A novel isotope pool dilution approach to quantify gross rates of key abiotic and biological processes in the soil phosphorus cycle

Efforts to understand and model the current and future behavior of the global phosphorus (P) cycle are limited by 10 the availability of global data on rates of soil P processes, as well as their environmental controls. We here present a novel isotope pool dilution approach using 33P labelling of live and sterile soils, which allows to obtain high quality data on gross fluxes of soil inorganic P (Pi) sorption and desorption, as well as of gross fluxes of organic P mineralization and microbial Pi uptake. At the same time, net immobilization of Pi by soil microbes and abiotic sorption can be easily derived and partitioned. Compared to other approaches, we used short incubation times (up 15 to 48 h), avoiding tracer re-mineralization, which was confirmed by separation of organic P and Pi using isobutanol fractionation. This approach is also suitable for strongly weathered and P impoverished soils, as sensitivity is increased by extraction of exchangeable bio-available Pi (Olsen Pi; 0.5 M NaHCO3) followed by Pi measurement using the malachite green assay. Biotic processes were corrected for desorption/sorption processes by using adequate sterile abiotic controls that exhibited negligible microbial and extracellular phosphatase activities. Gross 20 rates are calculated using analytical solutions of tracer kinetics, which also allows to study gross soil P dynamics under non-steady-state conditions. Finally, we present major environmental controls of gross P cycle processes that were measured for three P-poor tropical forest and three P-rich temperate grassland soils.


Introduction
Phosphorus (P) is a major limiting nutrient to terrestrial primary production, particularly so on highly weathered soils, as, e.g.found in the tropics.Globally, increasing imbalances between nitrogen (N) and P inputs (i.e.increasing N:P stoichiometry of inputs) caused by human activities and land-use changes through increased emissions of reactive N are suggested to lead to progressive P limitation of terrestrial ecosystems, and first signs thereof have been identified (Penuelas et al., 2013).A decrease in the relative P availability might have strong repercussions on future nutrient limitations of natural ecosystems, on food production and on carbon (C) sequestration (Penuelas et al., 2013;Penuelas et al., 2012;Yang et al., 2013).Efforts to understand and model the current and future global P cycle and its coupling to the global C and N cycles have been intensified, but are strongly limited by the availability of global data on soil gross P processes and their environmental controls (Reed et al., 2015).Large investments into new projects, experiments and models have therefore been recently undertaken to advance our understanding of the terrestrial P cycle, and to fill data gaps, e.g.IMBALANCE-P (http://imbalancep-erc.creaf.cat)and NGEE-TROPICS (http://ngee-tropics.lbl.gov).
Soil Pi availability is governed by transfers between pools of exchangeable P, immobilized/fixed P and occluded P, by slow release of Pi from mineral P through weathering of primary minerals, and by mineralization of organic P (Po) (Fig. 1) (Bünemann, 2015;Turner et al., 2007).In strongly weathered soils, primary mineral P pools are depleted, and the largest fraction of P is found in occluded and fixed pools, as well as in Po (Vitousek and Farrington, 1997;Yang and Post, 2011).Phosphorus limitation in such soils is further aggravated by their high P sorption potentials caused by high contents of Fe-Al (hydr)oxides (Goldberg and Sposito, 1985).Most of the immediate P needs of plants (and microbes) in natural and agricultural systems is supplied by Po mineralization, catalyzed by extracellular phosphatases that are released by soil microbes and plant roots (Richardson and Simpson, 2011), as well as by abiotic Pi desorption.Soil microbes and plant roots can promote the release of P from primary and secondary minerals by accelerating mineral dissolution and Pi desorption, through exudation of (phyto)siderophores and organic acids (Mander et al., 2012;Ryan et al., 2001).
Soil P cycling processes such as soil Pi sorption/desorption fluxes and gross Po mineralization rates, as well as the size of the exchangeable soil Pi pool have been measured by isotope exchange (IEK) techniques using 32 P or 33 P.These techniques are based on recurrent measurements of radiotracer recovery and Pi concentration in soil water extracts (Di et al., 1997;Frossard et al., 2011;Bünemann, 2015) (Table 1).A variety of IEK procedures and protocols are in use, and optimizations in methodology have been called for, particularly for Po mineralization (Bünemann, 2015).Only during the last decade common, accepted protocols have become adopted and are currently used to measure soil P processes following Oehl et al. (2001b).In this IEK approach in short-term experiments abiotic sorption/desorption processes from an isotopically exchangeable Pi pool are measured over a short time period in batch experiments (100 min, 1:10 (w:v) soil: water slurry, ± microbicides).This assumes that no microbial tracer uptake (blocked by microbicides) and no organic P mineralization occurs, and that soils are in a steady state i.e. don`t show changes in Pi concentration (Table 1).In such short-term IEK experiments the decrease in radioactivity (radiotracer recovery) in soil water is described by a power function: r(t)/R = r1min/R x t -n R is the added radioactivity and r(t) the radioactivity recovered at any time t in soil water extracts.The parameters r1min/R and n (slope of the regression indicating speed of isotopic exchange) are derived from the loglog regression of r(t) versus time.This is based on steady state assumptions, i.e. that Pi concentration in soil water extracts (CP) is constant.In some soils an extended version of this equation needs to be applied: r(t)/R = m x (t + m 1/n ) -n + rinf/R Here, rinf/R is the maximum possible dilution of the added radiotracer, approximated as the ratio of CP to total inorganic P in soils.n and m are derived from non-linear fitting procedures.Assuming that tracer and tracee behave similarly in the system, the specific activity of Pi in soil solution should reflect the specific activity of isotopically exchangeable P -termed E-value (in mg P kg -1 soil).E(t) = CP / (r(t)/R).
Isotopic dilution (E'(t)) is further measured over the full length of a moist soil incubation experiment lasting for several days to weeks, constituting the total amount of exchangeable Pi or isotope dilution caused by concurrent biological processes (Po mineralization) and physicochemical processes.Short-term exchange kinetics are then extrapolated over the full time period of the moist soil incubation (E(t)) (Fardeau et al., 1991).The difference between E'(t) and the extrapolated E(t)-value provides then the measure of gross Po mineralization.
The isotope pool dilution approach (IPD) of Kirkham and Bartholomew (1954) was developed as a general tracer approach to measure gross rates of soil element cycle processes, but was most frequently applied to nitrogen cycling processes such as organic N mineralization and nitrification (Booth et al., 2005).The IPD approach can however also be transferred to measure gross rates of P cycle processes (Di et al., 2000).It then also relies on the labelling of the Pi pool with 33 P or 32 P and on subsequent time-resolved measurements of concentrations and specific activities of Pi (Table 1, Figure 1B).However, in contrast to IEK techniques, changes in Pi concentrations and specific activities are then solved by mass balance equations developed specifically for gross rate calculations based on tracer studies (Kirkham and Bartholomew, 1954).In the following we list the criteria that have to be met by the IPD method to correctly determine gross rates of soil Po mineralization and soil Pi sorption/desorption (Di et al., 2000;Murphy et al., 2003;Kirkham and Bartholomew, 1954).
1.The tracer ( 32 Pi or 33 Pi) and tracee (unlabeled 31 Pi) behave identically and are well mixed.This is given for the different isotopes of P as long as radiotracer solution is homogeneously distributed in the soil and sufficient time is provided for isotope equilibration between added radiotracer and the native Pi pool.
2. The influx into the target (Pi) pool (i.e. the product of Po mineralization) has to be unlabeled (i.e.no tracer remineralization), in order for it to dilute the tracer: tracee ratio over time (Figure 1B and C).Tracer remineralization via microbial tracer assimilation, mortality and subsequent remineralization of labelled Po would result in an underestimation of Po mineralization, but can be avoided by short incubation times (1-2 days).
3. Abiotic release of Pi from a non-extractable pool (Pi desorption) causes an influx of unlabeled Pi into the target pool, resulting in an overestimation of the biotic process, Po mineralization, and has to be determined in parallel abiotic incubations of sterile soils.However, adequate abiotic controls with no contribution of biological processes has remained a major obstacle in measuring soil P dynamics with radiotracers, both in IEK and IPD experiments.Procedures in earlier studies ranged from short-term assays with no inhibitor addition as often performed in IEK assays (Spohn et al., 2013;Oehl et al., 2001b), to amendments of HgCl2, sodium azide, toluene or chloroform, and gamma irradiation or repeated autoclaving (Kellogg et al., 2006;Bünemann, 2015;Bünemann et al., 2007;Oehl et al., 2001b;Achat et al., 2010).
4. The soil extraction should target the bio-available exchangeable Pi pool.Pi in soil solution undergoes rapid equilibration with easily adsorbed Pi.An incomplete extraction of this pool causes an underestimation of Po mineralization rates, due to desorption from this pool, causing an influx of unlabeled tracer (together with unlabeled Pi) into the target pool, and thus violates assumption #2 of IPD assays.The commonly used soil water extractions target only a small fraction of this target pool, whereas standard soil P extractants, such as Olsen, Mehlich-3 or Bray-1, extract a larger fraction (Kleinman et al., 2001) and, therefore, are suggested to be better suited to extract the rapidly exchanging Pi pool (Kellogg et al., 2006).
5. The efflux from the isotopically labelled pool (i.e.microbial Pi immobilization and Pi sorption into a nonextractable pool) occurs at the ratio of tracer: tracee as present in the Pi pool at any specific time, with no discrimination between native Pi and added radiotracer (Figure 1B).A short pre-incubation time is therefore needed to allow for full mixing and isotopic equilibration of tracer and tracee (see point #1).
6. Changes in specific activity need to be measured specifically in the target pool, i.e. in extractable Pi for measurements of gross rates of Po mineralization and Pi sorption/desorption.However, most current approaches do not separate extractable Pi and Po but measure radioactivity in unfractionated extracts, including radiolabeled Po formed during the incubation, leading to an eventual overestimation of Po mineralization.7. The rates of Pi influx (Po mineralization, abiotic Pi release) and Pi efflux (biotic and abiotic Pi immobilization) need to be constant over the duration of incubation: (i) the initial phase of fast immobilization by sorption, microbial uptake and isotopic equilibration of radiotracer is excluded from calculations of gross rates, and (ii) incubation takes place within a suitable timeframe to avoid microbial turnover and 33 Po remineralization (see point #2).The minimum two time points necessary to measure concentration and specific activity of Pi for the IPD calculations should therefore lie in between the initial phase and the start of re-mineralization but it is recommendable to test more time points in the beginning to test time linearity of IPD rates for specific soil types.Mooshammer et al. (2012) adopted such a protocol for measurements of gross Po mineralization in decomposing plant litter, following the knowledge of IPD processes based on 15 N additions to study gross rates of soil N cycling (Hart et al., 1994;Murphy et al., 2003;Wanek et al., 2010;Braun et al., 2018).However, in plant litter P sorption and the abiotic release of Pi from sorbed P pools do not interfere.Consequently, the litter protocol cannot be directly transferred to soil studies.In the present study we developed an IPD protocol to assess soil P dynamics, based on the previous work for litter by Mooshammer et al. (2012) and soils by Kellogg et al. (2006).The protocol is based on IPD theory (Kirkham and Bartholomew, 1954;Di et al., 2000) applied to parallel incubations of live and sterile soil with 33 Pi tracer addition.Gross rates of Pi sorption (abiotic immobilization) and Pi desorption are determined in sterile soils, and allow correction of gross Po mineralization and microbial Pi immobilization rates in live soils.We used bicarbonate extractions to target the bio-available exchangeable Pi pool.To avoid tracer remineralization, we used short incubation periods (up to 2 days).To confirm that no significant amount of 33 Po was formed during incubation, Pi was also separated from Po based on isobutanol fractionation (Jayachandran et al., 1992).Pi concentrations were measured based on the phosphomolybdate blue protocol.At very low Pi concentrations, e.g. in tropical soils, that are below the detection limit of the phosphomolybdate blue method, Pi was determined by parallel measurements of Pi in bicarbonate extracts using the more sensitive malachite green assay (D'Angelo et al., 2001;Ohno and Zibilske, 1991).The protocol was tested rigorously with two different soils, and then applied to in total six soils (three tropical forest and three temperate grassland soils) to explore environmental controls on gross soil P dynamics.

