Soil solution phosphorus turnover: derivation ... · (Pierzynski and McDowell, 2005). The soil...

Biogeosciences 15 105ndash114 2018httpsdoiorg105194bg-15-105-2018copy Author(s) 2018 This work is distributed underthe Creative Commons Attribution 40 License

Soil solution phosphorus turnover derivation interpretationand insights from a global compilation of isotopeexchange kinetic studiesJulian Helfenstein1 Jannes Jegminat2 Timothy I McLaren1 and Emmanuel Frossard1

1Institute of Agricultural Sciences ETH Zurich Lindau 8315 Switzerland2Institute of Neuroinformatics University of Zurich and ETH Zurich Zurich 8057 Switzerland

Correspondence Julian Helfenstein (julianhelfensteinusysethzch)

Received 17 July 2017 ndash Discussion started 10 August 2017Revised 22 November 2017 ndash Accepted 23 November 2017 ndash Published 8 January 2018

Abstract The exchange rate of inorganic phosphorus (P) be-tween the soil solution and solid phase also known as soilsolution P turnover is essential for describing the kinetics ofbioavailable P While soil solution P turnover (Km) can bedetermined by tracing radioisotopes in a soilndashsolution sys-tem few studies have done so We believe that this is due toa lack of understanding on how to derive Km from isotopicexchange kinetic (IEK) experiments a common form of ra-dioisotope dilution study Here we provide a derivation ofcalculating Km using parameters obtained from IEK experi-ments We then calculated Km for 217 soils from publishedIEK experiments in terrestrial ecosystems and also that of18 long-term P fertilizer field experiments Analysis of theglobal compilation data set revealed a negative relationshipbetween concentrations of soil solution P and Km Further-more Km buffered isotopically exchangeable P in soils withlow concentrations of soil solution P This finding was sup-ported by an analysis of long-term P fertilizer field experi-ments which revealed a negative relationship between Kmand phosphate-buffering capacity Our study highlights theimportance of calculating Km for understanding the kineticsof P between the soil solid and solution phases where it isbioavailable We argue that our derivation can also be usedto calculate soil solution turnover of other environmentallyrelevant and strongly sorbing elements that can be tracedwith radioisotopes such as zinc cadmium nickel arsenicand uranium

1 Introduction

As an essential but often limiting nutrient phosphorus (P)plays a central role in food production and more efficientP management is key to improve food security (Tilman etal 2002 Syers et al 2008) Phosphorus limitation in agroe-cosystems is usually overcome by applying P fertilizers tothe soil surface However excessive applications of P fer-tilizer to soil can cause ecological societal and economicproblems First P fertilizer is largely derived from rock phos-phate which is a non-renewable resource and major depositsare located in only a few countries (Elser and Bennett 2011Obersteiner et al 2013) Second applications of P fertilizersto soils with a high P sorption capacity can be inefficient be-cause P largely accumulates in the soil in sparingly solubleforms (Roy et al 2016) Third leaching or runoff of P fertil-izer from agricultural land to aquatic and marine ecosystemscontributes to fish die-off and declining water quality (Car-penter et al 1998) To improve food security while reducingecosystem pollution it is essential that we improve our un-derstanding of soil P dynamics particularly the mechanismscontrolling P movement between the soil solid phase and thesoil solution where it is bioavailable

Plants take up P from the soil solution as ionic orthophos-phate (H2POminus4 or HPO2minus

4 ) via roots or mycorrhizal hyphae(Pierzynski and McDowell 2005) The soil solution typicallycontains low concentrations of P (Achat et al 2016) but thesoil solution can be replenished with P from the soil solidphase which can provide additional P for uptake by plants(Pierzynski and McDowell 2005) Therefore P exchange ki-netics or the rate at which the soil solution is replenished by

Published by Copernicus Publications on behalf of the European Geosciences Union

106 J Helfenstein et al Soil solution phosphorus turnover

P from the soil solid phase have important implications forthe P requirements of living organisms (Menezes-Blackburnet al 2016 Fardeau et al 1991) In this study we investigatea potential link between two different concepts phosphorus-buffering capacity and soil solution P turnover by analyzinga data set of global soils and P fertilizer experiments

Phosphorus-buffering capacity (PBC) is defined as theability of soil to moderate changes in the concentration ofsoil solution P (Pypers et al 2006 Olsen and Khasawneh1980 Beckett and White 1964) Historically PBC has beencalculated using Eq (1)

PBC=1conc of P in soil solution

1conc of P in the soil(1)

The traditional approach of determining PBC in soil is toadd various amounts of P to a soil suspension equilibrateand then measure the slope between adsorbed P and P in soilsolution (Olsen and Khasawneh 1980) Alternatively PBCcan be measured by analyzing the change in soil solution Pconcentration with regard to P budget in field P fertilizationexperiments (Morel et al 2000) These approaches have re-vealed that PBC is influenced by ambient temperature soilsolution pH and concentrations of P in the soil solution andis highly variable among soil types (Barrow 1983) One ofthe most important factors among soil types is the specificsurface area of FeAl oxides and clay minerals which are im-portant sites of P sorption (Geacuterard 2016) Whilst the afore-mentioned approaches are a useful and cost effective way tostudy soil P dynamics (Bolland and Allen 2003 Burkitt etal 2002 Barrow and Debnath 2014) they are not able todirectly determine the turnover of P in the solution

Soil solution P turnover (Km) is the mean rate of ex-change between phosphate ions in solution and inorganicphosphate in soil and can be calculated from parameters de-termined in an isotopic exchange kinetic (IEK) experiment(Fardeau 1996) Isotopic exchange kinetic experiments in-volve the use of P radioisotopes (32P or 33P) to directly mea-sure the exchange of P between the soil solid and solutionphases (Frossard et al 2011) They are based on the assump-tion that during the short-term experiments usually lasting100 min there is only physicochemical exchange but no bi-ological exchange (Oehl et al 2001) Measurements of iso-topically exchangeable P are a more accurate indicator of Pbioavailability than conventional soil tests based on chemicalextraction because the former involves a P radiotracer thatcan be directly measured and distinguished from all other Pions in the soil (Demaria et al 2005 Hamon et al 2002)Previous studies have shown that isotopically exchangeableP is the predominant source of P for most crops (Frossardet al 1994 Morel and Plenchette 1994) Though the IEKapproach does not consider root-induced pH alterations orsecretion of organic acids increased P availability due toroot exudates can be quantified by comparing isotopicallyexchangeable P with radioisotope uptake in plants (Hedleyet al 1982) Isotopic dilution in a soil solution system is

characterized by two statistically fitted parameters m and nwhich can be used to calculate Km using Eq (2) (Fardeau1985 Fardeau et al 1991)

