Isotopic dilution methods to determine the gross
transformation rates of nitrogen, phosphorus, and sulfur in soil: a
review of the theory, methodologies, and limitations.




Abstract: 
The rates at which nutrients are released to, and removed from, the
mineral nutrient pool are important in regulating the nutrient supply to
plants. These nutrient transformation rates need to be taken into
account when developing nutrient management strategies for economical
and sustainable production. A method that is gaining popularity for
determining the gross transformation rates of nutrients in the soil is
the isotopic dilution technique. The technique involves labelling a soil
mineral nutrient pool, e.g. [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN
ASCII] or [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and
monitoring the changes with time of the size of the labelled nutrient
pool and the excess tracer abundance (atom%, if stable isotope tracer is
used) or specific activity (if radioisotope is used) in the nutrient
pool. Because of the complexity of the concepts and procedures involved,
the method has sometimes been used incorrectly, and results
misinterpreted. This paper discusses the isotopic dilution technique,
including the theoretical background, the methodologies to determine the
gross flux rates of nitrogen, phosphorus, and sulfur, and the
limitations of the technique. The assumptions, conceptual models,
experimental procedures, and compounding factors are discussed. Possible
effects on the results by factors such as the uniformity of tracer
distribution in the soil, changes in soil moisture content, substrate
concentration, and aeration status, and duration of the experiment are
also discussed. The influx and outflux transformation rates derived
from this technique are often contributed by several processes
simultaneously, and thus cannot always be attributed to a particular
nutrient transformation process. Despite the various constraints or
possible compounding factors, the technique is a valuable tool that can
provide important quantitative information on nutrient dynamics in the
soilplant system. Additional keywords: nutrients, transformations, cycling, tracers, mineralisation, immobilisation. 


Subject: 
Plants
(Food and nutrition) Radioisotopes (Physiological aspects) Tracers (Biology) (Analysis) Mineral metabolism (Research) 
Authors: 
Di, H. J. Cameron, K. C. McLaren, R. G. 
Pub Date:  01/01/2000 
Publication:  Name: Australian Journal of Soil Research Publisher: CSIRO Publishing Audience: Academic Format: Magazine/Journal Subject: Agricultural industry; Earth sciences Copyright: COPYRIGHT 2000 CSIRO Publishing ISSN: 00049573 
Issue:  Date: Jan, 2000 Source Volume: 38 Source Issue: 1 
Geographic:  Geographic Scope: United States Geographic Code: 1USA United States 
Accession Number:  60589686 
Full Text: 
Introduction Nutrient transformations in the soil, e.g. mineralisation and immobilisation, or release and retention, play an important role in regulating the supply of nutrients such as nitrogen (N), phosphorus (P), and sulfur (S) to plants. Significant amounts of the nutrients taken up by plants are derived from mineralisation of the soil organic matter, while at the same time, nutrients applied to the soil in the form of mineral fertiliser are also converted to organic forms (McLaren and Cameron 1996). In recent years, organic wastes have been increasingly applied to farm land or plantation forests to recycle nutrients (Cameron et al. 1997; Bond 1998). Large proportions of the nutrients in the waste materials are in organic forms, and their plant availability depends on the rates at which the organic nutrients are mineralised by microbial decomposition (Cameron et al. 1995, 1996; Di et al. 1998a, 1998b; Zaman et al. 1999a). Where slowrelease fertilisers (e.g. phosphate rocks or elemental sulfur) are used, the nutrient supply depends on the rates at which the fertilisers are dissolved after they are applied to the soil (Di et al. 1994a; Condron et al. 1995). In the case of P, sorption or fixation (the removal of phosphate from soil solution to solid phase due to sorption or precipitation) is another important mechanism that affects phosphate supply to plants. The rates at which these nutrient transformations occur in the soil need to be taken into account when developing nutrient management strategies to match the nutrient supply to plant demand for economical and sustainable production. Excessive application rates or applications at the wrong time can result in high