2
Materials and methods

Soil materials and basic characterization
Soils (0-15 cm depth) were collected in summer 2015 from three temperate grassland sites in Austria and in spring 2015 from three tropical lowland forest sites in Costa Rica (Table 2).The grassland soils were extensively managed meadows, collected in Lower Austria (48° 13-20' N, 16° 12-17' E) in the vicinity of Vienna, at elevations between 170 and 320 m.The tropical forest soils were collected along a topographic gradient (ridge-slope-valley bottom) in wet evergreen old-growth forests in SW Costa Rica close to the National Park Piedras Blancas (8° 41' N, 83° 12' W, 110-250 m a.s.l.).Soils were sieved to 2 mm and stored in an air-dried state.Soil pH was measured in a 1:5 (w:v) mixture of air dried soil in water after 60 min of equilibration using an ISFET electrode (Sentron SI600 pH Meter).Soil texture was quantified using a miniaturized pipette/sieving protocol for 2-4 g air dried soils (Miller and Miller, 1987), using 4% sodium metaphosphate as a dispersant.Soil total C and total soil N content were determined after grinding oven dried soil in a ball mill, using an elemental analyzer (EA 1110, CE Instruments, Thermo Scientific).Temperate grassland soils were treated with 2 M HCl to remove carbonates, re-dried, ground and then analyzed by elemental analyzer for soil organic C. Total soil P and total soil Pi were measured after 0.5 M H2SO4 extraction of ignited soils (5 h at 450 °C in a muffle furnace; (O´Halloran and Cade-Menun, 2008)) and of untreated soils, respectively, by the malachite green method (Ohno and Zibilske, 1991;D'Angelo et al., 2001).
Total organic P was estimated by calculating the difference between total soil P and total soil Pi.We must however submit that ignition methods tend to overestimate soil organic P in highly weathered tropical soils (Condron et al., 1990).

Soil pre-treatment and assay of sterilization efficiency (abiotic controls)
Before starting the experiments, the soils were re-equilibrated from an air-dried state by rewetting to 60% water holding capacity for 6 days at 20 °C.Gravimetric soil water content and water holding capacity were determined prior to the experiment.Soils were then either sterilized twice, 48 and 2 h before start of the IPD experiments, by autoclaving at 121 °C for 60 min (sterile soils), or were kept at 20 °C (live soils, Fig. 2).Sterilization efficiency was checked based on soil enzyme activity measurements.Fluorescein diacetate (FDA) hydrolysis in soils was measured as a proxy of viable, active microbial biomass (Green et al., 2006;Schnurer and Rosswall, 1982), and the activity of acid phosphomonoesterases, which are extracellular enzymes involved in Po mineralization, was determined using methylumbelliferyl (MUF)-phosphate (Sirova et al., 2013;Marx et al., 2001).