Km =n

m1n

(2)

The importance of parameters m and n as well as their rela-tion to soil properties was recently investigated (Achat et al2016)

Despite several decades of using radioisotopes in P re-search and the potential relevance of soil solution P turnoverto understanding agricultural and natural ecosystems onlysix studies have published Km values and there has been nosynthesis of these values (Frossard et al 2011 Fardeau et al1991 Fardeau 1985 1993 Oberson et al 1993 Xiong etal 2002) We believe that this is because an intuitive deriva-tion of Km has never been published Whilst information onsoil solution P turnover remains limited Km values can eas-ily be calculated using data from previously published IEKexperiments

The first aim of our study was to provide a clear and in-tuitive derivation of the Km term Our second aim was tocalculate Km values from previously published IEK studieswhich resulted in a global data set of over 200 soils We thentested specific hypotheses related to concentrations of soil so-lution P and isotopically exchangeable P Our third aim wasto understand the relationship between PBC and Km Thisinvolved an additional data set based on long-term P fertil-izer field experiments which reported IEK results and the Pfertilizer budgets Lastly we carried out a sensitivity analysisof Km in order to assist in interpretation of future results

Our first hypothesis was that turnover of soil solution Pwould differ based on soil group More specifically we hy-pothesized that soil groups known to have higher concen-trations of sorption sites (such as Andosols and Ferralsols)would have faster turnover rates Our second hypothesis wasthat soils with higher concentrations of soil solution P (Pw)

would have lower values of Km compared to soil with lowerconcentrations of soil solution P This is because a high con-centration of sorption sites leads to fast adsorption and con-sequently low concentration of P in the solution Lastly wehypothesized that the dependence of isotopically exchange-able P on Pw and Km evolves with time

2 Materials and methods

21 Derivation of Km

A given volume of soil can be described as containing inor-ganic P in one of two states the soil phase or the soil solutionphase In any given time interval physicochemical reactionstransfer a fraction of P from the soil solution phase into thesolid phase The rate constant of this reaction is solution Pturnover Km (minminus1) Thus Km plays a critical role in deter-

Biogeosciences 15 105ndash114 2018 wwwbiogeosciencesnet151052018

J Helfenstein et al Soil solution phosphorus turnover 107

mining the time and amount of P that is potentially availableto plants At low values of Km there is little exchange

At equilibrium an underlying assumption of an IEK ex-periment the net flux between the phases is zero because ofthe balancing effect of the inverse flux ie the flux from thesoil phase to the solution phase through desorption and dis-solution In other words the inverse flux prevents us frommeasuring Km directly by fitting the temporal loss of P insoil solution If radioisotopes (for P either 32P or 33P) areinjected into the soil solution it becomes possible to exper-imentally eliminate the inverse flux Shortly after the injec-tion the radioisotope is not present in the solid phase andconsequently there is no inverse flux Equation (3) has beenfound to describe the resulting decline of radioisotope in so-lution (Fardeau et al 1991 Frossard et al 2011)

r(t)

R=m

(t +m

1n

)minusn

+r(infin)

R (3)

where r(t) is the radioactivity (Bq) measured at time t (min)R is the total amount of radioactivity added and m and n arethe model parameters that describe the rapid and slow physic-ochemical processes respectively Since Km is equivalent tothe decline rate of the radioisotope in the absence of an in-verse flux we analyze Eq (3) right after the injection (t = 0)and derive Eq (2) (for details on the derivation please seeSupplement)

Km is thus calculated in three steps first r(t)R is mea-sured then n and m are determined by nonlinear regressionand finally Eq (2) is applied A limitation of Km is that itdoes not take into account an indefinite number of P specieseach with their own exchange rate (Andersson et al 2016Menezes-Blackburn et al 2016 Geacuterard 2016) Also theIEK method as described above does not consider micro-bial uptake or mineralization of organic P (Oehl et al 2001)Therefore the variable Km should be considered as the av-erage P exchange rate of the soil solution with an indefinitenumber of solid inorganic P pools

22 Data set

We carried out a literature search for IEK studies reportingm n and Pw values based on the methodological approachof Fardeau et al (1991) Only values from topsoil layers(0ndash30 cm layer if reported) were compiled The data set in-cludes all papers cited by Achat et al (2016) in accordancewith our aforementioned selection criteria plus more recentpublications In addition data obtained from the publishedliterature were supplemented with unpublished data (sevensoils) from studies carried out in the Group of Plant Nutri-tion (ETH Zurich) This resulted in a final data set of 217soils taken from 41 references (see Supplement Table S1)The soils represented 19 soil groups across the world refer-ence base (IUSS Working Group WRB 2015) 26 countriesand all continents except Antarctica Eighty-five soils werefrom cropland 64 from grassland and 32 from forest while

for 36 soils land use was not specified Several studies (58soils) used a simplified version of Eq (3) Since the sim-plified version leads to only minor differences in parameterestimation we assumed that this would not affect calculationof Km (Fardeau et al 1991) To avoid overrepresentationsample sizes of two articles reporting many samples of sim-ilar soils were randomly reduced from 30 to 10 (Compaoreacuteet al 2003) and from 48 to 12 (Tran et al 1988)

In addition we carried out a literature search for IEK stud-ies on long-term P fertilizer field experiments We foundpublished data across 18 long-term experiment sites (Ober-son et al 1993 1999 Fardeau et al 1991 Gallet et al2003 Morel et al 1994) The soils represented the followingsoil groups (IUSS Working Group WRB 2015) CambisolsChernozems Ferralsols Fluvisols Gleysols and LuvisolsIn general the field experiments involved different types ofmineral and organic P fertilizers applied at varying rates Thedifference in inputs minus outputs led to a range in P budgetsfrom minus52 to 125 kg P haminus1 yrminus1

23 Data analysis

Isotopically exchangeable P (ie E values E(t) in mg kgminus1)the amount of P that can reach the soil solution within a giventime frame is calculated using Eq (4) (Hamon et al 2002Fardeau 1996)

E(t) = PwtimesR

r(t)(4)

