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\begin{document}

\title{Phosphorus Alleviation of Nitrogen-Suppressed Methane Sink in Global
Grasslands}



\author[1]{Lihua Zhang}%
\author[2]{Fenghui Yuan}%
\author[3]{Junhong Bai}%
\author[4]{Hongtao Duan}%
\author[4]{Xueying Gu}%
\author[4]{Longyu Hou}%
\author[5]{Yao Huang}%
\author[2]{Mingan Yang}%
\author[6]{Jin-Sheng He}%
\author[7]{Zhenhua Zhang}%
\author[4]{Lijun Yu}%
\author[8]{Changchun Song}%
\author[2]{David Lipson}%
\author[2]{Donatella Zona}%
\author[2]{Walter Oechel}%
\author[9]{Ivan Janssens}%
\author[2]{Xiaofeng Xu}%
\affil[1]{Minzu University of China}%
\affil[2]{San Diego State University}%
\affil[3]{Beijing Normal University}%
\affil[4]{Chinese Academy of Sciences}%
\affil[5]{Institute of Botany, Chinese Academy of Sciences}%
\affil[6]{Peking University}%
\affil[7]{Chinese Academy of Sciences, Northwest Institute of Plateau Biology}%
\affil[8]{Chinese Academy of Sciences Changchun Branch}%
\affil[9]{University of Antwerp}%


\vspace{-1em}



  
  \date{May 08, 2024}


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\selectlanguage{english}
\begin{abstract}
Grassland ecosystems account for more than 10\% of the global CH4 sink
in soils. A 4-year field experiment found that addition of P alone did
not affect CH4 uptake and experimental addition of N alone significantly
suppressed CH4 uptake, while concurrent N and P additions suppressed CH4
uptake to a lesser degree. A meta-analysis including 382 data points in
global grasslands corroborated these findings. Global extrapolation with
an empirical modeling approach estimated that contemporary N addition
suppresses CH4 sink in global grassland by 11\% and concurrent N and P
deposition alleviates this suppression by 6\%. The P alleviation of
N-suppressed CH4 sink is primarily attributed to substrate competition,
defined as the competition between ammonium and CH4 for the methane
monooxygenase enzyme. The N and P impacts on CH4 uptake indicate that
projected increases in N and P depositions might substantially affect
CH4 uptake and alter the global CH4 cycle.%
\end{abstract}%



\sloppy




\section*{Introduction}

{\label{introduction}}

Methane (CH\textsubscript{4}) is an important greenhouse gas,
contributing approximately 20\% to the anthropogenic climate warming
(IPCC 2013). Grasslands cover more than 20\% of the Earth's land surface
and typically serve as a net sink for atmospheric
CH\textsubscript{4}(Aronson \& Helliker 2010; Chen \emph{et al.} 2011;
Dijkstra \emph{et al.} 2013). However, this CH\textsubscript{4} sink may
be altered by the growing input of nutrients, particularly nitrogen (N)
(Galloway \emph{et al.} 2008), due to anthropogenic activities. While
previous studies have reported various impacts of N (particularly
NH\textsubscript{4}\textsuperscript{+}) addition on the oxidation of
atmospheric CH\textsubscript{4} in soil (Bollag \& Czlonkowski 1973;
Liebig \emph{et al.} 2008), it has become clear that N addition
typically suppresses this oxidation process, with few exceptions
(Aronson \& Helliker 2010; Liu \emph{et al.} 2017). This N-induced
suppression of CH\textsubscript{4} oxidation has been attributed to two
mechanisms. First, CH\textsubscript{4} and
NH\textsubscript{4}\textsuperscript{+} compete for the same methane
monooxygenase (MMO) enzyme (Gulledge \emph{et al.} 2004), which can
oxidize both CH\textsubscript{4} (to CH\textsubscript{3}OH) and
NH\textsubscript{4}\textsuperscript{+} (to
NO\textsubscript{2}\textsuperscript{-}) due to the similar molecular
structure of CH\textsubscript{4} and
NH\textsubscript{4}\textsuperscript{+} (Dunfield \& Knowles 1995;
Gulledge \emph{et al.} 2004). Second, the intermediates and end products
(primarily nitrite) of methanotrophic
NH\textsubscript{4}\textsuperscript{+} oxidation can be toxic to
methanotrophic bacteria, explaining the inhibition of
CH\textsubscript{4} consumption under increased N inputs (Schnell \&
King 1994; Bodelier \& Laanbroek 2004). According to the substrate
competition mechanism, added
NH\textsubscript{4}\textsuperscript{+}reduces the amount of
CH\textsubscript{4} consumed by methanotrophic bacteria, based on enzyme
kinetics (Davidson \& Schimel 1995; Singh \& Strong 2016), and inhibits
the growth of methanotrophic bacteria as oxidizing
NH\textsubscript{4}\textsuperscript{+} does not support
CO\textsubscript{2} fixation for cell growth (B\selectlanguage{ngerman}édard \& Knowles 1989;
Carlsen \emph{et al.} 1991; Gulledge \& Schimel 1998), further
suppressing the CH\textsubscript{4} oxidation (Gulledge \& Schimel
1998).

While the negative impact of N addition is thus well understood,
phosphorus (P) addition may alter this N-induced suppression on
CH\textsubscript{4} oxidation. In a recent study, P addition alone was
reported to enhance CH\textsubscript{4} oxidation (Veraart \emph{et
al.}2015). Given that P-fertilizer inputs and atmospheric P deposition
are also increasing globally (Mahowald \emph{et al.} 2008; Penuelas
\emph{et al.} 2012; Penuelas \emph{et al.} 2013), investigating P
impacts on CH\textsubscript{4} uptake rate, and especially its
interactions with the increasing N inputs, is important for better
understanding the role that aerobic soils play in the global atmospheric
CH\textsubscript{4}cycle.