33 P IPD assay
A schematic representation of the final IPD protocol can be found in Figure 2. Duplicate soil aliquots (2 g fresh weight) of sterile and live soil were amended each with 20 kBq 33 Pi (dilution of orthophosphoric acid phosphorus-33 radionuclide, 5 mCi mL -1 , i.e. 185 MBq mL -1 HCl-free water at specified date, Perkin NEZ080002MC).
Between 0.15-0.2mL of 33 P-label solution was added to each sample (Fig. 2); the volume added was adjusted for each soil type to obtain an optimal water content in each soil (~75 % water holding capacity).Soils were extracted with 30 mL (temperate soils) or 15 mL (tropical soils) of 0.5 M NaHCO3 (pH 8.5) after 4 and 24 h of incubation for 30 min on a horizontal shaker and filtered through ash-free cellulose filters.Lower extractant volumes in tropical and other P poor soils are used to reach higher Pi concentrations in the bicarbonate extracts for better quantification.
Thereafter isobutanol fractionation of the bicarbonate extracts was performed, separating Pi (into the organic phase) from Po (into the acidic aqueous phase) allowing measurement of the kinetics and specific activity of the Pi pool without interference of Po (Kellogg et al., 2006;Mooshammer et al., 2012).Isobutanol partitioning enables 100% recovery of Pi with no hydrolysis of Po (Jayachandran et al., 1992).For isobutanol fractionation each 1.5 mL of soil extracts, standards and blanks were amended by sequential addition of 1.5 mL acidified molybdate, 3 mL deionized water and 3 mL isobutanol.The acidified molybdate reagent consists of 5 g ammonium molybdate tetrahydrate ((NH4)6Mo7O24.4H2O)dissolved in 0.1 L 2.3 M H2SO4 (stable at room temperature for at least three months) and causes strong CO2 outgassing from the bicarbonate extracts.After addition of all reagents the vials were shaken overhead for 1 min and then rested for 10 min for phase separation.For later photometric quantification of Pi in the isobutanol phase, standards ranging from 320 to ~1 µM Pi (1:2 dilution series) and blanks, both of the same matrix as soil extracts (i.e.0.5 M NaHCO3), were prepared and underwent isobutanol fractionation together with the samples. 33P recovery standards were also prepared and processed through the isobutanol fractionation protocol, consisting of the same volume of extractant (15 or 30 mL) and 33 P tracer activity as added to soils (Fig. 2).
Pi in the isobutanol phase was quantified using the phosphomolybdate blue color reaction according to Murphy and Riley (1962).Briefly, each 1.5 mL of the upper organic phase were transferred to vials and amended with 2.1 mL molybdate free reducing agent, consisting of 1.32 g ascorbic acid dissolved in 250 mL antimony potassium tartrate (APT) solution (145.4 mg APT in 0.5 M H2SO4).The APT solution is stable at room temperature for >4 weeks, whereas the molybdate free reducing agent has to be prepared fresh daily.Thereafter samples were shaken overhead for 1 min and rested for 20 min for phase separation and color development.A volume of 250 µL of the blue isobutanol phase was then pipetted into a microtiter plate and absorbance was read at 725 nm with a microplate photometer (Tecan Infinite M200, Tecan Austria GmbH, Grödig, Austria).
In parallel to the phosphomolybdate blue reaction of Pi in the isobutanol phase, Pi concentrations were also determined directly in acidified bicarbonate extracts using the malachite green approach (D'Angelo et al., 2001).This method is 4-10 times more sensitive than the commonly used phosphomolybdate blue method and was chosen to account for the expectedly low Pi concentrations of the tropical soils.Standards for calibration of the malachite green method were prepared in 0.5 M NaHCO3, ranging from 50 to 0.039 µM Pi.Acidification of bicarbonate extracts and standards (blanks) was performed on 2.5 mL sample aliquots by adding 250 µL 2.75 M H2SO4 (Fig. 2).Of the acidified samples and standards, 200 µL were pipetted into a microtiter plate, 40 µL malachite green reagent A were added and incubated for 10 min.Then 40 µL reagent B were added and absorbance was read after 45 min at 610 nm with a microplate reader.Reagent A was prepared by adding 50 mL deionized water in an amber 0.1 L glass bottle, adding 16.8 mL concentrated H2SO4, stirring and dissolving 1.76 g ammonium heptamolybdate tetrahydrate ((NH4)6Mo7O24•4 H2O).Reagent B was prepared by heating 0.25 L of distilled H2O to 80°C in an amber 0.5 L glass bottle, dissolving 0.875 g PVA (polyvinyl alcohol, MW = 72000 g/mol) whilst continuously stirring, cooling to room temperature, and finally dissolving 87 mg malachite green oxalate in this solution.Both reagents are stable for >6 months at room temperature.
Radioactivity ( 33 P activity) was measured in 0.25 mL aliquots of acidified bicarbonate extracts and in 0.4 mL aliquots of the isobutanol phase, after addition of each 4 mL scintillation cocktail (Ultima Gold, Perkin Elmer), by liquid scintillation counting (Tri-Carb 1600 TR, Packard, Perkin Elmer) (Fig. 2).

Experiments
(i) Time kinetics: high resolution time kinetics of tracer and tracee dynamics ( 33 Pi, 31 Pi) were measured in two soils (temperate grassland, soil 4; tropical forest, soil 3; Table 2).After tracer addition to live and sterile soils in triplicates IPD assays were stopped by extraction with 0.5 M NaHCO3 after 0, 1, 2, 4, 8, 24, and 48 h.Time point 0 was assessed by adding the tracer solution and immediately extracting the soils with 0.5 M NaHCO3.
(ii) Microbial 33 P immobilization: the procedure outlined in chapter 2.3 can be combined with direct determination of microbial P by extraction with liquid chloroform-enriched salt solutions (Setia et al., 2012).We here tested a sequential extraction-liquid chloroform extraction (sECE) procedure.
After 24 h of soil incubation in experiment (i), soil samples (2 g fresh weight) were first extracted with 15 (soil 4) or 30 (soil 3) mL 0.5 M NaHCO3 for 30 min, centrifuged for 15 min at 10.000 g, and the supernatant was decanted.The soil residue was then re-extracted with 15 (30) mL 0.5 M NaHCO3 containing 3% (v:v) chloroform for 30 min and finally filtered through ash-free cellulose filters.
Volume corrections were applied for extractant absorption by the soil pellet after centrifugation.
Volume corrections were calculated as soil wet weight after centrifugation minus fresh weight weighed into each tube in grams, divided by the density of the bicarbonate solution (in g/mL), providing the carry-over of extractant from the first extraction (in mL).
(iii) Soil effects on tracer dynamics: live and sterile soils (2 g aliquots) of all 6 soils (Table 2) were measured in triplicates for 33 Pi activity and Pi concentrations, and assays were stopped after 0, 4 and 24 h.Net immobilization of 33 P and gross process rates were calculated for the time interval 4 to 24 h, and relationships between gross and net soil P processes and soil physicochemical parameters were tested.

Calculations of abiotic and biotic net 33 P immobilization
Additionally to the measurement of gross rates, abiotic net 33 P immobilization (net soil Pi fixation) and biotic net 33 P immobilization (net soil microbial Pi immobilization) were calculated based on the determination of the recovery of added tracer in soil extracts of live and autoclaved soils (see above) after 0, 1, 2, 4, 8, 24 and 48 hours.
Abiotic immobilization (in % added tracer) was estimated as 100 percent minus the percent 33 P recovery in autoclaved soils.Total immobilization was estimated as 100 minus the percent 33 P recovery in live soils.Biotic immobilization was calculated as the difference between total and abiotic immobilization.These data provide a rapid assessment of the abiotic versus microbial sink strengths for Pi, but do not represent gross rates.

Calculations of gross rates of soil P dynamics
Calculation of gross IPD rates followed the mass balance equations of Kirkham and Bartholomew (1954), as later applied by others for soil gross P fluxes (Kellogg et al., 2006;Mooshammer et al., 2012).In these gross P flux studies abiotic processes were not corrected for, Pi influx rates therefore representing the sum of biotic (organic P mineralization) and abiotic (desorption) processes, the latter of which do not play a significant role in decomposing litter being devoid of soil minerals (Mooshammer et al., 2012).However, to calculate gross Po mineralization for soils, gross rates of Pi desorption have to be corrected for in live soils.In the present study, this abiotic correction was performed by applying IPD calculations for influx (GI, gross influx; equation 1) for sterile soils (abiotic influx by Pi desorption) and live soils (total Pi influx), and taking the difference as biotic influx (i.e.gross Po mineralization).The same procedure was performed for tracer efflux (GE=gross efflux; equation 2) calculating gross immobilization fluxes for live soils (total Pi efflux) and sterile soils (Pi sorption), the difference providing gross rates of microbial Pi immobilization.Both abiotic corrections are based on the assumption that abiotic sorption/desorption processes are not affected by autoclaving, i.e. that these processes act similarly in sterile and in live soils.

Gross influx: 𝐺𝐺𝐺𝐺
where t1 and t2 represent incubation time (4 and 24 h; in days), C the soil Pi concentration (in µg Pi g -1 soil dry weight), SA the specific activity (in Bq µg -1 Pi) and LN the natural logarithm.Gross rates are therefore in µg Pi g - 1 soil dry weight d -1 .Net organic P mineralization rates can easily be derived by subtracting gross microbial Pi uptake from gross Po mineralization rates.
Due to the relatively rapid decline in 33 P activity by radioactive decay, all data were decay corrected back to the start of each experiment, i.e. the time point of tracer addition to the soil.This was done according to equation 3.
where Nt0 is the decay corrected 33 P activity in a sample (in Bq), Nt the measured 33 P activity at time of liquid scintillation counting, t is time (in days) elapsed between tracer addition and 33 P activity measurement, e=2.71828 and λ the decay constant of 33 P (0.0273539).