While IEK experiments only last several minutes E(t) val-ues can be extrapolated beyond the IEK experiment based onEqs (3) and (4) (Frossard et al 1994 Morel and Plenchette1994 Buehler et al 2003) Extrapolated E(t) values arehighly influenced by concentrations of Pw One of the mainchallenges of the IEK experiment is the accurate and precisedetermination of Pw particularly in high P-fixing soils (Ran-driamanantsoa et al 2013) Analysis involving E(t) couldonly be performed for studies that reported Pinorg in additionto Pw m and n

To examine the relationship between Km and isotopicallyexchangeable P E(t) was calculated for t = 0 to 129 600 min(equal to 3 months) using Eq (4) First we calculated the dif-ference between E(1) and E(0) as log10(E(1)) ndash log10(E(0))We then tested if Km was a significant predictor of this differ-ence using linear regression To determine the timespan overwhich Km affected E(t) we performed linear regression be-tween Km and E(t) at t = 1 to 129 600 min We also carriedout linear regression with Pw and Pinorg as predictors of E(t)

over the aforementioned time points respectively Duringdata analysis we noticed that different Pw levels were dif-ferently sensitive to predictor variables Therefore we usedJenks natural breaks optimization to systematically partitionthe Pw data into three clusters using R package ldquoclassIntrdquo(Bivand et al 2015)

wwwbiogeosciencesnet151052018 Biogeosciences 15 105ndash114 2018

To show sensitivity of Km we assumed relative standarddeviations (standard deviationmean ) of 10 for each re-ported m and n Uncertainty was then approximated usingthe partial derivatives approach for error propagation (Eq 5Ku 1966) By assuming independent errors of the two fittedparameters we obtain an upper bound on the error of Km(Weiss et al 2006)

sKm =

radic(partKm

partm

)2

s2m+

(partKm

partn

)2

s2n (5)

We used R (R Core Team 2017) for all statistical analy-ses and to create the images All model regressions werechecked and the model fit determined using significance offit (p = 005) and the regression coefficient (R2)

24 Analysis of long-term field experiments

The P fertilizer budgets were calculated as the averageannual input of P fertilizer minus that of crop offtake(kg P haminus1 yrminus1) Each site had three to four P treatmentsusually one with a negative budget one with a balanced bud-get and one with a positive budget To determine the effectof P budget on Pw and Km we calculated the slope of linearregressions between P budget and Pw The slope of the linerelating Pw to P budget can be taken as a field PBC sincethe slope of Pw corresponds to the change in Pw over thechange in soil P concentration (Eq 1) Next we investigatedif there was a relationship between the thus-determined PBCand Km

3 Results and discussion

31 Global analysis of P turnover in the soil solution(Km)

The turnover rate of P in the soil solution ranged 9 orders ofmagnitude from 10minus2 to 106 minminus1 across the 217 soils sur-veyed (Fig 1) However approximately half of the soils hada P turnover rate within the range of 100 to 102 minminus1 Cleardifferences in Km between different soil groups suggest thatKm is related to soil properties governing kinetics of inor-ganic P in the soil solution system Surface soil horizons ofFerralsols had the highest values of Km followed by An-dosols and Cambisols (Fig 1) High Km values of Ferralsolssuggest that P in these soils is rapidly adsorbed ie thesesoils have a high P-buffering capacity Three of the four low-est Km values were found in Podzols soils which are knownto have low P-sorbing capacity (Chen et al 2003 Achat etal 2009)

Fardeau Morel and Boniface (Fardeau et al 1991)showed that Km is largest for small values of n and m andbecomes smaller as n approaches 05 and as m approaches1 Values of n and m have often been found to correlate

Figure 1 Violin plots of P turnover (Km) for different world ref-erence base soil groups Only soil groups with at least five obser-vations were plotted The number of observations in each violin iswritten next to the plot Violin plots were made using the R packageldquovioplotrdquo (Adler 2005)

with soil properties (pH carbonate concentration oxalate-extractable AlFe organic matter etc Tran et al 1988 De-maria et al 2013 Frossard et al 1993 Achat et al 2013)A global compilation study showed that low values of n oc-cur for soils with low concentrations of oxalate-extractableAl and Fe which are indicative of amorphous Al and Fe ox-ides (Achat et al 2016) In contrast low values of m tendto occur for soils with a low ratio of organic C to Al andFe oxides (Achat et al 2016) The high Km values of Fer-ralsols are due to extremely low m values (mean= 0025SD= 0012 n= 26) and are consistent with low ratios oforganic C to Al and Fe oxides typically reported in thesesoils (Randriamanantsoa et al 2013) The Podzols in thedata set on the other hand have distinguishably high m val-ues (Mean= 050 SD= 043 n= 14) consistent with thelow Al and Fe oxide content of the upper horizon of Pod-zols (Achat et al 2009) However small sample sizes persoil group and large spans in soil properties even within soilgroups mean that group-specific Km values should not beover-interpreted

Figure 2 Simple linear regression between soil solution P turnover(Km) and soil solution P concentration (Pw) for 217 soils Theequation is given by log10(Km)= 126minus 0960times log10(Pw) withF = 127 p lt 10minus15 and R2

= 037 Dashed lines represent the95 confidence interval

32 Relationship between soil solution P turnover (Km)

and concentration of soil solution P (Pw)

There was a negative correlation between Km and Pw asshown in Fig (2) and described in Eq (6)

log10(Km)= 126minus 0960times log10(Pw) (6)

with F = 127 p lt 10minus15 and R2= 037 The two variables

Pw and Km are important in governing plant-available P be-cause the former describes the amount of P in solution andthe latter describes the rate at which it is exchanged Att = 1 min the highest values of E(t) occurred for soils withhigh values of Km and Pw whereas the lowest values of E(t)

occurred for soils with low values of Km and Pw (Fig S1in the Supplement) The relationship was less clear at t = 1day (Fig S1) However the trend that lowest E values oc-curred for soils with a low Km and low Pw is still apparent att = 1 day

The negative correlation between Km and Pw confirms oursecond hypothesis that soils with high Pw would have lowKm and is in accordance with findings from other studiesusing different methodological approaches For example ithas been observed that sorption is less pronounced on heavilyfertilized soils due to more negative surface charge (Barrowand Debnath 2014) In our study high Km values imply thepresence of many potential binding sites where P may ad-sorb or precipitate This leads to a rapid exchange betweensorption sites and the soil solution as solution P quicklybinds to a new site Consequently Pw is low On the otherhand slower turnover rates of P in the soil solution and highPw occur when P-binding sites are few or saturated