Atmospheric deposition and fertilizer inputs of N and P have increased
across the globe since the industrial revolution (Mahowald \emph{et
al.}2008; Blankinship \emph{et al.} 2010; Penuelas \emph{et al.} 2013;
Brahney \emph{et al.} 2015; Wang \emph{et al.} 2017). Increased inputs
of N may reduce the CH\textsubscript{4} sink strength of grassland
ecosystems, with potentially important feedbacks to the global climate
system (Templer \emph{et al.} 2012; Tian \emph{et al.} 2015). The
interactive effect of N + P additions on CH\textsubscript{4} oxidation
has been reported as neutral (Lund \emph{et al.} 2009) or positive
(Zhang \emph{et al.} 2014), and P has been found to alleviate the N
suppression on CH\textsubscript{4} oxidation (Zhang \emph{et al.} 2014);
however, the mechanisms by which P alters the N suppression of
atmospheric CH\textsubscript{4} oxidation in soils remain elusive. We
therefore integrated a 4-year field manipulation experiment, a
meta-analysis, and an empirical modeling approach to investigate the
effects of N + P additions on CH\textsubscript{4} flux in grasslands and
the underlying mechanisms.

\section*{Materials and Methods}

{\label{materials-and-methods}}

\subsection*{Field Experiment}

{\label{field-experiment}}

The field experiment was conducted in Duolun County (42°02'N, 116°70'E,
1324 m a.s.l.), a semiarid temperate steppe in Inner Mongolia, northern
China. The multiple-year mean annual precipitation and mean annual
temperature are approximately 385 mm and 2.1°C, respectively. The
topography is characterized by low foothills at elevations of 1150-1800
m. Soil is Calcis-orthic Aridisol (the US Soil Taxonomy classification),
with 62.75 ± 0.04\% sand, 20.30 ± 0.01\% silt and 16.95 ± 0.01\% clay
(Wu \emph{et al.} 2010). The dominant plant species include \emph{Stipa
krylovii} , \emph{Artimesia frigida} , \emph{Potentilla acaulis}
,\emph{Cleistogenes squarrosa} , \emph{Allium bidentatum}
and\emph{Agropyron cristattum} .

To assess the nitrogen (N) and phosphorus (P) impacts on
CH\textsubscript{4} flux, a block design experiment with different
combinations of N and P additions was established in early 2013 and run
to 2016. A complete random design, with three block replicates, was
adopted to address the high spatial heterogeneity. There were four
experimental treatments (i.e., control (CK), N addition (N), P addition
(P), both N and P additions (N+P)), which were randomly assigned to four
6 m × 6 m plots in each block. Two chambers for greenhouse gas
measurement were set up in each plot. All blocks were separated with a
3-m buffer zone. The N and P were applied twice per month from May to
September during 2013-2016; we sprayed the fertilizer solution to ensure
that the application was evenly distributed in the plots. The dose of N
addition was 100 kg N ha\textsuperscript{-1} y\textsuperscript{-1} as
NH\textsubscript{4}NO\textsubscript{3} solution; this dose was selected
because it meets the N required to sustain the local maximum vegetation
productivity (Bai \emph{et al.} 2010). We monitored the atmospheric N
deposition and estimated it to be 20.4 kg N
ha\textsuperscript{-1}y\textsuperscript{-1} in our experimental site in
2012. The dose of P was 100 kg P ha\textsuperscript{-1}
y\textsuperscript{-1}, equivalent to previous nutrient addition
experiments in grasslands (Phoenix \emph{et al.} 2003). The plots with
both N and P additions received the same amounts of N and P as in the
N-only or P-only addition treatments. Control plots were not fertilized,
but rather watered with the same amount of water as used in the
fertilizer solutions; the water used to dissolve N and P was
approximately 800 ml, which is equivalent to 0.8 mm for a 1
m\textsuperscript{2} plot, a pre-treatment field experiment found that
this small amount of water addition did not cause any significant
changes in water supply, thus unlikely to have altered the ecosystem
functions.

Over the study period, soil and plant properties were measured
(Supplementary Online Materials). Soil samples were collected to a depth
of 10 cm once per year during 2013-2016. Six soil cores were randomly
taken in each plot and mixed completely. The measured soil variables
included ammonium (NH\textsubscript{4}\textsuperscript{+}) and nitrate
(NO\textsubscript{3}\textsuperscript{-}), soil pH, soil organic carbon
(SOC), soil total nitrogen (STN), soil total phosphorus (STP), soil
microbial biomass carbon (MBC) and soil microbial biomass nitrogen
(MBN). It should be noted that no nitrite was detected at our field
site. The measured vegetation variables included aboveground biomass,
plant total carbon (PTC) and total nitrogen (PTN).

\subsection*{\texorpdfstring{Field Measurements of
CH\textsubscript{4}Flux}{Field Measurements of CH4Flux}}

{\label{field-measurements-of-ch4-flux}}

A static chamber technique was used to measure the
CH\textsubscript{4}flux (Song \emph{et al.} 2009; Zhang \emph{et al.}
2017). Stainless steel permanent bases (50 × 50 × 12 cm) with a
3-cm-deep groove for water sealing were inserted into soil down to a
depth of 12 cm in the plots approximately one month before the
experiment started in the first year. The chamber base was left in the
field for one month before any flux measurement; this was to let the
system evolve into an equilibrium state, avoiding any potential
disturbances to methanogens and methanotrophs and thus the
CH\textsubscript{4} flux. An opaque stainless-steel top chamber (50 cm
height) with heat-isolation was installed over the base, with bottom in
the groove. The grooves were filled with water for sealing the chamber.
Two electric fans were installed inside the chamber to mix the air in
the headspace continuously and thoroughly during the measurements (Fan
\emph{et al.}2007). Sixty-ml gas samples were collected at 10-min
intervals for 30 min using sixty-ml syringes with airtight stopcocks.
Simultaneously, the air temperature and pressure in the chamber were
measured, and the soil temperature and moisture were measured at a 5 to
10-cm depth using a thermometer (Spectrum Technologies, Inc. East -
Plainfield, Illinois) and a portable soil moisture measuring kit ML2x
(ThetaKit, Delta-T Devices, Cambridge, UK), respectively. The
CH\textsubscript{4}concentrations of the gas samples were analyzed using
a gas chromatograph (Agilent 7890A, Agilent Technologies Limited Co.,
USA) equipped with flame ionization detector (FID) using 60--80 mesh 13
XMS column (2 mm inner diameter and 2 m long), with an oven temperature
of 55°C. Pure nitrogen was used as carrier gas at a flow speed of 30 ml
min\textsuperscript{-1}, and the CH\textsubscript{4} flux was determined
from the linear slope of the mixing ratio changes in four samples taken
at 0, 10, 20 and 30 min after chamber closure. The
CH\textsubscript{4}flux was measured weekly from May to September in
2013, 2014, 2015 and 2016, respectively.