Statistics
Regressions were performed in Sigmaplot 13.0 (Systat Software, Inc.) and group differences were tested by oneway and two-way ANOVA followed by Tukey's HSD test in Statgraphics Centurion XVIII (Statpoint Technologies, Inc.).Variance homogeneity was tested by Levene's test and if necessary data were log, square root or rank transformed to meet assumptions of homoscedasticity and normal distribution.

Soil characterization
Temperate grassland soils had a pH between 6.3 and 6.8, with a silt loam to sandy loam texture (Table 2).Soil organic C contents ranged between 48 and 127 mg C g -1 , soil N from 2.3 to 5.0 mg N g -1 and soil total P from 0.44 to 0.82 mg P g -1 .Tropical forest soils had a pH between 4.1 and 4.2, and soil texture varied between silt, silt loam and sandy loam.Soil organic C contents were lower, at 26 to 31 mg C g -1 , soil N ranged from 2.2 to 2.6 mg N g -1 , and soil total P from 0.09 to 0.17 mg P g -1 .Organic P comprised a larger fraction of total P in tropical forest soils (64-76%) than in temperate grassland soils (22-57%).Extractable soil Pi was higher in temperate grasslands (4.2-13.1 µg P g -1 soil dry weight) compared to tropical forest soils (0.07-0.13 µg P g -1 soil dry weight).Acid phosphomonoesterase activities of tropical forest soils (1396-2346 nmol MUF released g -1 dry weight h -1 ) markedly exceeded those in temperate grasslands (233-256 nmol MUF released g -1 dry weight h -1 ).

Abiotic controls: soil sterilization efficiency
A separation of biotic and abiotic processes is based on the comparison of gross rates using the IPD assay in live versus autoclaved soils, where the latter should not exhibit any microbial activity (no FDA hydrolysis activity) and no extracellular enzyme activities (no MUF-phosphatase activity), in order to serve as abiotic controls.An incomplete inhibition of extracellular phosphatase activities would lead to an underestimation of biological processes and therefore of gross Po mineralization.Our results show that two consecutive treatments of the soils by autoclaving, with a 48 hours incubation in between, effectively reduced microbial metabolic activity as shown by the reduction in soil FDA hydrolysis by 90% in soil 4 and by 97-99% in all other soils (Fig. 3).Autoclaved soils did not show any increase in soil microbial activity during the two days of incubation.On the contrary, the inhibition of FDA hydrolysis even increased from 1 hour (all soil average: 94%) towards 24 and 48 hours after sterilization (average: 97-99%).The inhibition of extracellular acid phosphatase activity was almost complete in tropical soils (95-97%) and strongly reduced in temperate soils (79-80%).Similar to FDA hydrolysis the extent of inhibition of phosphatase activity increased from day 0 (average: 86%) to day 1 and 2 (average: 88-89%, Fig. 3).

Comparison of isobutanol fractionation and direct measurements of Pi and 33 P activity
Soil Pi concentrations measured by the malachite green method directly in acidified bicarbonate extracts were compared to those measured after isobutanol fractionation by phosphomolybdate blue reaction, including both live and sterile soils.Both approaches yielded similar soil Pi concentrations, and the relationship showed no bias (slope = 0.979±0.033,mean±1SE), with a coefficient of determination of 0.92 (Fig. 4B).The malachite green method is much more sensitive and therefore produced more reliable results for the low-P soils from the three tropical forests.
Moreover, the relationship between 33 P recoveries by isobutanol fractionation and by direct measurements in acidified bicarbonate extracts had a slope less than 1 (slope=0.875±0.010;Fig. 4A), indicating no significant formation of 33 Po during soil incubations.We also found no 33 Po formation in other soils using the same measurement protocols, e.g. from the Jena biodiversity experiment (82 plots of temperate grassland varying in soil texture and plant biodiversity, slope=0.891±0.017)and from French Guyana (24 soils from two primary forest regions, with soils sampled across topographic gradients, slope=1.043±0.020)(same regression types as in Fig. 3A; data not shown).The specific activities of Pi were indistinguishable between both approaches for temperate soils (slope=0.977±0.064,R 2 = 0.93, P<0.0001; Fig. 4C) but varied strongly for the tropical soils, where soil Pi measurements in the isobutanol fraction were at or below the limit of detection of the phosphomolybdate blue method.Specific activities of Pi were initially higher in live than in sterile soils (Fig. 4C).This was caused by the addition of the same amount of radiotracer to both, sterile and live soils, but autoclaving caused a flush of Pi from lysed soil microbes, which effectively lowered the specific activities of Pi in sterile soils.

Sensitivity of the IPD assay
The sensitivity of this assay is greatly improved relative to traditional ones, by using a combination of bicarbonate extractions and malachite green Pi measurements.The detection limit of the IPD approach was 0.12 µg P g -1 soil dw d -1 , based on three times the standard deviation of gross Po mineralization, measured for the three tropical soils (each measured in triplicates), and therefore fully suitable across all soil types tested so far.However, the precision suffers from IPD equations that combine uncertainties from four measurements, two Pi concentrations and two radioactivity measurements for the two time points in live as well sterile soils.The coefficients of variation (CV) ranged between 1.0 and 22.1% (average 10.0%) for Pi concentration across temperate and tropical soils, and between 1.5 and 22.1% (average 9.6%) for SA, the two major input variables into the IPD equation.CVs increased towards lower Pi concentrations and higher SA values, i.e. closer to the detection limit of the malachite green method.The CVs might be reduced by working with larger soil aliquots (increase from 2 to 5 or 10 g soil fresh weight) and by duplicate measurements of all samples.Purely methodological CVs were lower, at about 2.5 and 0.9% for Pi measurements by malachite green in the range 3-12 and 12-120 µM, respectively, and 0.8% for liquid scintillation counting.Therefore, much of the shown variability derived from differences between biological soil replicates.However, the variability found here compares well with CVs published for soil Pi concentrations of 2-10% (Bünemann et al., 2007) and 20-25% (Bünemann et al., 2012), and CVs for measured E values that are calculated from Pi concentrations and 33 P recoveries analogous to SA values ranged between 6-16% (Bünemann et al., 2007), 8-19% (Bünemann et al., 2012) and 9-10% (Randriamanantsoa et al., 2015) across a range of cultivated and non-cultivated soils from temperate to tropical regions.These variations naturally propagate into higher errors in the measured rates of soil P cycling and increase the limit of detection and the limit of quantification of the various methods.

Time kinetics
During the first hour of the incubation, we found a rapid drop in 33 P recovery and in the SA of Pi (Fig. 4), while soil Pi concentrations increased slightly (Fig. S1).Thereafter a dynamic equilibrium between added 33 P tracer and the soil Pi pool was reached and concentrations of extractable Pi remained constant.A plot of ln( 33 P recovery) versus time of both live and sterile soils showed that the consumption of 33 P occurred linearly between 4 and 48 h in the temperate soil and between 2 and 24 h in the tropical soil (Fig. 5).Similarly, the plot of ln(SA of Pi) versus time showed a linear relationship from 4 to 48 h in the temperate soil and for 2 to 48 h in the tropical soil, particularly in live soils (Fig. 5), showing constant dilution of the isotopic signature of the pool over time.The regressions became insignificant in the sterile tropical soil, as 33 P recovery and SA declined more slowly.The data clearly show that abiotic 33 P processes (i.e.decreases in 33 P recovery and SA of Pi over time in sterile soils) occurred, particularly in the temperate soil, and this over a prolonged period of time.More importantly, the dynamics of abiotic 33 P processes changed over time: rapid abiotic immobilization during the initial 0-4 h was followed by a period of slower but linear tracer immobilization.