33 Soil solution P turnover (Km) as a buffer ofisotopically exchangeable P (E(t))

We found that Km is an important buffer of isotopically ex-changeable P As t increases E(t) values diverge from Pwand eventually approach Pinorg Interestingly the range ofE(t) values decreased with time (Fig 3a) While Pw val-ues ranged almost 4 orders of magnitude E(1) values onlyranged 3 orders of magnitude Furthermore differences in E

values among soils of low middle and high Pw decreasedwith time We found that the difference between log10(E(1))

and log10(E(0)) was strongly correlated with log10(Km)

(F = 615 p lt 10minus15 and R2= 079) Thus soils with fast

rates of Km had large increases in E(t) compared to soils withslow rates of Km which showed little difference in E(t) fromE(0) to E(1) Furthermore soils with the largest increases inE(t) had low concentrations of Pw but high values of Km(Fig 3b)

While it is evident that E(t) and Km are related sinceboth variables are calculated from the same isotope exchangekinetic parameters the dependency reveals that many soilswith low concentrations of Pw attained E values comparableto other soils due to extremely high soil solution P turnoverrates (Fig 3b) One can thus interpret that a soil with highKm has a higher PBC and that a majority of P applied asfertilizer will be quickly adsorbed On the other hand highturnover means that there is a large flux of P ions throughthe soil solution and phosphate ions in solution are quicklyreplaced through desorption when plants take up P If soilswith E(1min) value of over 5 mg P kgminus1 are considered highlyP fertile (Gallet et al 2003) high P fertility can be found inboth soils with high Pw andor soils with low Pw but highKm (Fig S1) Soils with low Pw and low Km such as mostLixisols also have low E values Thus P fixing by soils isreversible and says little about P availability

34 Time frame over which Km buffers isotopicallyexchangeable P (E(t))

On which time frame is E(t) dependent on Km By perform-ing linear regressions among Pw Km and Pinorg respec-tively and E(t) for t = 1 min to 3 months we found thatthe fits are strongly dependent on Pw class (high middlelow) Based on Jenks natural breaks optimization three clus-ters of Pw were determined 0008ndash016 (n= 46) 016ndash19(n= 94) and 19ndash425 mg kgminus1 (n= 77) Calculating the R2

of the regression as a function of time showed that for theclass of high-Pw soils Pw explained 60 of variability inE(t) at 1 min (Fig 4a) However Pw lost power as a pre-dictor of E(t) rapidly explaining only 20 of variability byt = 60 min In contrast soils with low concentrations of Pwshowed no relationship between values of E(t) and Pw evenat short time spans Thus the concentration of P in the soilsolution has a strong legacy on plant P availability for soilswith high Pw at short time spans but does not indicate P

Figure 3 Soil solution P turnover (Km) as a driver of available P (E(t)) While there is a large range in P availability at t = 0 (Pw) thisvariability becomes smaller and gradually uncoupled from Pw class for longer time frames (t = 1 1440 129 600 min a) The growth in Pavailability between t = 0 and t = 1 is dependent on Km (b) Simple linear regression between Km and the difference between E(1) and E(0)

is given by log10(E(1)

)minus log10

(E(0)

)= 0170+0357times log10(Km) with F = 615 p lt 10minus15 and R2

= 079 n= 170 Red orange andgreen colors refer to classes of low middle and high Pw as determined by Jenks natural breaks optimization In (b) dashed lines representthe 95 confidence interval

Figure 4 R2 of simple linear regressions between isotopically exchangeable P (E(t)) explained by predictors Pw (a) Km (b) and Pinorg (c)as a function of time Regressions were fit separately for each class of Pw (low middle high) as determined by Jenks natural breaks opti-mization Low Pw = 0008ndash016 mg kgminus1 (n= 46) middle Pw = 016ndash19 mg kgminus1 (n= 94) and high Pw = 19ndash425 mg kgminus1 (n= 77)

availability in soils with low concentrations of Pw In thesesoils values of E(t) are primarily driven by Km (Fig 4b)Eventually both Km and Pw lose predictive power as E(t)

inevitably approaches Pinorg (see Eq 4 Fig 4c) Howeverpredictive power of Pinorg is again dependent on Pw class

E(t) over time spans between 1 min and 3 months weredifferently related to predictors Pw Km and Pinorg depend-ing on concentrations of Pw The effect of Km on E(t) isthus strongly dependent on Pw In P-depleted soils the kineticcomponent is crucial in predicting a soilrsquos P availability Anunderestimation of the kinetic components of P availabilitywill lead to over-fertilization of P-fixing soils In more P-richsoils however P availability can be relatively accurately as-

sessed with static measures ie the concentration of P in thesolution and the total inorganic P in the soil

35 Km buffers fertilizer application in long-termfertilizer experiments

There was a positive relationship between Pw and Pbudget across all 18 long-term P fertilizer experimen-tal sites which is consistent with the study of Morel etal (2000) However the slopes spanned 3 orders of mag-nitude from 0007 (mg P kgminus1 soil)(kg P haminus1 yrminus1Ferralsol Colombia Oberson et al 1999) to 39(mg P kgminus1 soil)(kg P haminus1 yrminus1 Chernozem CanadaMorel et al 1994) This shows that soil solution P is more

Figure 5 Simple linear regression between phosphorus-bufferingcapacity (PBC) and soil solution P turnover (Km) for 18 long-termP fertilizer experiments PBC was calculated as the slope of the re-gression between Pw and P budget PBC was found to correlate withKm as given by log10(PBC)= minus0481minus0482timeslog10(Km) withR2 of 040 (F = 108 p = 00047) Dashed lines represent 95 confidence interval

strongly buffered in some soils than others Results from thefertilizer experiments thus confirm that in high P-sorbingsoils such as Ferralsols additions of P fertilizers may lead toonly incremental increases in solution P concentration (Royet al 2016) However this does not necessarily translate toP availability (Pypers et al 2006)

PBC on the field experiments taken as the slope of Pw in-crease with increasing P budget was negatively dependenton Km (F = 108 p = 00047 and R2