The CH\textsubscript{4} fluxes were linearly interpolated and
sequentially cumulated to estimate the total flux over growing seasons
(Zhang \emph{et al.} 2017). The linear interpolation was adopted due to
two reasons: (1) it has been widely used in previous studies and has
been suggested to be effective for seasonal interpolation of ecological
variables (Song \emph{et al.} 2009; Nikiema \emph{et al.} 2011); (2) the
auxiliary data to assist annually interpolation was lacking. Throughout
this analysis, positive fluxes represent gas uptake by the grassland
ecosystems.

\subsection*{Meta-analysis}

{\label{meta-analysis}}

A meta-analysis was conducted to investigate the N and P impacts on
CH\textsubscript{4} across global grasslands. We collected publications
by searching for ``nitrogen and phosphorus'', ``methane'',
``grassland'', and ``upland'' in Google Scholar in July 2016, and later
updated in September 2018. The search returned 6230 publications. A few
criteria were then used to screen these publications for our purpose.
The criteria applied to determine whether or not to use the data were:
(1) it must be manipulation experiments with either external N and/or P
addition; (2) the field measurements must cover at least one full
growing season, which makes the estimation of annual budget more
reliable; (3) the studies report clear information for the field site
that is useful when extracting edaphic and meteorological data from
global datasets. For sites without clear latitude and longitude, we
Googled and found their geographic coordinates with country and site
names. Finally, 35 papers were selected for data extraction. When the
data were presented in figures, we extracted mean values and standard
errors using GraphClick (http://www.arizona-software.ch/graphclick/).
For studies with measurements from different N and P addition levels in
one paper, they were extracted and treated as independent data points.

Finally, we compiled a comprehensive dataset of 382 data points for
meta-analysis (\textbf{Figs. S4 and S5} ). The dataset covers the major
grassland types across the globe and all experiments were carried out
between 1980-2017. For all field experiments, the atmospheric
depositions of N and P from the global dataset were treated as
background rate and were added to the reported N and/or P addition
rates. Since a majority of the data points from Yu et al. did not
contain N or P deposition (Yu \emph{et al.} 2017), we used the extracted
contemporary nutrient deposition (Mahowald \emph{et al.} 2008), based on
latitudes and longitudes, as nutrient inputs. Every
CH\textsubscript{4}flux rate corresponds to one site with auxiliary
information including latitude, longitude, and factors such as N
deposition, P deposition, soil temperature (ST), soil moisture (SM),
soil pH, soil organic carbon (SOC), bulk density (BD), and clay content
(CL). Across the studies in our data set, the N and P treatments fell
within the ranges of 0\textasciitilde{}200 kg N ha\textsuperscript{-1}
and 0\textasciitilde{}50 kg P ha\textsuperscript{-1}, respectively. The
non-growing season CH\textsubscript{4} flux is normally not available
for most field experiments, therefore, the annual rate of
CH\textsubscript{4} uptake (kg
C-CH\textsubscript{4}ha\textsuperscript{-1} yr\textsuperscript{-1})
thereafter was calculated by the ratio of the growing season to
non-growing season CH\textsubscript{4} uptake as reported by a few
studies (Li \emph{et al.} 2012; Yue \emph{et al.} 2016).

The soil properties for each point data site were extracted from global
datasets according to their latitude and longitude. Specifically, the
soil pH, SOC, BD and clay were retrieved from the Re-gridded Harmonized
World Soil Database v1.2 in the Oak Ridge National Laboratory
Distributed Active Archive Center for Biogeochemical Dynamics (available
online: https://daac.ornl.gov/SOILS/guides/HWSD.html); soil temperature
and moisture for the top 10 cm were from the NCEP/DOE AMIP-II Reanalysis
(Reanalysis-2):
http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.derived.surfaceflux.html).

\subsection*{Global Extrapolation}

{\label{global-extrapolation}}

The data for the grassland distribution were derived from the Global
Mosaics of the standard MODIS land cover type data product (MCD12Q1)
from http://glcf.umd.edu/data/lc/index.shtml. The spatial coverage is
-180.0° \textasciitilde{} 180.0° in longitude, and -64.0°
\textasciitilde{} 84.0° in latitude. The global land cover data sets are
available as ESRI ASCII Grid format files and was re-projected to be
consistent with soil and climate datasets (\textbf{Fig. S4} ). The
global simulations were carried out at a spatial resolution of 0.5° ×
0.5°. According to the definition of Food and Agriculture Organization
of the United Nations (FAO), any geographic area dominated by natural
herbaceous plants including grasslands, prairies, steppes, and savannahs
with coverage of at least 10\% was designated as grassland
(Latham\emph{et al.} 2014). The annual CH\textsubscript{4} uptake was
determined by summing up all grassland grids (equation 1). For the model
simulation, we set N and P depositions to pre-industrial level to
represent ambient condition, N set to pre-industrial level and P set to
contemporary level represent P addition, P set to pre-industrial and N
set to contemporary represent N addition, both N and P were set to
contemporary level to represent N and P concurrent treatment.

Both climate and soil data were resampled and re-projected to be
consistent through NCL (NCAR Command Language, current version 6.4.0).
The data with higher resolution were uniformly transformed to the lowest
resolution at 0.5° × 0.5°. Based on the calculated
CH\textsubscript{4}uptake rate in every grid and grid area of grassland,
we scaled up the results from this analysis by multiplying them for
target CH\textsubscript{4} uptake with the corresponding grid areas
currently summarized:

\(F(CH4)=\sum_{k=0}^{n}{\left(\frac{n}{k}\right){\text{CH}_{4}}_{k}A_{k}}\)(1)

where F(CH\textsubscript{4}) is the sum of the global grassland
CH\textsubscript{4} uptake expressed as Tg
C-CH\textsubscript{4}year\textsuperscript{-1}, and CH\textsubscript{4k}
is the CH\textsubscript{4} uptake rate in kth grid as kg
C-CH\textsubscript{4}ha\textsuperscript{-1} y\textsuperscript{-1}, and
A\textsubscript{k} is the area of the kth grid (\textbf{Fig. S8} ).