Net 33 P immobilization by abiotic and biotic processes
Abiotic net 33 P immobilization (net soil P fixation) increased markedly from 0 to 48 h in the grassland soil (17 to 58% of added tracer), while it reached 83% almost instantaneously in tropical soil and further increased to 90% after 48 h (Fig. 6A).Similar patterns were found across all 6 soils, with significantly higher abiotic net immobilization in tropical than temperate soils, increasing in both with time from 0 to 4 and 24 h (Fig. 6C).Biotic (microbial) net 33 P immobilization ranged from 3 to 8% in the tropical soil and 8 to 17% in the temperate soil in the time kinetics experiment, with a significant increase in the temperate but not in the tropical soil (Fig. 6B).
Similarly, biotic net 33 P immobilization was low but increased with time in all three tropical soils (3 to 6%), while it was significantly higher in temperate soils but increased (soil 6) or decreased (soil 2 and 4) with time (Fig. 6D).
Microbial immobilization was very fast, with almost instantaneous 33 P uptake by microbes (sampling at 0 h), ranging between 3% (tropical soils) and 15-38% (temperate soils).Given the strong changes in both abiotic and biotic net 33 P immobilization, we suggest that it is best to measure them after 24 (up to 48) h.
Sequential extraction-liquid chloroform-extraction (sECE) was applied to directly follow net 33 P uptake by microbes, whereas biotic net 33 P immobilization was estimated indirectly as the difference in net 33 P immobilization by live and sterile soils.In the two measured soils, sECE estimates of microbial net 33 P uptake were higher than the microbial net 33 P immobilization estimates (temperate soil: 24.6% vs. 16.0%, and tropical soil: 16.8% vs. 7.5%, for direct and indirect estimates, respectively).This indicates incomplete extraction of exchangeable Pi prior to microbial lysis with chloroform and re-extraction.

33 P pool dilution rates of abiotic and biotic processes
We calculated gross Pi influx and efflux rates for live and sterile soils.Calculated rates of sterile soils provide estimates of gross rates of soil Pi sorption and desorption, and the difference between live and sterile soils give the biotic influx (gross Po mineralization) and efflux (gross microbial Pi uptake).Gross Po mineralization significantly differed between soils, with two out of three temperate soils (0.48 to 2.03 µg P g -1 dw d -1 ) exhibiting higher rates than two out of three tropical soils (0.08 to 0.15 µg P g -1 dw d -1 ) (Fig. 7A).Gross rates of Pi sorption in temperate soils (2.06 to 6.14 µg P g -1 dw d -1 ) were higher than in tropical soils (0.15 to 0.32 µg P g -1 dw d -1 ), and a similar trend was found for gross rates of microbial Pi uptake (temperate: 0.44 to 1.13 µg P g -1 dw d -1 , tropical: 0.05 to 0.12 µg P g -1 dw d -1 ; Fig. 7B).Gross rates of soil Pi desorption were significantly higher in temperate soils (1.44 to 3.63 µg P g -1 dw d -1 ) than in tropical soils (0.04-0.14 µg P g -1 d -1 , Fig. 7A).The relative contribution of Po mineralization to total Pi release into the soil Pi pool ranged between 25.0 and 73.8%, with two tropical P-poor soils showing the highest contributions (Fig. 7C).Contributions of biological processes to gross Pi immobilization did not differ between soils (range 11.5% to 34.9%).

Physicochemical and biological controls on soil Pi processes
Gross Po mineralization was strongly positively correlated with total soil P (R 2 =0.87,P<0.01, Fig. 8A) and to total as well as extractable soil Pi concentration (R 2 >0.83,P<0.05, Fig. 8B) but not to soil organic P or its contribution to soil total P, nor to soil organic C, soil texture or soil acid phosphatase activity (Table S1).Gross abiotic Pi release rates through desorption and dissolution were strongly positively related to total soil P and bicarbonate soil Pi (R 2 =0.97 and 0.98, respectively, both P<0.001, Fig. 8C and Table S1), but not to other parameters such as soil pH, soil texture, and soil organic C content.Gross Pi sorption rates exceeded gross Pi desorption rates approximately 2-fold, but both were strongly related (R 2 =0.99,P<0.001, Fig. 8E).Gross Pi sorption rates were strongly positively related to soil total P (R 2 =0.96,P<0.001, Fig. 8D), soil total Pi (R 2 =0.88,P<0.05, Table S1) and bicarbonate soil Pi (R 2 =0.99,P<0.001, Table S1), but neither to soil pH, soil organic C, nor to clay content or soil texture.Abiotic net Pi immobilization was most strongly and negatively related to soil pH (R 2 =0.95,P<0.001, Fig. 8L) and weakly to soil Pi sorption (R²=0.59,P=0.073, Fig. 8J).Gross microbial Pi uptake rates were directly proportional to microbial biomass P measured by sECE (R 2 =0.95,P<0.01, Fig. 8G), and positively related to net microbial Pi immobilization (R 2 =0.85,P<0.01, Fig. 8I).We found a negative curvilinear relationship between net immobilization rates by sorption and microbes (R 2 =0.97,P<0.001, Fig. 8F).

Discussion
About a decade ago Kellogg et al. (2006) compared two IEK techniques with an IPD approach, identifying several biases of the different approaches and making recommendations for further development.The authors highlighted IPD approaches with soil extractions using 0.5 M sodium bicarbonate as best suited, for potentially any type of soil.However, this approach is currently underused and had issues with abiotic controls.IPD methods are stateof-the-art to measure gross processes of soil N cycling (Murphy et al., 2003), but have rarely been applied to soil P cycling processes (Mooshammer et al., 2012;Di et al., 2000;Kellogg et al., 2006).We here present a novel and versatile approach to derive quantitative estimates of soil P cycling processes that drive soil P availability in low to high P soils.The approach quantifies gross rates of soil Po mineralization and the abiotic release of Pi from nonextractable soil Pi pools (Pi desorption and dissolution), both causing gross influx of Pi into the soil available Pi pool.Furthermore, gross rates of Pi immobilization by soil sorption and precipitation and by microbial uptake processes are derived from the same data by calculating the efflux from the soil Pi pool in sterile soils (abiotic) and in live minus sterile soils (biotic processes), respectively.
In contrast to many earlier IEK assays the IPD approach presented here is based on real isotope pool dilution theory (Kirkham and Bartholomew, 1954), and not on curvilinear extrapolation of E values (Table 1).
Moreover, IEK assays of Po mineralization necessitate steady-state conditions (constant Pi and microbial biomass P pools, and constant rates of isotope exchange and respiration) to allow extrapolation of short-term exchange processes to the full length of the moist soil incubation experiments.IPD approaches can accommodate non-steady state conditions as caused by flush effects and disturbances (Mooshammer et al., 2017) or as induced by addition of organic matter.The equations to estimate IPD rates can easily be solved for soils where target pool concentrations increase (net mineralization) or decrease (net immobilization) over time and where microbial biomass P changes (Kirkham and Bartholomew, 1954), and do not necessitate constant pool sizes as wrongly suggested previously (Di et al., 2000;Randhawa et al., 2005).