= 040 Fig 5) Inother words soils with higher Km values were characterizedby slower increases in Pw at similar yearly P inputndashoutputbudgets and vice versa Both PBC and Km are measureswhich describe the exchange of P between the soil solutionand solid phases (Olsen and Khasawneh 1980 Fardeau etal 1991) However the two have never been directly relatedData from long-term field experiments enabled us to compareKm to field-scale PBC The fact that the two are correlated infertilizer field experiments thus underlines our findings fromthe global soil investigation that Km and PBC provide infor-mation on the same underlying processes

36 Implications for using Km

Most previous studies involving isotopic exchange kineticshave focused on analyzing m n and E values (Frossard etal 1993 Achat et al 2016 Tran et al 1988 Breacutedoire etal 2016) However m and n are simply statistical parame-ters whereas Km can be readily interpreted in terms of soilprocesses (Fardeau et al 1991) Km is the mechanism be-hind PBC and is useful in explaining P availability Howeverwhen using Km it is important to be aware of its limitations(as described in the methods section) and its sensitivity to theparameters m and n (Fig 6) Depending on the study a rel-atively large uncertainty for Km may be acceptable because

Figure 6 Relative standard deviations (RSDs) of Km after errorpropagation assuming 10 uncertainty in m and n input parame-ters The plot shows the m and n values from the 217 soils includedin this global compilation study Uncertainty in Km was approxi-mated using the partial derivatives approach Bubble size and colorrelates to the RSD of Km for the plotted m and n combination

differences in Km between soils or treatments often vary onorders of magnitude (Frossard et al 2011 Fardeau et al1991) However for low values of m andor n Km calcula-tion becomes very sensitive to uncertainty in m andor n andrelative errors may be much higher than 100 (Fig 6) Fu-ture studies should take this into account and conduct appro-priate error propagation or consult Fig 6 to get an overviewof sensitive m and n ranges

While we focused our analysis on P studies the derivationof Km as well as the finding that there is extremely rapid ex-change between solid and liquid phases is equally relevantfor other nutrients andor pollutants with strongly sorbingion species The isotope exchange kinetic approach has alsobeen successfully applied to study availability of Zn (Sinajet al 1999) Cd (Gray et al 2004 Geacuterard et al 2000) Ni(Echevarria et al 1998) As (Rahman et al 2017) and U(Clark et al 2011) and applications are also plausible forother elements with radioisotopes Isotope exchange kineticstudies with Zn Cd and Ni have used the same method asstudies on P analyzed here also modeling the decline in ra-dioactivity using Eq (3 Gray et al 2004 Sinaj et al 1999Echevarria et al 1998) For such studies the derivation ofKm as it is presented here is directly transferable and mightprovide additional useful information for understanding soilndashsolution exchange

37 Environmental implications

Our study provides new insight into the diffusion-basedmechanisms of P buffering across a large range of soil typesPrior to this study little was known about soil solution Pturnover rate as Km had previously been calculated by only

a handful of studies Our analysis of 217 soils showed thatKm is inversely proportional to Pw and is an important de-terminant of plant-available P Biological adaptations to Pavailability have received a lot of attention as it has beenshown that plant communities have different strategies for Pnutrition depending on P availability (Lambers et al 2008)Indeed biological activity acts as an important buffer ofP availability in many ecosystems with higher fluxes ofbiological P often occurring when there are lower fluxesof physicochemical P (Buumlnemann et al 2016 2012) Ourglobal compilation of 217 samples demonstrated there is an-other buffer of soil solution P which is independent of bi-ological activity and exclusively diffusion-based Soils witha low concentration of P in the soil solution tend to have ahigh P turnover rate thus buffering isotopically exchange-able P values This does not mean that negative balances of Pwill improve the availability of soil P for plant uptake ratherit explains why changes in P availability are not as large assuggested by more drastic changes in Pw

Our findings complement the notion that there are twocategories of soils in regard to P dynamics In many low-Pw soils sorption is extremely high and the soil solutionis buffered from P inputs or outputs (Barrow and Debnath2014) For these soils the prevalence of sites with fast ex-change rates is crucial to assure a steady flux of P to the soilsolution (Fig 3b) In terms of agricultural management insuch a soil P fertilization has to be higher than P output viacrop removal to account for the buffering effect (Roy et al2016) However once a soil reaches a certain P level andbinding sites are saturated by phosphate and other anions Pexchange is less important and fertilizer inputs can be low-ered to equal crop offtake (Syers et al 2008) For these soilsadditional P inputs will be directly reflected by an increase inP in the soil solution and P availability is largely driven bythe amount of P in the soil solution (Fig 4a) A better under-standing of P kinetics in soil will allow more effective nutri-ent management to meet the dual goals of improving agricul-tural production while reducing fertilizer use and pollution

Data availability The global soil and fertilizer field experimentdata sets used in this study are available in the Supplement

Information about the Supplement

The derivation of Km a table presenting isotope exchange ki-netic properties of soils used in the study and figures relatingE values to Pw and Km are available in the Supplement

Supplement The supplement related to this article is availableonline at httpsdoiorg105194bg-15-105-2018-supplement

Author contributions The project was conceived and carried outby JH with support from EF TM and JJ JJ provided the derivationof Km JH prepared the manuscript with contributions from all co-authors

Competing interests The authors declare that they have no conflictof interest

Acknowledgements We thank Astrid Oberson for her helpfulcomments The project was funded by the Swiss National ScienceFoundation (project no 200021_162422) which is gratefullyacknowledged

Edited by Soumlnke ZaehleReviewed by two anonymous referees

References

Achat D L Bakker M R Augusto L Saur E DousseronL and Morel C Evaluation of the phosphorus status of P-deficient podzols in temperate pine stands combining isotopicdilution and extraction methods Biogeochemistry 92 183ndash200httpsdoiorg101007s10533-008-9283-7 2009

Achat D L Bakker M R Augusto L Derrien D Galle-gos N Lashchinskiy N Milin S Nikitich P Raudina TRusalimova O Zeller B and Barsukov P Phosphorus statusof soils from contrasting forested ecosystems in southwesternSiberia effects of microbiological and physicochemical prop-erties Biogeosciences 10 733ndash752 httpsdoiorg105194bg-10-733-2013 2013

Achat D L Pousse N Nicolas M Breacutedoire F and AugustoL Soil properties controlling inorganic phosphorus availabil-ity general results from a national forest network and a globalcompilation of the literature Biogeochemistry 127 255ndash272httpsdoiorg101007s10533-015-0178-0 2016

Adler D vioplot Violin plot R Package version 02 2005Andersson K O Tighe M K Guppy C N Milham P J