\subsection*{Statistical Analysis and Uncertainty
Analysis}

{\label{statistical-analysis-and-uncertainty-analysis}}

We used a one-way ANOVA analysis (ANOVA; R package) followed by Duncan's
post-hoc test to examine the N and P impacts on annual
CH\textsubscript{4} uptake rate, soil
NH\textsubscript{4}\textsuperscript{+} and
NO\textsubscript{3}\textsuperscript{-}, and plant N content. A stepwise
multivariate analysis was adopted to evaluate the response of the soil
plant and microbial communities to environmental factors as well as
their correlations with each other. A number of key variables, including
N input rate, P input rate, soil temperature, soil pH, soil organic
carbon density, bulk density, and clay content, are kept in the multiple
linear equation to quantify their impact on CH\textsubscript{4} flux
(Equation 2).

A structure equation model (SEM) was used to explore how nutrient (N, P
and N + P)-induced changes in CH\textsubscript{4} uptake considering
meteorological, plant, edaphic factors, and microbial biomass. The
``lavaan'' package
(https://cran.r-project.org/web/packages/lavaan/lavaan.pdf) for R
program (version 3.4) was used for the structural equation modeling.
Data used in the SEM and linear regression analyses were calculated as
the mean of every year during the four years (\textbf{Figs. S2 and 3} ).
Prior to the SEM procedure, we conducted principal component analysis
(PCA) to remove the redundant variables for meteorological factors, soil
edaphic parameters, plant and microbial parameters. Meanwhile, due to
the strong multicollinearity among other variables, the variance
inflation factor (VIF) was used to quantitatively select the right
factor for SEM model (VIF \textless{} 5). One SEM model (Fig. S3) was
used to disentangle the direct and indirect environmental impacts on the
CH\textsubscript{4} uptake, and the other (Fig. 3) was used to analyze
the N and P impacts on CH\textsubscript{4} uptake. A conceptual model
was created to represent the key linkages and connecters between
different parameters. The fitted conceptual model was further modified
with ``mod\_ind'' (within the R package ``lavaan'') to yield a reliable
multivariate causal network. The SEM results were evaluated with the
comparative fit index (CFI), the normed fit index (NFI), and the
chi-square test (\selectlanguage{greek}χ\selectlanguage{english}\textsuperscript{2}). The chi-square value is the
traditional measure for evaluating the overall model fit and accessing
the magnitude of discrepancy between the sample and fitted covariance
matrices; NFI is an incremental fit index that assesses the model by
comparing the chi-square value of the model to the null model that
assumes that all variables are uncorrelated; CFI is a revised form of
the NFI that takes into account sample size; the model fits with NFI
\textgreater{} 0.95 and CFI \textgreater{} 0.95, indicating a good SEM
(Hooper \emph{et al.} 2008).

The Latin Hypercube Sampling based Monte Carlo method was adopted to
quantify the uncertainties of the global grassland
CH\textsubscript{4}uptake under different treatments (Control, N, P and
N+P conditions) estimated by the empirical models. The LHS approach has
been used in our previous study (Xu 2010); detailed procedure can be
found in\textbf{Supplementary Online Material} .

\section*{Results}

{\label{results}}

\subsection*{\texorpdfstring{A Field Experiment for N and P Impacts on
CH\textsubscript{4}Uptake}{A Field Experiment for N and P Impacts on CH4Uptake}}

{\label{a-field-experiment-for-n-and-p-impacts-on-ch4-uptake}}

The field experiment showed that the N-only and concurrent N + P
additions treatments significantly suppressed CH\textsubscript{4} uptake
over the entire duration of the experiment (2013-2016, \textbf{Fig. 1a}
). Suppression of CH\textsubscript{4} oxidation by N addition and N + P
additions amounted to -16.3\% (p \textless{} 0.01) and -7.9\% (p = 0.04)
relative to the control plots in 2013, -7.8\% (p\textless{}0.01) and
-1.8\% (p=0.10) in 2014, -12.3\% (p\textless{}0.01) and -6.6\%
(p\textless{}0.01) in 2015, and -18.3\% (p\textless{}0.01) and -12.5\%
(p\textless{}0.01) in 2016, respectively (\textbf{Fig. 1d} ). Over the
study period, the average annual CH\textsubscript{4} uptake rates were
2.94 \selectlanguage{ngerman}± 0.07 kg C-CH\textsubscript{4} ha\textsuperscript{-1} in control
plots, 2.54 ± 0.04 kg C-CH\textsubscript{4} ha\textsuperscript{-1} in N
addition plots, and 2.73 ± 0.06 kg
C-CH\textsubscript{4}ha\textsuperscript{-1} in N + P addition plots
(\textbf{Fig. 1a} ). In comparison with the ambient treatment, the
P-only treatment slightly and not statistically significantly stimulated
CH\textsubscript{4} uptake throughout the experiment: +7.4\% (p = 0.12)
in 2013, +4.0\% (p = 0.09) in 2014, +1.2\% (p = 0.2) in 2015, and +2.3\%
(p = 0.16) in 2016, respectively (\textbf{Fig. 1d} ). Overall, P
addition alone did thus not affect CH\textsubscript{4} uptake, N
addition alone suppressed CH\textsubscript{4} uptake, and concurrent N +
P additions suppressed CH\textsubscript{4} uptake to a lower degree,
suggesting that P addition alleviates the N suppression of
CH\textsubscript{4} uptake in semiarid grasslands (\textbf{Figs. 1a and
1d} ).

{[}Insert Figure 1 here{]}

\subsection*{\texorpdfstring{A Meta-analysis of N and P Impacts on
CH\textsubscript{4} Uptake in
Grasslands}{A Meta-analysis of N and P Impacts on CH4 Uptake in Grasslands}}

{\label{a-meta-analysis-of-n-and-p-impacts-on-ch4-uptake-in-grasslands}}

To investigate the universality of these N and P effects on
CH\textsubscript{4} uptake in grassland soils, we carried out a global
meta-analysis to quantify the responses of CH\textsubscript{4} uptake
rates in grassland ecosystems to nutrient addition treatments (N-alone,
P-alone, and concurrent N + P additions) (\textbf{Fig. 2} ). This global
meta-analysis showed that, relative to the control treatments, N
addition and concurrent N + P additions cause significant declines in
annual CH\textsubscript{4} uptake: -27\% (p \textless{} 0.01) and -14\%
(p \textless{} 0.01), respectively (\textbf{Fig. 2} ). The smaller
inhibition effect of concurrent N + P additions than the N-only addition
on CH\textsubscript{4} uptake (p = 0.02) (\textbf{Fig. 2} ) is
consistent with the results of our field experiment (\textbf{Figs. 1a
and2} ).