losses by leaching or surface runoff (Cameron et al. 1997; Di et al. 1999). The nutrients lost not only represent an economic loss for the farmer but may also result in the contamination of the wider environment (Ledgard et al. 1996; Cameron et al. 1997). One of the important tools that has been used to study the rates of nutrient transformations in the soil is the isotope dilution method to determine the gross rates of release into, or removal from, a mineral nutrient pool (Kirkham and Bartholomew 1954; Di et al. 1994b, 1994c, 1994d; Barraclough 1995). This method involves labelling a mineral nutrient pool with an isotopic tracer and then measuring the changes with time of the amounts of the labelled nutrient and the isotopic ratio in the labelled nutrient pool. The rates of influx to and outflux from the labelled nutrient pool are then calculated using equations formulated on the basis of tracer kinetics. Although the equations for calculating the flux rates have been available since the 1950s, it is not until recently that the technique has become popular for studying nutrient cycling in agroecosystems (e.g. Davidson et al. 1991; Wessel and Tietema 1992; Di 1991; Di et al. 1994b; Smith et al. 1994; Monaghan and Barraclough 1995, 1997; Murphy et al. 1997; Zaman et al. 1999a, 1999b). The delay in the application of this technique may reflect a combination of the complexity of the equations initially derived, and the high cost associated with the use of isotopes. However, the increased availability of isotopes and analytical instruments for their analysis may have increased the recent interest in this technique. The objective of this paper is to discuss the concepts, the methodologies, and the limitations of this technique in studying the transformations of N, P, and S in the soil. The techniques for studying the 3 nutrients are discussed together to aid the study of their comparative transformation rates. It is not the intention of this paper to provide an exhaustive review of all studies involving the use of isotope dilution. The main aim is to provide a clear description of the techniques with regard to their assumptions, procedures, and conditions under which they may or may not be applicable. It is hoped that this will facilitate the wider application of the techniques and ensure that they are used correctly, particularly by firsttime users. Theory In 1954, Kirkham and Bartholomew published a set of equations for using tracer data to determine the gross rates of mineralisation and immobilisation of nutrients in the soil. The equations formulated were based on nitrogen transformations in the soil, using the [15.sup.N] stable isotope as the tracer. Recent applications of the isotopic dilution method have therefore been largely to the study of N transformations in the soil (e.g. Davidson et al. 1991; Smith et al. 1994; Monaghan and Barraclough 1995, 1997; Zaman et al. 1999a, 1999b). Isotopic dilution methods have also been developed and used to study in vivo kinetics in animal and biomedical research (Shipley and Clark 1972). More recently, an isotopic dilution technique to study the gross rates of phosphate release and retention in the soilplant system has been developed (Di 1991; Di et al. 1994b). These isotopic dilution methods are all based on compartmental analysis of tracer kinetics. A compartment in tracer studies refers to a space or chemical form in which the isotope tracer is uniformly and instantaneously dispersed. Fluxes into or out of the compartment are random processes for the isotopic tracers and tracees (i.e. the unlabelled mineral nutrient). The isotopic dilution technique to study the gross transformation rates of nutrients in the soil involves labelling a mineral nutrient pool (e.g. [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] or [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) that may be regarded as a compartment, and monitoring the rate at which the isotopic tracer is diluted, as nutrients are released into the labelled pool and removed from the pool simultaneously (Fig. 1). The rate at which the nutrient is released into the labelled pool is termed the influx rate ([F.sub.1]), and the rate at which the nutrient is removed from the pool is termed the outflux rate ([F.sub.O]). [Figure 1 ILLUSTRATION OMITTED] The analytical solutions of the equations to calculate [F.sub.l] and[ F.sub.o] are based on the following assumptions (Kirkham and Bartholomew 1954; Barraclough et al 1985; Di et al. 1994b). (1) The isotopes of the mineral nutrient (the tracer and