McLaren T I Schefe C R and Lombi E XANES Demon-strates the Release of Calcium Phosphates from Alkaline Ver-tisols to Moderately Acidified Solution Environ Sci Technol50 4229ndash4237 httpsdoiorg101021acsest5b04814 2016

Barrow N J A mechanistic model for describing the sorptionand desorption of phosphate by soil J Soil Sci 34 733ndash750httpsdoiorg101111j1365-23891983tb01068x 1983

Barrow N J and Debnath A Effect of phosphate status on thesorption and desorption properties of some soils of northern In-dia Plant Soil 378 383ndash395 httpsdoiorg101007s11104-014-2042-8 2014

Beckett P H T and White R E Studies on the phos-phate potentials of soils Plant Soil 21 253ndash282httpsdoiorg101007bf01377744 1964

Bivand R Ono H Dunlap R and Stigler M classInt ChooseUnivariate Class Intervals R package version 01-24 2015

Bolland M D A and Allen D G Phosphorus sorption by sandysoils from Western Australia effect of previously sorbed P on P

buffer capacity and single-point P sorption indices Soil Res 411369ndash1388 httpsdoiorg101071SR02098 2003

Breacutedoire F Bakker M R Augusto L Barsukov P A DerrienD Nikitich P Rusalimova O Zeller B and Achat D LWhat is the P value of Siberian soils Soil phosphorus statusin south-western Siberia and comparison with a global data setBiogeosciences 13 2493ndash2509 httpsdoiorg105194bg-13-2493-2016 2016

Buehler S Oberson A Sinaj S Friesen D K and FrossardE Isotope methods for assessing plant available phospho-rus in acid tropical soils European J Soil Sci 54 605ndash616101046j1365-2389200300542x 2003

Buumlnemann E K Oberson A Liebisch F Keller F An-naheim K E Huguenin-Elie O and Frossard E Rapidmicrobial phosphorus immobilization dominates gross phos-phorus fluxes in a grassland soil with low inorganicphosphorus availability Soil Biol Biochem 51 84ndash95httpsdoiorg101016jsoilbio201204012 2012

Buumlnemann E K Augstburger S and Frossard E Dom-inance of either physicochemical or biological phospho-rus cycling processes in temperate forest soils of contrast-ing phosphate availability Soil Biol Biochem 101 85ndash95httpsdoiorg101016jsoilbio201607005 2016

Burkitt L L Moody P W Gourley C J P and Hannah M CA simple phosphorus buffering index for Australian soils SoilRes 40 497ndash513 httpsdoiorg101071SR01050 2002

Carpenter S R Caraco N F Correll D L HowarthR W Sharpley A N and Smith V H Nonpointpollution of surface waters with phosphorus and nitro-gen Ecol Appl 8 559ndash568 httpsdoiorg1018901051-0761(1998)008[0559NPOSWW]20CO2 1998

Chen C R Condron L M Sinaj S Davis M R SherlockR R and Frossard E Effects of plant species on phosphorusavailability in a range of grassland soils Plant Soil 256 115ndash130 httpsdoiorg101023a1026273529177 2003

Clark M W Harrison J J and Payne T E The pH-dependence and reversibility of uranium and thorium bind-ing on a modified bauxite refinery residue using isotopicexchange techniques J Colloid Interf Sci 356 699ndash705httpsdoiorg101016jjcis201101068 2011

Compaoreacute E Frossard E Sinaj S Fardeau J C and MorelJ L Influence of land-use management on isotopically ex-changeable phosphate in soils from Burkina Faso Commun SoilSci Plan 34 201ndash223 httpsdoiorg101081css-1200174262003

Demaria P Flisch R Frossard E and Sinaj S Exchangeabilityof phosphate extracted by four chemical methods J Plant NutrSoil Sc 168 89ndash93 httpsdoiorg101002jpln2004214632005

Demaria P Sinaj S Flisch R and Frossard E Soil prop-erties and phosphorus isotopic exchangeability in croppedtemperate soils Commun Soil Sci Plan 44 287ndash300httpsdoiorg101080001036242013741896 2013

Echevarria G Morel J L Fardeau J C andLeclerc-Cessac E Assessment of Phytoavailabilityof Nickel in Soils J Environ Qual 27 1064ndash1070httpsdoiorg102134jeq199800472425002700050011x1998

Elser J and Bennett E Phosphorus cycle A broken biogeochem-ical cycle Nature 478 29ndash31 2011

Fardeau J C Cinegravetique drsquoegravechange des ions phosphate dans lessystegravemes sol-solution Vegraverification expegraverimentale de lrsquoegravequationthegraveorique CR Acad Sci Paris 300 371ndash376 1985

Fardeau J C Le phosphore assimilable des sols sa repreacutesen-tation par un modegravele fonctionnel agrave plusieurs compartimentsAgronomie 13 317ndash331 1993

Fardeau J C Dynamics of phosphate in soils An isotopic outlookFert Res 45 91ndash100 httpsdoiorg101007bf007906581996

Fardeau J-C Morel C and Boniface R Phosphate ion trans-fer from soil to soil solution kinetic parameters Agronomie 11787ndash797 1991

Frossard E Feller C Tiessen H Stewart J W BFardeau J C and Morel J L Can an isotopic methodallow for the determination of the phosphate-fixing ca-pacity of soils Commun Soil Sci Plan 24 367ndash377httpsdoiorg10108000103629309368807 1993

Frossard E Morel J L Fardeau J C and Brossard MSoil isotopically exchangeable phosphorus A comparisonbetween E and L values Soil Sci Soc Am J 58 846ndash851httpsdoiorg102136sssaj199403615995005800030031x1994

Frossard E Achat D L Bernasconi S M Fardeau J-C JansaJ Morel C Randriamanantsoa L Sinaj S and Oberson AThe use of tracers to investigate phosphate cycling in soilndashplantsystems edited by Buumlnemann E K Springer Heidelberg 59ndash91 2011

Gallet A Flisch R Ryser J-P Frossard E and SinajS Effect of phosphate fertilization on crop yield and soilphosphorus status J Plant Nutr Soil Sc 166 568ndash578httpsdoiorg101002jpln200321081 2003

Geacuterard E Echevarria G Sterckeman T and Morel J LCadmium Availability to Three Plant Species Varying in Cad-mium Accumulation Pattern J Environ Qual 29 1117ndash1123httpsdoiorg102134jeq200000472425002900040012x2000