Soil sterilization
33 P IPD experiments in soils differ from the more common 15 N IPD variants for gross N processes (Murphy et al., 2003), since the persistence of abiotic P processes over time (Figs. 5 and 6) needs to be accounted for via the use of sterile soils.Our data clearly show that the dynamics of abiotic 33 P processes change over time.Therefore, the IPD rates in the sterile soils need to be measured over the same time period and under similar environmental conditions as in the live soils.It is likely insufficient to extrapolate from short-term (100 min) batch incubations run under very different conditions to correct for abiotic processes in the respective live moist soil incubations over weeks.Bünemann et al. (2007) indicated that batch incubations (1:10 (w:v) soil: water suspensions) have higher water-soluble and isotopically exchangeable Pi concentrations (measured as extractable Pi and as E values) and tended to have higher tracer recoveries (measured as r/R, i.e. water-soluble 33 Pi recovered relative to total 33 Pi added) compared to moist soil incubations.Incubation conditions should therefore also match between live and sterile soils.
We chose autoclaving as the sterilization procedure as other procedures only reduce or eliminate microbial activity (gamma irradiation, azide, mercuric chloride, toluene or chloroform treatment) but do not curtail extracellular enzyme activities (Blankinship et al., 2014;Wolf et al., 1989;Tiwari et al., 1988;Oehl et al., 2001b).
Given that Po mineralization is mediated by extracellular phosphatases, previous isotope experiments using shortterm batch experiments with or without microbicides or γ-irradiation therefore did not inhibit phosphatases and therefore did not allow to separate abiotic and biotic processes of Pi release in soils.While application of phosphatase inhibitors might be another viable option, we are only aware of one study testing this; application of silver nanoparticles to soils showed a general inhibitory effect on soil enzymes (Shin et al., 2012).Previous tests in our laboratory with two commercial phosphatase inhibitor cocktails (Sigma-Aldrich) at 10-fold of the recommended final concentration did not significantly decrease IPD rates in two soils (data not shown), indicating an insufficient inhibition of extracellular phosphatases.However, more rigorous tests of soil enzyme activities with synthetic substrates (e.g.MUF-Pi) and of P mineralization based on 33 P-IPD using increasing concentrations and different types of commercial phosphatase inhibitor cocktails might make clear whether this approach is viable or not.In contrast, autoclaving soils twice was highly efficient in suppressing biological activities, and those soils had no or very low extracellular enzyme activity and no residual microbial metabolic activity.Previous studies showed (almost) total inhibition of hydrolytic enzyme activities (including phosphomonoesterases) by autoclaving, in a wide range of arable, grassland and forest soils (Serrasolsas et al., 2008;Kedi et al., 2013;Blankinship et al., 2014;Tiwari et al., 1988).Other studies demonstrated successful killing of bacterial and fungal cells in soils by autoclaving (Carter et al., 2007;Blankinship et al., 2014;Serrasolsas and Khanna, 1995b;Alphei and Scheu, 1993)).
Most importantly, the final step in Po mineralization is catalyzed by phosphomonoesterases, which were fully inactivated by autoclaving in all soils tested so far.
It must be noted that autoclaving could potentially alter the physicochemical properties of soils, thereby affecting abiotic sorption-desorption kinetics.Despite this, in previous studies autoclaving up to two times and steam sterilization did neither affect the cation exchange capacity, nor base saturation, soil surface area, contents of total organic carbon and total nitrogen, and only slightly soil pH (Wolf et al., 1989;Tanaka et al., 2003;Serrasolsas and Khanna, 1995b).Autoclaving might however weaken soil aggregates and therefore increase the number of sites accessible for sorption-desorption processes that were previously hidden in aggregates.
However, we did not find clear support for or against this in the literature as autoclaving only weakly affected soil aggregate size distribution, causing a 0.5 to 1% increase in clay-sized compared to silt-sized aggregates (Berns et al., 2008).In contrast, aggregate stability and aggregation increased upon autoclaving in two other studies (Lotrario et al., 1995;Salonius et al., 1967).Effects of autoclaving on soil aggregation and soil P dynamics could be tested by measuring P processes rates on intact aggregates <2 mm and after destroying them by ultrasonication or grinding.In our study autoclaving caused a pulse of labile P into the available soil P pool due to the lysis of microbial biomass (Fig. S1), as has also been demonstrated for P and N by Serrasolsas and Khanna (1995a, b).
Soil Pi concentrations increased significantly in the autoclaved soils studied here, but only by an average of 1.86fold in the three temperate soils and by 1.65-fold in the three tropical forest soils, which was in the range found by others, e.g.1.3-to 1.6-fold (Skipper and Westermann, 1973) and 1.5-to 1.6-fold (Anderson and Magdoff, 2005) but lower than reported elsewhere, e.g.2.6-to 11-fold (Serrasolsas and Khanna, 1995a).Autoclaving was also demonstrated to increase the tracer recovery (r/R) and decrease the velocity of its decline over time as expected due to loss of microbial biomass (Bünemann et al., 2007).Autoclaving therefore slightly affects the soil Pi pool, but most likely has minor effects on its abiotic sorption/desorption dynamics while it inhibits biological reactions.
Nonetheless, the effects of microbial lysis on Pi sorption-desorption could be tested in sterile soils by adding increasing concentrations of non-labelled Pi alongside the 33 Pi tracer and then could be corrected for in future 33 P-IPD experiments.As stated earlier, changes in Pi concentration caused by autoclaving can easily be accounted for in IPD approaches, as long as abiotic process rates remain unaffected by the treatment.However, the estimation of the contribution of abiotic and biotic processes is based on calculating the difference in P fluxes between sterile and non-sterile soils.This assumes that biotic and abiotic fluxes are additive while there is potential that both processes compete for available Pi.In this case we would overestimate abiotic process rates in autoclaved soils, due to lack of competition by biotic processes.This could effectively cause an underestimation of biotic processes i.e. organic P mineralization and microbial Pi uptake.To date we have no approach at hand to cope with this potential bias.Overall, there is therefore potential for method improvement, particularly in terms of using abiotic controls circumventing autoclaving (e.g.bacteriozides combined with phosphomonoesterase inhibitors) or correcting for autoclave-induced changes in aggregation and in soil Pi content.

Soil Pi extraction using bicarbonate
Similar to 15 N IPD assays, where salt extractions are employed to target the available inorganic or organic N pool (Murphy et al., 2003;Wanek et al., 2010;Hu et al., 2017), we focused on the potentially bio-available, saltextractable Pi pool that reflects the plant-(and microbial) accessible amount of soil Pi better (Fardeau et al., 1988;Olsen et al., 1954;Horta and Torrent, 2007) than the water extractable Pi pool that is mostly assessed with soil IEK methods.The applied 0.5 M NaHCO3 extraction (pH 8.5, Olsen P) promotes the displacement of Pi (and the extraction of labile Po), particularly from Al-Fe (hydr)oxides and soil organic matter, by competition of bicarbonate anions with Pi.The underlying process is an increase of the negative charge on surfaces and a decrease of the concentration and activity of Ca 2+ and Al 3+ , thereby increasing P solubility in acid to alkaline soils (Horta and Torrent, 2007;Schoenau and O'Halloran, 2008;Demaria et al., 2005).Several studies compared soil P tests like Bray III, resin P, and Olsen-P to soil water Pi and plant P uptake in order to assess how well they reflect the available Pi pool.These studies demonstrated that soil tests like bicarbonate extractions (Olsen-P), resin P and DGT (diffusive gradients in thin films technique) closely resembled the SA values of Pi extracted by water or 10 mM CaSO4 or from plants (Six et al., 2012;Fardeau et al., 1988;Demaria et al., 2005).Others further showed that isotopically exchangeable Pi in soil water extracts (E values) and those extracted by plant roots in plant growth experiments (L values) also were strongly related (Bühler et al., 2003;Frossard et al., 1994).Bicarbonate extracted 8-to 22-fold greater amounts of exchangeable Pi compared to water and SA of Pi in bicarbonate extracts reached 66-90% of the SA values measured in soil water extracts (Demaria et al., 2005).IPD approaches require fast extractions to quickly terminate the assay after 4 and 24 h, which renders water extractions (generally 16 h), resin P (16 h) and DGT (up to 48 h in low P soils; (Six et al., 2012)) impossible.Bicarbonate extractions only take 30-60 min and therefore represent a viable alternative.Moreover, it makes the IPD assay on average 8-fold more sensitive as a greater amount of exchangeable Pi is extracted by bicarbonate than with water (Kleinman et al., 2001).Underestimation of this labile Pi pool -even if specific activities thereof are correctly measured -also causes underestimation of IPD rates given that Pi concentrations linearly affect IPD rates according to IPD equations 1 and 2 above.

Microbial P dynamics
We observed very fast microbial Pi immobilization in live soils (within minutes; extraction started directly after tracer addition), causing net immobilization of 33 P by 3-38%.Similar results were reported within 1.5 to 4 h by others, ranging from 6-37% (Bünemann et al., 2012;Kellogg et al., 2006).This has two major repercussions: (i) rapid uptake might cause microbial Pi assimilation and efflux or exudation of 33 Po metabolites without microbial death and turnover.However, the comparison between specific activities and 33 P recoveries of the direct measurement and after isobutanol fractionation (see below, and Fig. 3) showed that no significant release of microbial 33 Po occurred during the 24 and 48 h incubations.The short extraction times used in this study also decrease the likelihood of significant hydrolysis of Po compounds.(ii) Rapid microbial 33 Pi uptake clearly rules out the use of Po mineralization assays that measure abiotic IEK in short-term batch experiments (100 min) without addition of a microbicide or without prior sterilization and then extrapolate these "abiotic" process rates to the full experimental duration.
Microbial Pi uptake can be derived indirectly as the difference in 33 P recovery between live and sterile soils (Fig. 5, this study), more directly by sECE (this study), or by parallel water or bicarbonate extraction with and without addition of liquid chloroform or hexane (measuring resin strip or extractable Pi), or by chloroform fumigation extraction (Bünemann et al., 2012;Oberson et al., 2001;Oehl et al., 2001a;Spohn and Kuzyakov, 2013).
Microbial net 33 P immobilization measured by direct sECE was higher relative to the difference in 33 P immobilized in live minus sterile soils, pointing towards (i) overestimation of microbial net 33 P immobilization by sECE due to incomplete extraction of non-microbial 33 Pi by one-time bicarbonate extraction prior to sECE, or (ii) overestimation of abiotic sorption processes by autoclaving.In favor of (i) repeated extractions of soils with Bray I-extractant showed that soils continued to release P at lower rates in subsequent extractions after readily extractable P was removed by the first extraction (Serrasolsas et al., 2008;Messiga et al., 2014).Repeated extractions with bicarbonate also showed that the first extraction only removed 67-78% of the 33 Pi that was extractable with three consecutive extractions (D.Wasner, data not shown).In favor of (ii) (Kellogg et al., 2006) found higher net 33 P immobilization or sorption in sterile compared to live soils.This was interpreted as a lack of microbial competition for P in sterile soils.However, we found a weak positive relationship (R=0.749,P=0.087; Table S1) between gross microbial Pi uptake and gross Pi sorption.This opposes the idea of strong competition between sorption and microbial uptake on the basis of gross process measurements.Another possible mechanism underlying (ii) could be changes in soil structure and reactive surfaces enhancing soil P sorption.