{[}Insert Figure 2 here{]}

\subsection*{\texorpdfstring{Mechanisms of N and P impacts on
CH\textsubscript{4}uptake}{Mechanisms of N and P impacts on CH4uptake}}

{\label{mechanisms-of-n-and-p-impacts-on-ch4-uptake}}

Based on various statistical analysis, we hypothesize that the following
mechanisms underpin the N and P impacts on CH\textsubscript{4} uptake.
Whereas experimental N addition leads to an accumulation of mineral N
(NH\textsubscript{4}\textsuperscript{+} and
NO\textsubscript{3}\textsuperscript{-}) in the soil (N-only compared
with control), P addition enhances plant N uptake and N accumulation in
vegetation biomass (N+P treatment compared with N-only addition)
(\textbf{Figs. 1b, 1c, S1, 3a, 3b, 3c, and 3d} ). In our field
experiment, P-only addition significantly decreased soil
NH\textsubscript{4}\textsuperscript{+} content (p \textless{}
0.01,\textbf{Fig. 1b} ), but did not significantly affect plant N
content (P-only addition compared with control) (p = 0.35, \textbf{Fig.
1c} ). The concurrent N + P additions, in contrast, did stimulate N
accumulation in vegetation to a much higher degree than N addition alone
(p \textless{} 0.01, \textbf{Fig. 1c} ). This increase in vegetation N
accumulation significantly reduced soil
NH\textsubscript{4}\textsuperscript{+} content under the N + P additions
treatment compared to the N-only treatment (p \textless{}
0.01,\textbf{Fig 1b} ). Therefore, the P addition substantially
stimulates plant growth and plant uptake of
NH\textsubscript{4}\textsuperscript{+}(Dijkstra et al., 2012), which
reduces the NH\textsubscript{4}\textsuperscript{+} concentration in
soils and thereby alleviates the N suppression of CH\textsubscript{4}
uptake (\textbf{Fig. S1} ).

{[}Insert Figure 3 here{]}

To disentangle the contribution of the various potential drivers, we
applied structural equation models (SEM) to quantify the environmental
controls of CH\textsubscript{4} uptake (all factors were classified into
four groups: meteorology, microbes, plant, and edaphic
factors,\textbf{Figs. S2 and S3} ) using the field experiment's data
(\textbf{Figs. 3a, 3b, 3c, and 3d} ). Our models considered how nutrient
additions directly or indirectly affects CH\textsubscript{4} uptake
(\textbf{Figs. 3 and S3} ). The SEM results suggest that under control
(non-fertilized) conditions, the impact of meteorology on
CH\textsubscript{4} uptake was directly (\selectlanguage{greek}β \selectlanguage{english}= -0.33, standardized
coefficient) or indirectly mediated through microbes (\selectlanguage{greek}β \selectlanguage{english}= -0.8,
standardized coefficient) and plants (\selectlanguage{greek}β \selectlanguage{english}= -0.21, standardized
coefficient) (\textbf{Fig. S3a} ). N and P additions affected
CH\textsubscript{4} uptake indirectly through edaphic factors (N
treatment: \selectlanguage{greek}β \selectlanguage{english}= 0.5, standardized coefficient, \textbf{Fig. S3b} ; N+P
treatment: \selectlanguage{greek}β \selectlanguage{english}= 0.37, standardized coefficient, \textbf{Fig. S3d} ). Soil
NH\textsubscript{4}\textsuperscript{+} had a direct negative effect and
plant N content had a positive effect on the CH\textsubscript{4} uptake
under control conditions and in all nutrient addition treatments
(\textbf{Figs. 3a, 3b, 3c, and 3d} ). Meanwhile, added N stimulated the
accumulation of soil NH\textsubscript{4}\textsuperscript{+} (N
treatment: \selectlanguage{greek}β \selectlanguage{english}= 0.45), added P had a positive impact on plant P and soil
P, but had no impact on soil NH\textsubscript{4}\textsuperscript{+};
while the N + P treatment had a negative impact on soil
NH\textsubscript{4}\textsuperscript{+} (\selectlanguage{greek}β \selectlanguage{english}= -0.18). Compared to the
control, the N addition strengthened the negative effect of
NH\textsubscript{4}\textsuperscript{+} on CH\textsubscript{4} uptake (\selectlanguage{greek}β
\selectlanguage{english}ranging from -0.57 to -0.77) (\textbf{Figs. 3a and 3b} ); P addition did
not change the negative effect of
NH\textsubscript{4}\textsuperscript{+}(\selectlanguage{greek}β \selectlanguage{english}= -0.57) and the positive
effect of plant N (\selectlanguage{greek}β \selectlanguage{english}= 0.34) (\textbf{Figs. 3a and 3c} ); N + P
additions strengthened the suppression effect of soil
NH\textsubscript{4}\textsuperscript{+} (\selectlanguage{greek}β \selectlanguage{english}changing from -0.57 to -0.72)
(\textbf{Figs. 3a and 3d} ). These results showed that
CH\textsubscript{4} uptake is highly associated with soil N and P
contents in semiarid grasslands.