Geacuterard F Clay minerals ironaluminum oxides and their contribu-tion to phosphate sorption in soils ndash A myth revisited Geoderma262 213ndash226 httpsdoiorg101016jgeoderma2015080362016

Gray C W McLaren R G Guumlnther D and Sinaj S An assess-ment of cadmium availability in cadmium-contaminated soils us-ing isotope exchange kinetics Soil Sci Soc Am J 68 1210ndash1217 httpsdoiorg102136sssaj20041210 2004

Hamon R E Bertrand I and McLaughlin M J Use and abuseof isotopic exchange data in soil chemistry Soil Res 40 1371ndash1381 httpsdoiorg101071SR02046 2002

Hedley M J White R E and Nye P H Plant-inducedchanges in the rhizosphere of rape (Brassica-napus var ndashEmerald) seedlings 3 Changes in L value soil phosphatefractions and phosphatase-activity New Phytol 91 45ndash56httpsdoiorg101111j1469-81371982tb03291x 1982

IUSS Working Group WRB World reference base for soil resources2014 update 2015 International soil classification system fornaming soils and creating legends for soil maps World Soil Re-sources Reports No 106 Rome FAO 2015

Ku H Notes on the use of propagation of error formulas Jour-nal of Research of the National Bureau of Standards Section CEngineering and Instrumentation 70 263 1966

Lambers H Raven J A Shaver G R and Smith S E Plantnutrient-acquisition strategies change with soil age Trends EcolEvol 23 95ndash103 httpsdoiorg101016jtree2007100082008

Menezes-Blackburn D Zhang H Stutter M Giles C D DarchT George T S Shand C Lumsdon D Blackwell M Wear-ing C Cooper P Wendler R Brown L and HaygarthP M A holistic approach to understanding the desorption ofphosphorus in soils Environ Sci Technol 50 3371ndash3381httpsdoiorg101021acsest5b05395 2016

Morel C and Plenchette C Is the isotopically exchangeable phos-phate of a loamy soil the plant-available P Plant Soil 158 287ndash297 httpsdoiorg101007bf00009502 1994

Morel C Tiessen H Moir J O and Stewart J WB Phosphorus transformations and availability un-der cropping and fertilization assessed by isotopicexchange Soil Sci Soc Am J 58 1439ndash1445httpsdoiorg102136sssaj199403615995005800050023x1994

Morel C Tunney H Pleacutenet D and Pellerin S Trans-fer of phosphate ions between soil and solution Per-spectives in soil testing J Environ Qual 29 50ndash59httpsdoiorg102134jeq200000472425002900010007x2000

Oberson A Fardeau J C Besson J M and Sticher H Soilphosphorus dynamics in cropping systems managed accordingto conventional and biological agricultural methods Biol FertSoils 16 111ndash117 httpsdoiorg101007bf00369411 1993

Oberson A Friesen D K Tiessen H Morel C and Stahel WPhosphorus status and cycling in native savanna and improvedpastures on an acid low-P Colombian Oxisol Nutr Cycl Agroe-cosys 55 77ndash88 httpsdoiorg101023a10098130084451999

Obersteiner M Pentildeuelas J Ciais P van der Velde M andJanssens I A The phosphorus trilemma Nat Geosci 6 897ndash898 httpsdoiorg101038ngeo1990 2013

Oehl F Oberson A Sinaj S and Frossard E Organic phospho-rus mineralization studies using isotopic dilution techniques SoilSci Soc Am 65 780ndash787 2001

Olsen S R and Khasawneh F E Use and limitations of physical-chemical criteria for assessing the status of phosphorus in soilsin The Role of Phosphorus in Agriculture edited by Kha-sawneh F E Sample E C and Kamprath E J AmericanSociety of Agronomy Crop Science Society of America SoilScience Society of America Madison WI 361ndash410 1980

Pierzynski G M and McDowell R W Chemistry Cycling andPotential Movement of Inorganic Phosphorus in Soils in Phos-phorus Agriculture and the Environment edited by Sims J Tand Sharpley A N Agronomy Monograph 46 American So-ciety of Agronomy Crop Science Society of America and SoilScience Society of America Madison WI 53ndash86 2005

Pypers P Delrue J Diels J Smolders E and Merckx R Phos-phorus intensity determines short-term P uptake by pigeon pea(Cajanus cajan L) grown in soils with differing P buffering ca-pacity Plant Soil 284 217ndash227 httpsdoiorg101007s11104-006-0051-y 2006

Rahman M S Clark M W Yee L H Comarmond MJ Payne T E Kappen P and Mokhber-Shahin L Ar-senic solid-phase speciation and reversible binding in long-term contaminated soils Chemosphere 168 1324ndash1336httpsdoiorg101016jchemosphere201611130 2017

Randriamanantsoa L Morel C Rabeharisoa L Douzet JM Jansa J and Frossard E Can the isotopic exchangekinetic method be used in soils with a very low wa-ter extractable phosphate content and a high sorbing ca-pacity for phosphate ions Geoderma 200ndash201 120ndash129httpsdoiorg101016jgeoderma201301019 2013

R Core Team R A language and environment for statistical com-puting R Foundation for Statistical Computing Vienna Austria2017

Roy E D Richards P D Martinelli L A Coletta L DLins S R M Vazquez F F Willig E Spera S A Van-Wey L K and Porder S The phosphorus cost of agri-cultural intensification in the tropics Nat Plants 2 16043httpsdoiorg101038nplants201643 2016

Sinaj S Maumlchler F and Frossard E Assessment ofisotopically exchangeable zinc in polluted and non-polluted soils Soil Sci Soc Am J 63 1618ndash1625httpsdoiorg102136sssaj19996361618x 1999

Syers J K Johnston A and Curtin D Efficiency of soil andfertilizer phosphorus use Reconciling changing concepts of soilphosphorus behaviour with agronomic information Food andAgriculture Organization of the United Nations Rome 2008

Tilman D Cassman K G Matson P A Naylor R and PolaskyS Agricultural sustainability and intensive production practicesNature 418 671ndash677 httpsdoiorg101038nature010142002

Tran T S Giroux M and Fardeau J C Ef-fects of soil properties on plant-available phospho-rus determined by the isotopic dilution phosphorus-32 method Soil Sci Soc Am J 52 1383ndash1390httpsdoiorg102136sssaj198803615995005200050033x1988