tracee) behave identically in the transformation processes in the soil (i.e. microbes do not discriminate between the isotopes). (2) The nutrient that is released into the labelled pool is not artificially labelled, i.e. with tracer to tracee ratio at the background level. (3) The ratio of tracer to tracee of the outflux nutrient is in proportion to that in the labelled pool. For radioisotopes, this ratio is expressed as the specific activity, which is the radioactivity per unit mass of the nutrient (e.g. Bq/[micro]g P) above the background. For stable isotopes, such as [sup.15]N, this is expressed as the atom% [sup.15]N excess abundance above the background (0.3663 atom%). (4) The influx rates ([F.sub.1]) and outflux rates ([F.sub.O]) are constant over the period for which they are calculated. Equations to calculate the influx and outflux rates Let q equal the quantity of the added tracer in the labelled mineral nutrient pool; Q equal the quantity of the tracer plus tracee in the labelled mineral nutrient pool; A equal the tracer excess abundance (atom%) (if stable isotope is used) in the labelled nutrient pool, i.e. the ratio of the tracer over the sum of tracer and tracee, q/Q, above the background, or specific activity (if radioisotope is used); and t equal time. For a mineral nutrient pool at a nonsteady state, i.e. [F.sub.I] [is not equal to] [F.sub.O], when a single dose of tracer is introduced into this mineral nutrient pool, the tracer is assumed to be uniformly mixed with the nutrient (tracee) in the pool, resulting in an excess tracer abundance or specific activity. Thereafter, the influx of nutrient (not labelled) will dilute the tracer in the pool. At the same time, the outflux will remove the tracer and tracee at a ratio in proportion to the tracer abundance or specific activity in the labelled nutrient pool. The [F.sub.O] by itself will not reduce the tracer abundance or specific activity in the labelled pool, but will contribute to their decline in combination with [F.sub.I], as the nutrient entering the pool is diluting decreasing amounts of q remaining in the labelled pool. The rate at which the added tracer in the labelled pool is lost through [F.sub.O] is: (1) dq/dt = [F.sub.O] [multiplied by] A(t) The total quantity of the nutrient in the labelled pool, Q, is controlled by [F.sub.I] and [F.sub.O]. The rate of change in Q is thus: (2) dQ/dt = [F.sub.I]  [F.sub.O] The amount of the added tracer remaining in the labelled pool at any point in time is the product of the size of the total nutrient pool and the tracer abundance (atom%) or specific activity: (3 q(t) = Q(t) [multiplied by] A(t) or in its derivative form: (4) dq/dt = Q(t) [multiplied by] dA/dt + A(t) [multiplied by] dQ/dt The equations to calculate [F.sub.I] and [F.sub.O] can be derived by rearranging the above equations followed by integration: (5) [F.sub.I] = [([Q.sub.1]  [Q.sub.2])[multiplied by] ln([A.sub.1]/[A.sub.2])]/[([t.sub.2]  [t.sub.1]) [multiplied by] ln([Q.sub.1]/[Q.sub.2])] (6) [F.sub.O] = [F.sub.I]  [([Q.sub.2]  [Q.sub.1])/([t.sub.2]  [t.sub.1])] where [Q.sub.1] and [Q.sub.2] are the quantities of tracer plus tracee, and [A.sub.1] and [A.sub.2] are tracer excess abundances (atom%), or specific activities (corrected to the same reference time to account for radioactive decay), at 2 points in time [t.sub.1] and [t.sub.2], respectively, after the labelling of the mineral nutrient pool. Eqns 5 and 6 are for nonsteadystate conditions and are not applicable to steadystate conditions, where [F.sub.I] = [F.sub.O] = F, and Q remains constant with time. Under such conditions, the change in the tracer excess abundance or specific activity in the labelled nutrient pool follows (Di et al. 1994b): (7) A(t) = [A.sub.0] [multplied by] [e.sup.[(F/Q)t]] Rearranging Eqn 7 gives the formula to calculate the flux rate: (8) [F.sub.I] = [F.sub.O] = F = [ln([A.sub.0]/[A.sub.t])] [multiplied by] Q/t = [ln([A.sub.1]/[A.sub.2])] [multiplied by] Q/([t.sub.2]  [t.sub.1]) Eqns 5 and 6 are used more widely because the mineral nutrient pool in many cases is not at a steady state (i.e. [Q.sub.1] [is not equal to] [Q.sub.2]). However, in natural soilplant systems, the nutrient dynamics may well be at a steadystate ([Q.sub.1] = [Q.sub.2]), and Eqn 8 should then be used to calculate the flux rates. The final formulae to calculate the influx and outflux rates given by Kirkham and Bartholomew (1954) and Barraclough (1995) were in slightly more complex forms than Eqns 5, 6, and 8 derived above, but they can be rearranged to give the same