\subsection*{\texorpdfstring{Global Estimation of P alleviation of
N-suppressed CH\textsubscript{4} Sink in
Grasslands}{Global Estimation of P alleviation of N-suppressed CH4 Sink in Grasslands}}

{\label{global-estimation-of-p-alleviation-of-n-suppressed-ch4-sink-in-grasslands}}

We further developed an empirical model to quantify the N and P impacts
on soil oxidation of atmospheric CH\textsubscript{4} across global
grasslands, using existing global datasets of soil properties and
meteorology (Methods ). Two thirds of the compiled data were used for
model fitting, while the remaining one third of the data was used for
model validation (\textbf{Fig. S7} ). The best fitting equation obtained
with the stepwise regression procedure was:

F\textsubscript{CH4} = m + a \selectlanguage{ngerman}× N + b × P + c × ln(N) × ln(P) + d × ST +
e × pH + f × SOC + g × BD + h × CL (2)

where F\textsubscript{CH4} is the annual CH\textsubscript{4} uptake
rate; N is the nitrogen input in g
ha\textsuperscript{-1}y\textsuperscript{-1}; P is the phosphorus input
rate in g ha\textsuperscript{-1} y\textsuperscript{-1}; ln represents
the natural logarithm; ST is soil temperature (K); pH is the soil pH
value; SOC is soil organic carbon content (in \%); BD is bulk density (g
cm\textsuperscript{-3}); CL is clay content (in \%); m is the incept of
the function; and a, b, c, d, e, f, g, and h are coefficients. The
coefficients and key parameters for the regression are listed
in\textbf{Table S1} . The model explained more than 37\% of the
variation in CH\textsubscript{4} uptake rate across the globe
(\textbf{Fig. S7} ).

{[}Insert Figure 4 here{]}

We then applied the empirical model to estimate the
CH\textsubscript{4}sink strength of global grasslands (\textbf{Fig. S8}
), under four treatments: ambient (\emph{i.e.} pre-industrial) levels of
N and P depositions, elevated N deposition (contemporary N deposition
and pre-industrial P deposition), elevated P deposition (contemporary P
deposition and pre-industrial N deposition), and concurrently elevated N
+ P depositions (contemporary N and P depositions) (\textbf{Fig. 4} ).
Simulated global grassland CH\textsubscript{4} sinks amounted to 4.43 ±
0.20 Tg C-CH\textsubscript{4} y\textsuperscript{-1} for the ambient
scenario, 3.92 ± 0.16 Tg C-CH\textsubscript{4} y\textsuperscript{-1} for
the elevated N scenario, 4.60 ± 0.22 Tg
C-CH\textsubscript{4}y\textsuperscript{-1} for the elevated P scenario,
and 4.18 ± 0.18 Tg C-CH\textsubscript{4} y\textsuperscript{-1}, for the
N + P scenario (\textbf{Fig. 4} ). Addition of N-only thus suppressed
the global grassland CH\textsubscript{4} sink by \textasciitilde{}0.50
Tg C (\textasciitilde{}11.4\%), while concurrent P deposition alleviated
this suppression by more than half (\textasciitilde{}5.8\%).

\subsection*{\texorpdfstring{Conceptual Model for P Alleviation of
N-suppressed
CH\textsubscript{4}Sink}{Conceptual Model for P Alleviation of N-suppressed CH4Sink}}

{\label{conceptual-model-for-p-alleviation-of-n-suppressed-ch4-sink}}

Based on our field experiments, the global meta-analysis, and the
empirically-derived insights of N and P impacts on
CH\textsubscript{4}uptake, we here propose a conceptual framework that
summarizes the possible mechanisms underlying the interactive impacts of
N and P additions on CH\textsubscript{4} uptake (\textbf{Fig. 5} ). In
this conceptual model, MMO represents the whole group of enzymes
responsible for CH\textsubscript{4} oxidation under aerobic conditions
(Dunfield \& Knowles 1995) (\textbf{Fig. 5a} ). Under ambient conditions
(e.g. pre-industrial N and P deposition), grassland productivity is
generally limited by low soil N availability (Ladwig \emph{et al.} 2012)
and by low soil P availability in more than half of the grasslands
(Fay\emph{et al.} 2015) and grassland plant species have therefore
optimized their N uptake and allocation processes during ecological
succession (Bai \emph{et al.} 2004). Soil N does not leach under these
low-N conditions and available N is either assimilated by plants or
immobilized by soil microbes. Because soil mineral N (particularly
NH\textsubscript{4}\textsuperscript{+}) is maintained at a low level,
competition with CH\textsubscript{4} for the MMO enzyme is weak
(\textbf{Fig. 5a} ). In contrast, sustained or high N addition will push
the system out of N limitation and result in
NH\textsubscript{4}\textsuperscript{+} accumulation in the soil
(\textbf{Fig.5b} ). This in turn strengthens the competition with
CH\textsubscript{4} for the MMO enzyme, thereby suppressing the
oxidation of atmospheric CH\textsubscript{4} in grassland soils
(\textbf{Fig. 5b} ). If N and P are concurrently added, the added P
stimulates vegetation growth and uptake of mineral N, especially
NH\textsubscript{4}\textsuperscript{+}, and thus alleviates the
N-induced suppression of CH\textsubscript{4} oxidation. (\textbf{Fig.
5c} ). This theoretical framework emphasizes the substrate competition
theory when explaining the P alleviation of N-suppression on
CH\textsubscript{4} uptake.

{[}Insert Figure 5 here{]}

\section*{Discussion}

{\label{discussion}}

Results from both the field experiments and the global meta-analysis
support the substrate competition theory as a predominant mechanism
explaining P alleviation of N-suppression of CH\textsubscript{4} uptake
in global grassland. A number of studies have concluded that soil
NH\textsubscript{4}\textsuperscript{+} content is a major driver of
CH\textsubscript{4} uptake suppression in drylands (Dunfield \& Knowles
1995; Gulledge \& Schimel 1998). The toxic impact of nitrite on
methanotrophic activity might be another reason for this suppression
(Dunfield \& Knowles 1995). In our field site, however, the toxic impact
of nitrite on methanotrophic bacteria (Schnell \& King 1994) most likely
did not contribute to the inhibited CH\textsubscript{4} uptake because
no nitrite was detected in the soil, a widespread phenomenon in
semi-arid grasslands (Holst \emph{et al.} 2007; Giese \emph{et al.}2013;
Zhang \emph{et al.} 2017). Therefore, we conclude that substrate
competition remains the best theory to explain the P alleviation of
N-suppression of CH\textsubscript{4} oxidation.