Weiss N A Holmes P T and Hardy M A Course in ProbabilityPearson Addison Wesley 2006

Xiong L M Zhou Z G Fardeau J C Feng G L andLu R K Isotopic assessment of soil phosphorus fertilityand evaluation of rock phosphates as phosphorus sources forplants in subtropical China Nutr Cycl Agroecosys 63 91ndash98httpsdoiorg101023a1020501007558 2002

Abstract
Introduction
Materials and methods
- Derivation of Km
- Data set
- Data analysis
- Analysis of long-term field experiments
- - Results and discussion
  - - Global analysis of P turnover in the soil solution (Km)
    - Relationship between soil solution P turnover (Km) and concentration of soil solution P (Pw)
    - Soil solution P turnover (Km) as a buffer of isotopically exchangeable P (E(t))
    - Time frame over which Km buffers isotopically exchangeable P (E(t))
    - Km buffers fertilizer application in long-term fertilizer experiments
    - Implications for using Km
    - Environmental implications
    - - Data availability
      - Supplement
      - Author contributions
      - Competing interests
      - Acknowledgements
      - References

Page 2: Soil solution phosphorus turnover: derivation ... · (Pierzynski and McDowell, 2005). The soil solution typically contains low concentrations of P (Achat et al., 2016), but the soil

P from the soil solid phase have important implications forthe P requirements of living organisms (Menezes-Blackburnet al 2016 Fardeau et al 1991) In this study we investigatea potential link between two different concepts phosphorus-buffering capacity and soil solution P turnover by analyzinga data set of global soils and P fertilizer experiments

Phosphorus-buffering capacity (PBC) is defined as theability of soil to moderate changes in the concentration ofsoil solution P (Pypers et al 2006 Olsen and Khasawneh1980 Beckett and White 1964) Historically PBC has beencalculated using Eq (1)

PBC=1conc of P in soil solution

1conc of P in the soil(1)

The traditional approach of determining PBC in soil is toadd various amounts of P to a soil suspension equilibrateand then measure the slope between adsorbed P and P in soilsolution (Olsen and Khasawneh 1980) Alternatively PBCcan be measured by analyzing the change in soil solution Pconcentration with regard to P budget in field P fertilizationexperiments (Morel et al 2000) These approaches have re-vealed that PBC is influenced by ambient temperature soilsolution pH and concentrations of P in the soil solution andis highly variable among soil types (Barrow 1983) One ofthe most important factors among soil types is the specificsurface area of FeAl oxides and clay minerals which are im-portant sites of P sorption (Geacuterard 2016) Whilst the afore-mentioned approaches are a useful and cost effective way tostudy soil P dynamics (Bolland and Allen 2003 Burkitt etal 2002 Barrow and Debnath 2014) they are not able todirectly determine the turnover of P in the solution

Soil solution P turnover (Km) is the mean rate of ex-change between phosphate ions in solution and inorganicphosphate in soil and can be calculated from parameters de-termined in an isotopic exchange kinetic (IEK) experiment(Fardeau 1996) Isotopic exchange kinetic experiments in-volve the use of P radioisotopes (32P or 33P) to directly mea-sure the exchange of P between the soil solid and solutionphases (Frossard et al 2011) They are based on the assump-tion that during the short-term experiments usually lasting100 min there is only physicochemical exchange but no bi-ological exchange (Oehl et al 2001) Measurements of iso-topically exchangeable P are a more accurate indicator of Pbioavailability than conventional soil tests based on chemicalextraction because the former involves a P radiotracer thatcan be directly measured and distinguished from all other Pions in the soil (Demaria et al 2005 Hamon et al 2002)Previous studies have shown that isotopically exchangeableP is the predominant source of P for most crops (Frossardet al 1994 Morel and Plenchette 1994) Though the IEKapproach does not consider root-induced pH alterations orsecretion of organic acids increased P availability due toroot exudates can be quantified by comparing isotopicallyexchangeable P with radioisotope uptake in plants (Hedleyet al 1982) Isotopic dilution in a soil solution system is

characterized by two statistically fitted parameters m and nwhich can be used to calculate Km using Eq (2) (Fardeau1985 Fardeau et al 1991)

Km =n

m1n

(2)

The importance of parameters m and n as well as their rela-tion to soil properties was recently investigated (Achat et al2016)

Despite several decades of using radioisotopes in P re-search and the potential relevance of soil solution P turnoverto understanding agricultural and natural ecosystems onlysix studies have published Km values and there has been nosynthesis of these values (Frossard et al 2011 Fardeau et al1991 Fardeau 1985 1993 Oberson et al 1993 Xiong etal 2002) We believe that this is because an intuitive deriva-tion of Km has never been published Whilst information onsoil solution P turnover remains limited Km values can eas-ily be calculated using data from previously published IEKexperiments

The first aim of our study was to provide a clear and in-tuitive derivation of the Km term Our second aim was tocalculate Km values from previously published IEK studieswhich resulted in a global data set of over 200 soils We thentested specific hypotheses related to concentrations of soil so-lution P and isotopically exchangeable P Our third aim wasto understand the relationship between PBC and Km Thisinvolved an additional data set based on long-term P fertil-izer field experiments which reported IEK results and the Pfertilizer budgets Lastly we carried out a sensitivity analysisof Km in order to assist in interpretation of future results

Our first hypothesis was that turnover of soil solution Pwould differ based on soil group More specifically we hy-pothesized that soil groups known to have higher concen-trations of sorption sites (such as Andosols and Ferralsols)would have faster turnover rates Our second hypothesis wasthat soils with higher concentrations of soil solution P (Pw)

would have lower values of Km compared to soil with lowerconcentrations of soil solution P This is because a high con-centration of sorption sites leads to fast adsorption and con-sequently low concentration of P in the solution Lastly wehypothesized that the dependence of isotopically exchange-able P on Pw and Km evolves with time

2 Materials and methods

21 Derivation of Km

A given volume of soil can be described as containing inor-ganic P in one of two states the soil phase or the soil solutionphase In any given time interval physicochemical reactionstransfer a fraction of P from the soil solution phase into thesolid phase The rate constant of this reaction is solution Pturnover Km (minminus1) Thus Km plays a critical role in deter-

r(t)

R=m

(t +m

1n

)minusn

+r(infin)

R (3)

22 Data set

23 Data analysis

E(t) = PwtimesR

r(t)(4)

sKm =