GWR model is better in identifying factors influencing SOC spatial distribution. Furthermore, the AICC value of the GWR model is lower than that of the MLR model, suggesting a better model fit18.
Table 3 Diagnostic information of the MLR and GWR residual models for SOC.
Full size table

Five-fold cross-validation was used to verify and evaluate the interpolation accuracy of the geographically weighted regression kriging model (GWRK) and the regression kriging model (RK). Soil sample data were divided randomly into five parts, and then one part was designated as a verification set and was only used for evaluation of model accuracy. The remaining ones were used for spatial interpolation in model formation. The above process was carried out five times to obtain the simulated value of SOC of the data set. The average error and correlation coefficients are used to evaluate and verify the prediction accuracy of each model. Results show that the RMSE value of the GWRK model (3.5) is less than that of the RK model (3.8), suggesting the GWRK model is superior. This also suggests there are many factors to consider when studying the auxiliary variables of spatial distribution characteristics of SOC content, which requires us to consider not only the fitting of environmental auxiliary variables but also additional spatial and structural information.
Factors controlling SOC content spatial distribution
The spatial variation of SOC content, which is related to the environmental auxiliary variables, has predictable geospatial characteristics. Five key indicators (those that loaded high on the first five PCA axes) were identified: normalized vegetation difference index, integrated land use index, slope, aspect, and elevation. These five factors and results of GWRK model fitting were used to estimate the spatial distribution of SOC content and results are shown in Fig. 3. Coefficients of explanatory factors vary with location.
Figure 3

Explanatory variable coefficients in the GWRK model for SOC and spatial distribution of R2. Use the GWRK model to analyze the influencing factors of SOC and obtain the fitting result graph of the GWRK model. (a) NDVI, (b) Integrated land use index, (c) Slope, (d) Aspect, (e) Elevation, (f) R2. All figures were generated by ArcGIS 10.1.

Full size image

The coefficient with the largest absolute value is the main controlling variable in a geographical location19. Compared with the other four environmental explanatory factors, absolute values of NDVI coefficients are highest. The influence of NDVI on the spatial distribution of SOC content decreased from the mideast to the northwest and the southeast. This suggests that the higher the vegetation coverage, the greater the control on the SOC content. The other four environmental auxiliary factors play a more secondary role.
The integrated land use index ranks second in importance to NDVI. Its influence on SOC spatial distribution is reflected in the northeast, northwest, and southeast. In the northeast part of the study area, La is positively correlated with SOC content which suggests vegetation cover will promote the accumulation of SOC. In the northwest and southeast of the study area, the integrated land use index (La) is negatively correlated with SOC.
The slope and aspect have a major influence on the spatial distribution of SOC content in the central and western areas. Some low-slope areas are disturbed by human activities. When the slope increases limiting human activities, the impact of slope on SOC is positively correlated. The sunny slope side is conducive to SOC accumulation. In the western and central areas, the elevation is positively correlated with SOC content. As the altitude increases, the vegetation coverage is higher which will promote the accumulation of SOC. In the eastern areas, the elevation is negatively correlated with SOC because of farming and other factors.
Regions with the best model fits are distributed in the eastern and central parts of the study area, whereas regions with weaker fits are in the northwest. More

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