A recent study in tropical forest postulated that P mitigation of the
N-suppressed CH\textsubscript{4} oxidation might due to P stimulation of
methanotrophic activities, although it further concluded it might be a
minor contribution due to the trivial fraction of microbial biomass
taken in by CH\textsubscript{4} oxidation bacteria (Zhang \emph{et
al.}2011). This mechanism was postulated, but not supported by empirical
data (Zhang \emph{et al.} 2011). Enhanced methanotrophic activity by
P-enrichment is thus one possible mechanism, yet it remains to be
empirically confirmed as a predominant mechanism. More molecular and
genomic analysis of the linkages between microbial mechanisms and
ecosystem function remain needed to mechanistically elucidate and
predict the CH\textsubscript{4} oxidation in a changing environment
(Xu\emph{et al.} 2016). Combined, the field experiment, meta-analysis,
and global empirical modeling analysis unambiguously demonstrate that
P-stimulated soil N depletion mitigate the N-induced reduction of
CH\textsubscript{4} uptake.

Both the global meta-analysis and modeling results indicate a widespread
impact of N and P on CH\textsubscript{4} uptake in grassland.
Summarizing all grids with treatment impacts compared with ambient
grids, we found that N suppression of CH\textsubscript{4} uptake occurs
in over 90\% of global grasslands; the pervasive N suppression is
consistent with reported N suppression of CH\textsubscript{4} uptake in
many ecosystems (Mosier \emph{et al.} 2003; Chen \emph{et al.} 2013;
Liu\emph{et al.} 2017; Zhang \emph{et al.} 2017). Model results suggest
that P alleviation of N-suppression of CH\textsubscript{4} uptake occurs
in over 89\% of the global grasslands (\textbf{Fig. 4} ). Considering
the limited studies on P impacts on CH\textsubscript{4} uptake
(Veraart\emph{et al.} 2015), more field experiments on this aspect are
needed. Estimates of the global grassland sink for CH\textsubscript{4}
have been made in a large number of studies, yielding a broad range of
1.9 - 9.3 Tg CH\textsubscript{4} yr\textsuperscript{-1} (Potter \emph{et
al.}1996; Ridgwell \emph{et al.} 1999; Curry 2007; Zhuang \emph{et
al.}2013; Yu \emph{et al.} 2017). Our result (5.9 Tg
CH\textsubscript{4}y\textsuperscript{-1}) falls within the range of
previous studies. According to our empirical model, increased N
deposition reduced the grassland CH\textsubscript{4} sink by 11\%, which
was similar to another modeling study (10\%) (Zhuang \emph{et al.}
2013), but lower than the value reported in a data synthesis study
(38\%) (Liu \& Greaver 2009).

The effects of N and P depositions on CH\textsubscript{4} uptake were
quantified, yet a few issues should be paid attention to when
interpreting the results. First, we quantified the potential
CH\textsubscript{4} patterns under four N and P deposition scenarios,
but did not consider the contributions of other changing environmental
factors, such as increasing atmospheric
CO\textsubscript{2}concentrations, and shifting land management
practices, which have been shown to be important determinants of
CH\textsubscript{4} flux (Xu\emph{et al.} 2010). Second, our
global-scale estimates of CH\textsubscript{4} uptake were based on a
simple empirical model. Intensive data-model integration and model-
model inter-comparisons are still needed to better quantify the
uncertainties in these CH\textsubscript{4} budgets. Third, the
meta-analysis was carried based on the most comprehensive dataset for
the impacts of N and P additions on CH\textsubscript{4} flux in global
grassland; however, the uneven distribution of the field observational
dataset might cause biases in the global analysis of nutrient impacts.
This unequal spatial distribution of field observations exist for eddy
covariance towers (Baldocchi \emph{et al.} 2001), vegetation data
(Kattge \emph{et al.}2011), and soil data (Xu \emph{et al.} 2013). This
problem needs to be resolved for reaching a more accurate global
extrapolation and increasing our understanding of the functioning of
terrestrial ecosystems. Deposition and addition of N and P take place in
many forms, including inorganic and organic, dry and wet deposition. Due
to limited data availability (Mahowald \emph{et al.} 2008) and field
experiments (Wang \emph{et al.} 2015), the impacts of various N and P
forms in atmospheric depositions could not be fully investigated in the
present study. Understanding the impacts of different N and P forms on
CH\textsubscript{4} oxidation still remains to be fully investigated.

\section*{Conclusion}

{\label{conclusion}}

With a combination of a field experiment, a meta-analysis, and an
empirical modeling approach we found that the substrate competition
theory is most likely the predominant mechanism explaining the P
alleviation of the N-suppression of CH\textsubscript{4} uptake, and we
further estimated that contemporary atmospheric N deposition suppresses
the CH\textsubscript{4} sink in global grasslands by 11.4\% while P
deposition alleviates this suppression by 5.8\%.

This study is among the first attempts to quantify the P impacts on the
N suppression of soil oxidation of atmospheric CH\textsubscript{4} in
global grasslands. It advocates model development to incorporate P
mechanisms not only for the nutrient impacts on carbon cycling, but also
for a more accurate projection of the CH\textsubscript{4} budget of
terrestrial ecosystems.

\textbf{Acknowledgements}

This study was partially supported by the Northeast Institute of
Geography and Agroecology, Chinese Academy of Sciences, and the ``Top
Notch'' program in China. C.S. is supported by the National Natural
Science Foundation of China (41125001). L.Z. was partially supported by
National Key Research and Development Program of China (2016YFC0500601)
and the National Natural Science Foundation of China (41371111). X.X.
acknowledged the financial assistance provided by the SPRUCE and NGEE
Arctic projects, which are supported by the Office of Biological and
Environmental Research in the Department of Energy Office of Science.
J.B. was partially supported by the Interdisciplinary Research Funds of
Beijing Normal University. I.A.J. acknowledge support from the European
Research Council Synergy Grant IMBALANCE-P (ERC-2013-SyG-610028). Dr.
Natalie M. Mahowald at Cornell University kindly shared her data of
global depositions of N and P for this study.

\textbf{Additional information}

\textbf{Supplementary Information} accompanies this paper at
https://doi.org/\ldots{}

Fig. S1 Correlation between NP-induced changes in soil total N content
and NP-induced changes in plant N content. \selectlanguage{greek}Δ\selectlanguage{english}PTN equals plant total
nitrogen under concurrent N+P treatment minus plant total nitrogen under
N only condition. Additions; \selectlanguage{greek}Δ\selectlanguage{english}STN equals soil total nitrogen under
concurrent N+P treatment minus soil total nitrogen under N only
condition. The log-transformation was used to producing variables
following normal distribution.