Comparison of isobutanol fractionation with direct measurements of Pi and 33 P activity
We showed that 33 P IPD assays can be performed specifically on the Pi pool using isobutanol fractionation in high P soils.However, due to low production or persistence of 33 Po, results closely conformed with measurements run without Pi-Po fractionation by malachite green and direct 33 Ptotal estimates.This was ascertained for forest soils from French Guyana and Costa Rica, and for grassland soils from Austria and Germany (data not shown for French Guyana and Germany).Isobutanol fractionation has previously been applied in radiotracer studies on P dynamics in soils (Kellogg et al., 2006) and litter (Mooshammer et al., 2012), to ascertain the separation of Pi from any possible radiolabeled Po contaminant, however without comparison to SA in unfractionated bicarbonate extracts.Oehl et al. (2001a) also applied isobutanol fractionation to water extracts of fumigated and control soils, demonstrating that with long extraction times (16 h), 33 Pi activities in water extracts with and without isobutanol fractionation were comparable.It was suggested that 33 Po possibly released during fumigation was cleaved by soil phosphatases during extraction.This may not apply for short-term extractions (e.g.0.5 M NaHCO3 for 30 min, as used in this study) where hydrolysis by phosphatases would not necessarily occur due to short contact times.
Measurements of 33 P isotope pool dilution in soils based on bicarbonate extracts can therefore be interchangeably be performed by (i) direct measurements of 33 Ptot and Pi in acidified bicarbonate extracts and after (ii) isobutanol fractionation on 33 Pi and Pi.However, this needs to be validated for other types of soil, and may change significantly after longer incubation periods (weeks), when microbial 33 Pi uptake, assimilation and turnover causes the release of 33 Po into the soil.The short cut by performing direct measurements of Pi concentration and 33 P in acidified bicarbonate extracts comes along with 4-to 10-fold greater sensitivity of the malachite green assay relative to phosphomolybdate blue measurements of soil Pi.Another option to increase the measurement sensitivity for Pi (and possibly also for 33 Pi) for strongly sorbing low-P soils has been adopted by Randriamanantsoa et al. (2013), based on concentration of the phosphomolybdate blue complex from a large volume of extract into a smaller volume of hexane, with subsequent phase separation (Murphy and Riley, 1962).This allowed to decrease limits of quantification of Pi by 66-fold compared to the classical Murphy-Riley protocol, and 14-fold compared to the malachite green procedure (Randriamanantsoa et al., 2013) but involves the handling of large volumes of radiolabeled extracts.

Time kinetics
During the first minutes, equilibration between tracer and tracee was not achieved, indicated by the enhanced extractability of added tracer ( 33 Pi) relative to more strongly bonded native tracee (soil exchangeable Pi).The fast process of equilibration caused very rapid declines in SA of Pi during the first few minutes.Thereafter, microbial uptake and soil P fixation caused a rapid draw down of extractable 33 Pi and thereby a further decrease in the SA of soil Pi while soil Pi concentrations did not change after the initial phase of tracer-tracee equilibration (Fig. 4).
These processes slowed down within the first 1-2 h but did not seize, and declines in 33 P recoveries and in the SA of Pi occurred over the whole incubation period, in sterile as well as live soils.Thereafter time kinetics of IPD were relatively constant between 4 and 24 h for both, temperate and tropical soils, as shown by the linearity of the relationship in a plot of ln(SA of Pi) versus time.This linear relationship is conceptionally different from the plot of log(recovery, r/R) versus log(time) in short-term IEK batch experiments, that provides the parameter "n", i.e.
the slope or the rate of decline in tracer recovery due to sorption over time (Bünemann, 2015).Based on constant IPD rates in the above-mentioned time interval we advise to run 33 P pool dilution experiments for an incubation period of 4 to 24 h.This time frame is well within the linear range, as it lies after the rapid abiotic equilibration, and is long enough to allow significant pool dilution to occur for sensitive measurements of organic P mineralization.Longer incubation times are not recommended due to the risk of 33 Po release from dying microbes, potentially causing a 33 Pi reflux through remineralization, violating a major assumption of IPD theory.

Comparison of Po mineralization rates with published values
The detection limit of the IPD approach was 0.12 µg P g -1 soil dw d -1 .In comparison, the detection limits for gross Po mineralization by the IEK approach were 0.20 µg P g -1 soil d -1 by the modified protocol including hexane concentration of phosphomolybdate blue for tropical soils (Randriamanantsoa et al., 2015) and 0.6-2.6 µg P g -1 soil d -1 by the traditional IEK approach on temperate soils (Bünemann et al., 2007).Values of gross Po mineralization measured via IPD in this study ranged between 0.08-0.15µg P g -1 soil dw d -1 in tropical forest soils and 0.48-2.03µg P g -1 soil dw d -1 in temperate grassland soils and were therefore well in the range of those compiled for IEK measurements by Bünemann (2015) for 14 different soils, including temperate arable, grassland and forest soils (0.1-12.6 µg P g -1 soil dw d -1 ) and one tropical arable soil (0.8 µg P g -1 soil dw d -1 ).To date, highest gross Po mineralization rates were reported for decomposing beech litter, i.e. 22.5-86.3µg P g -1 soil dw d -1 (Mooshammer et al., 2012).A direct comparison of the present IPD and the IEK approaches on the same soils might help to clarify how far the approaches really deviate or converge in their gross Po mineralization rate estimates.