Fig. S2 Bivariate correlations between variables used in structure
equation models (observational dataset)

Fig. S3 Structural equation models of meteorology, plant, edaphic and
microbial biomass as predictors of CH\textsubscript{4} uptake for (a)
control (n=96, \selectlanguage{greek}χ\selectlanguage{english}\textsuperscript{2}=2.041, DF=2, CFI=1, NFI=0.99), (b) N
addition only (n=96, \selectlanguage{greek}χ\selectlanguage{english}\textsuperscript{2}=0.667, DF=2, CFI=1,
NFI=0.997), (c) P addition only (n=96, \selectlanguage{greek}χ\selectlanguage{english}\textsuperscript{2}=1.946, DF=2,
CFI=1, NFI=0.991) and (d) concurrent N+P additions (n=96,
\selectlanguage{greek}χ\selectlanguage{english}\textsuperscript{2}=2.079, DF=2, CFI=1, NFI=0.99) (black lines
represent positive paths; red lines represent negative paths; solid
lines indicate significant impacts {[}p\textless{}0.05{]}; dotted lines
indicate non-significant impacts {[}p\textgreater{}0.05{]}).

Fig. S4. Spatial distribution of the data points for the whole dataset
used for meta-analysis; 382 data points distributed across the global
grasslands, covering major grassland types, spanning major climate zones

Fig. S5. The correlation matrix of the key variables in the dataset used
for meta-analysis (noted most variables are not in normal distribution,
indicating the needs of log-transformation in further analysis and model
development)

Fig. S6. Correlation between NH\textsubscript{4}\textsuperscript{+} and
total inorganic N
(NH\textsubscript{4}\textsuperscript{+}+NO\textsubscript{3}\textsuperscript{-}).

Fig. S7. Comparison of modeled CH\textsubscript{4} with the compiled
CH\textsubscript{4} uptake.

Fig. S8. Frequency distribution of the best estimates of
CH\textsubscript{4} oxidation across global grasslands (CK:
pre-industrial N and P; N: the model simulation with pre-industrial P
and contemporary N inputs; P: N: the model simulation with contemporary
P and pre-industrial N inputs; NP: model simulations with contemporary N
and P depositions).

Table S1 Correlation coefficients for the regression between independent
variables and CH\textsubscript{4} uptake rates based on the
comprehensive data (R\textsuperscript{2} = 0.44; P \textless{} 0.001);
it is used as the empirical model for global estimation of N and P
impacts on CH\textsubscript{4} uptake in grasslands

\textbf{Competing interests:} The authors declare no competing
interests.



\textbf{Figure Legends}

\textbf{Fig. 1} Differential effects of N, P, and concurrent N and P
additions on surface CH\textsubscript{4} flux, soil
NH\textsubscript{4}\textsuperscript{+} and plant N content in semiarid
grassland from 2013 to 2016. (a) Net nutrient effects on mean
CH\textsubscript{4} uptake; (b) Net nutrient effects on soil
NH\textsubscript{4}\textsuperscript{+} content in top 50 cm; and (c) Net
nutrient effects on plant N content. The error bars indicate the
standard error of means (n = 3 \selectlanguage{ngerman}× 2). Different letters represent
significant differences among treatments (p\textless{}0.05) by the
one-way ANOVA. (d) N and P effects on CH\textsubscript{4} uptake as
normalized to the control treatment in semiarid grassland from 2013 to
2016; error bars indicate the standard error (note that the N + P all
have suppression impact but in a lesser degree)

\textbf{Fig. 2} A meta-analysis of N and P effects on
CH\textsubscript{4} uptake in grassland ecosystems (percentage is used
to report the N and P impacts)

\textbf{Fig. 3} Structural equation modeling (SEM) for the relative
controls of soil NH\textsubscript{4}\textsuperscript{+} content, soil P
content, plant N and plant P on CH\textsubscript{4} flux under various
treatments; (a) ambient (n=96, \selectlanguage{greek}χ\selectlanguage{english}\textsuperscript{2}=1.389, DF=0,
CFI=0.986, NFI=1), (b) N addition (n=96, \selectlanguage{greek}χ\selectlanguage{english}\textsuperscript{2}=5.671,
DF=0, CFI=0.968, NFI=1), (c) P addition (n=96,
\selectlanguage{greek}χ\selectlanguage{english}\textsuperscript{2}=1.644, DF=0, CFI=0.993, NFI=1) and (d) concomitant
N + P additions (n=96, \selectlanguage{greek}χ\selectlanguage{english}\textsuperscript{2}=10.347, DF=0, CFI=0.943,
NFI=1) (black lines represent positive paths; red lines represent
negative paths; the solid lines represent the path is statistically
significant {[}p\textless{}0.05{]}; the dotted lines represent
non-significant effects {[}p\textgreater{}0.05{]}).

\textbf{Fig. 4} The model simulated contemporary (2005-2014)
CH\textsubscript{4} oxidation and N and P impacts across global
grasslands; (a) absolute CH\textsubscript{4} flux (Kg C
ha\textsuperscript{-1} y\textsuperscript{-1}) under ambient condition
(pre-industrial N + P deposition); (b) relative impact of N deposition
(contemporary N deposition and pre-industrial P deposition) compared to
the ambient condition; (c) relative impact of P deposition
(pre-industrial N deposition and contemporary P deposition) compared to
the ambient condition; (d) relative impact of N + P depositions
(contemporary N + P depositions) compared to the ambient condition.

\textbf{Fig. 5} Graphic diagram showing substrate competition between
CH\textsubscript{4} and NH\textsubscript{4}\textsuperscript{+} for
methane monooxygenase (MMO); under ambient condition (left panel), N
addition condition (middle panel), and concomitant N + P additions
(right panel); the trivial soil NH\textsubscript{4}\textsuperscript{+}is
in weak competitive equilibrium with CH\textsubscript{4} for MMO under
ambient condition; and the added NH\textsubscript{4}\textsuperscript{+}
shifts the competitive equilibrium and thus reduces the
CH\textsubscript{4} oxidation; the P addition pushes the shifted
equilibrium back and alleviates the N suppression on CH\textsubscript{4}
oxidation by stimulating N cumulation in vegetation biomass.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/3}

\end{center}
\end{figure}

\textbf{Figure 3}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/4}

\end{center}
\end{figure}

\textbf{Figure 4}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Figure 5}

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