Physicochemical and biological controls on soil Pi processes
We found that gross Po mineralization was strongly positively correlated to total soil P but not to soil organic P, soil organic C, soil texture or soil acid phosphatase activity.This indicates that gross Po mineralization might rather be driven by total P than by soil enzyme activity, and that total soil Po does not well represent the Po fraction accessible to soil phosphatases.A few studies demonstrated positive correlations between gross Po mineralization and soil Po (Lopez-Hernandez et al., 1998) or litter Po (or its inverse C:P; (Mooshammer et al., 2012)).However, Wyngaard et al. (2016) did not find this relationship of gross Po mineralization with total soil Po but with the Po content of the coarse soil fraction only, which points into a similar direction as our results.Moreover, Po mineralization might be controlled rather by soil phosphodiesterases targeting DNA, RNA, teichoic acids and phospholipids, than by phosphomonoesterases that are responsible for the final extracellular dephosphorylation of Po.In contrast to our results, positive relationships were found between gross Po mineralization and phosphomonoesterase activities in two studies (Spohn et al., 2013;Oehl et al., 2004), however not across studies (Bünemann, 2015).A larger set of soils varying in soil pH, texture and mineralogy might therefore provide better insights into the controls of soil Po mineralization, such as effects by extracellular phosphatase activity (phosphomonoesterases and phosphodiesterases), and the availability, stabilization and accessibility of organic P in soils, among others.Moreover, high Pi availability (i.e., bicarbonate Pi) strongly suppressed phosphomonoesterase activity in soils, causing a negative correlation between the enzyme activity and extractable Pi.In contrast, extractable Pi was positively related to gross Po mineralization, indicating that high-Pi conditions suppressed phosphatase production but not Po mineralization across these soils.This was also found as a positive correlation between gross Po mineralization and water-extractable Pi by others (Schneider et al., 2017).
The contribution of gross Po mineralization to total Pi supply including Pi desorption from exchangeable Pi pools and dissolution ranged between 25 and 74%, with a trend towards larger contributions in low-P tropical soils (35-74%) compared to temperate soils (25-51%).This clearly demonstrates that biological processes contribute importantly to the Pi supply in soils, particularly in low-P soils, as also pointed out by (Bünemann, 2015).In low-P forest soils biological processes were shown to dominate over physicochemical processes, while in P-rich forest soils abiotic processes controlled gross Pi supply rates (Bünemann et al., 2016).It was also found that the contributions of microbial processes decreased with soil depth, where in deep soils diffusive fluxes (i.e. gross Pi desorption) dominated the soil Pi supply due to low total Po contents relative to total P (Achat et al., 2012;Achat et al., 2013).
Gross abiotic Pi release rates through desorption and dissolution were strongly positively related to total soil P and bicarbonate Pi, but not to other parameters such as soil pH, soil texture, and soil organic C content.In contrast to the weak effects of soil pH and texture on gross soil Pi supply, soil mineralogy and particularly oxalateextractable Fe and Al as proxy for Fe-Al (hydr)oxides play a major role in controlling abiotic dynamics of phosphate ions in soils, across the full range from acidic to alkaline soils (Achat et al., 2016).Fe-Al (hydr)oxides provide large positively-charged surface areas in weathered soils that are highly reactive to phosphate ions, more so than clay minerals such as kaolinite, illite and others (Hinsinger, 2001;Regelink et al., 2015).Soil mineralogy might therefore provide further interesting insights into the controls of abiotic processes as demonstrated by (Achat et al., 2011;Achat et al., 2016), but can also affect Po mineralization through strong effects on the sorption strength of organic matter and of Po compounds.Moreover, the elsewhere reported positive relations of Pi availability and Pi desorption with soil organic C contents was explained by competitive sorption of Pi and SOC or DOC to reactive surfaces such as positively charged metal (hydr)oxides (Regelink et al., 2015;Achat et al., 2016).
Gross Pi sorption rates exceeded gross Pi desorption rates approximately 2-fold but both were strongly related, indicating close and rapid cycling of available Pi through sorption-desorption processes.The observed rates indicate that soils immobilized more Pi then they mobilized by abiotic processes, causing an intermediate draw down of available Pi pools.Two processes work against this draw down of Pi in soils, i.e.Po mineralization and microbial P release through turnover and lysis.Moreover, plants (and microbes) might also desorb this sorbed Pi by release of phytosiderophores and organic acids and thereby replenish Pi and re-inject it in the organic P cycle.
Similar to the soil C-N cycle we might also expect an active "bank mechanism" regulating nutrient and C sequestration in soils (Fontaine et al., 2011).At high nutrient availability priming effects are low, allowing the sequestration of nutrients and SOC build-up.At low nutrient availability microbes (and plants) release nutrients from SOM and from mineral surfaces stimulated by root exudates, effectively mining inorganic and organic P stored in soils.
The strong positive relationship between gross Pi sorption rates and soil total P, soil total Pi and bicarbonate soil Pi, and the lack of relationship with soil pH, soil organic C, clay content and soil texture highlights again that specific soil minerals, particularly metal (hydr)oxides and to a lesser extent clay minerals such kaolinite, factors not fully captured by soil pH and soil texture alone, are responsible for Pi sorption in soils (Regelink et al., 2015).In IEK experiments it was found that the rate of abiotic Pi depletion from soil solution through sorption was positively related to Al-Fe (hydr)oxide content and negatively to soil organic C divided by Al and Fe oxide content (Achat et al., 2016;Tran et al., 1988).The strong negative relation between abiotic net Pi immobilization and soil pH re-confirms that strongly weathered, acid tropical soils have a higher P sorption and fixation capacity than temperate soils.
Finally, gross microbial Pi uptake rates were directly proportional to microbial biomass P measured by sECE.We also found greater Pi immobilization potentials through sorptive reactions (28-92%) than through biological sinks (5-37%) in the soils studied here.The importance of rapid net uptake of tracer by soil microbes has been demonstrated also by other studies, e.g.(Bünemann et al., 2012).However, the presented IPD approach for the first time allowed to estimate gross rates of microbial Pi uptake in addition to net microbial Pi immobilization.Gross rates of microbial uptake were calculated from the IPD approach, not necessitating the application of any extraction factor to calculate microbial biomass P from chloroform-labile P (kEP-factor).The use of extraction factors becomes necessary when studying net Pi uptake over prolonged time periods in tracer experiments and for correction of net Po mineralization rates (Bünemann, 2015;Bünemann et al., 2007).

Application and modeling
The combination of this IPD assay with advanced numerical modeling approaches, as applied by Müller and Bünemann (2014), might further enhance the precision of estimates of simultaneously occurring soil P cycle processes and thereby advance the knowledge of major controls of the transformations and fluxes of this important nutrient in terrestrial ecosystems.There is an ever-increasing need of high quality data on soil P processes, even more so to calibrate terrestrial biogeochemical models and incorporate nutrient controls on plant productivity in global models.This IPD approach may provide highly important quantitative data to implement soil P cycling processes into global biogeochemical models.This will further enhance our current understanding of nutrient controls on the global terrestrial C cycle and improve our capabilities to predict future changes by increasing discrepancies in N and P inputs into the terrestrial biosphere.

Figure 1 .
Figure1.Schematic representation of (A) major fluxes of soil P processes controlling the availability of inorganic P (Pi) in soils, and of (B) the isotope pool dilution principle showing influxes of unlabeled Pi ( 31 P) into the available Pi pool labelled by a spike of 33 Pi, and efflux of Pi at the ratio of 33 P: 31 P as present in the target pool.Biotic and abiotic processes of influx and efflux are presented.This causes (C) a decline in the specific activity of Pi i.e.33 Pi: 31 Pi declines over time in sterile soils (abiotic processes only) and live soils (biotic plus abiotic processes),

Figure 2 .
Figure 2. Schematic overview of the final isotope pool dilution (IPD) procedure.Abbreviations: MG, malachite green procedure and MR, Murphy-Riley procedure to measure Pi concentrations; LSC, liquid scintillation counting to measure radioactivity in extracts.Isobutanol fractionation separates dissolved Pi from Po and thereby allows highly specific measurements of concentrations and 33 P activities in Pi, without interference by 33 Po.Direct acidification of bicarbonate extracts measures dissolved Pi using malachite green but LSC quantifies the sum of

Figure 3 .
Figure 3. Response of soil enzyme activities to autoclaving: Percentage inhibition of (A) fluorescein diacetate (FDA) hydrolysis as a proxy for the inhibition of live, cell-bound microbial enzyme activity and of (B) MUFphosphomonoesterase activity as a proxy for the inhibition of extracellular enzyme activity.Temperate grassland

Figure 4 .(
Figure 4. Relationship between (A) 33 P recoveries as measured directly in acidified bicarbonate extracts and after isobutanol fractionation, relative to the added tracer amount, and between (B) Pi concentrations measured by the malachite green method in acidified bicarbonate extracts and after isobutanol fractionation following the phosphomolybdate blue approach.(C) Comparison of specific activities (SA) of Pi measured in acidified

Figure 5 .Figure 6 .Figure 7 .Figure 8 .
Figure 5. Test for linearity of change in 33 P recoveries (A, B) and in specific activities of Pi (C, D) over time, for a temperate grassland soil (A, C) and a tropical forest soil (B, D).Data presented are for 33 P measured directly in bicarbonate extracts of live soils (closed circles) and sterile soils (open circles), and are shown on y-axes in a logarithmic manner (LN).Regression lines follow exponential decay which in this linear -LN plot appears as Delineation of the causes could be performed by a comparison of sECE with liquid chloroform-fumigation extraction (CFE) i.e. parallel assessments of microbial 33 P uptake, using a comparison of 33 P in bicarbonate versus bicarbonate+liquid chloroform or bicarbonate+liquid hexane extracts.Given the continued extraction of Pi from exchangeable Pi pools in serial extraction tests, parallel determination of microbial P and 33 P by CFE is recommended compared to sequential extractions by sECE.

Table 1 .
Comparison of traditional isotope exchange kinetic (IEK) experiments and the novel isotope pool dilution (IPD) approach to measure organic P mineralization.