forms. The results calculated from these different forms of equations should be the same. In addition to the analytical solution described above to derive the formulae to calculate [F.sub.I] and [F.sub.O], numerical modeling and nonlinear parameter estimation methods have been used in trying to overcome some of the restrictive assumptions (e.g. nonconstancy of transformation rates and remineralisation of immobilised [sup.15]N) (e.g. Mayrold and Tiedje 1986; Bjarnason 1988; Wessel and Tietema 1992; Smith et al. 1994). The reader is referred to the paper by Smith et al. (1994) for a detailed comparison of these different approaches. Bjamason (1988), for example, found that when the period of study was extended beyond 2 weeks, erroneous results were obtained if corrections were not made for remineralisation; in a system where both remineralisation and nitrification occurred, it was recommended that the model/optimisation technique was preferred to the traditional analytical approach. A similar conclusion was reached by Wessel and Tietema (1992) after comparing the analytical and numerical approaches. However, Smith et al. (1994) carried out a detailed comparison of the various approaches and found that both the analytical and the numerical methods have advantages and weaknesses. The analytical approach was shown to be particularly appropriate for experiments of short duration to minimise errors due to remineralisation of immobilised [sup.15]N and changing transformation rates. The numerical approach is more appropriate for experiments of longer duration when the system is at or near steadystate so that multiple observations can be made for the N pools and transformation rates when they are constant. The methodologies discussed below are based on the assumptions for the analytical solution described above. Nitrogen transformation rates Conceptual model The isotopic dilution technique has been used to quantify the gross transformation rates of N in grassland soils (e.g. Davidson et al. 1991; Zaman et al. 1999a, 1999b), in forest soils (e.g. Tietema and Wessel 1992), in aerobic and anaerobic soil suspensions (e.g. Smith et al 1994), soils incorporated with organic materials (e.g. Monaghan and Barraclough 1995, 1997; Sparling et al. 1995), at different soil depths (e.g. Murphy et al. 1998), and soils treated with nitrification inhibitors (Nishio et al. 1985; Guiraud et al. 1989; Chalk et al. 1990). Other applications of the technique have been reviewed by Smith et al. (1994). Fig. 2. shows the conceptual model on which the isotopic dilution technique was developed for studying N transformation rates. The dominant process contributing to [F.sub.I] in Fig. 2a is the mineralisation of organic N, releasing [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] into the labelled [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool and diluting the isotopic tracer added. However, depending on the experimental conditions, [F.sub.I] may also include other processes that yield [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to the labelled [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool. For instance, atmospheric deposition of N (including [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) may be significant in some places, and if the experiment is conducted outdoors, this N input should be taken into account as part of the [F.sub.I] determined. If this input is negligible and no [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] fertiliser is applied, then [F.sub.I] in Fig. 2a will represent predominantly the gross N mineralisation rate (see Limiting factors section below for other possible compounding factors). [F.sub.O] may consist of several processes, including microbial immobilisation, nitrification, clay fixation, plant uptake, volatilisation, and leaching, depending on the conditions under which the experiment is conducted. Under laboratory incubation conditions without growing plants, nitrification and microbial immobilisation will be the major processes making up [F.sub.O]. In unconfined field conditions with growing plants, however, volatilisation, plant uptake, and leaching can be significant. Therefore, whereas [F.sub.I] may be understood in many cases as representing the gross rate of N mineralisation, [F.sub.O] does not represent a single process. However, under laboratory incubation conditions, where there are no [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] losses by leaching and plant uptake, and if clay fixation is deemed to be negligible, then the nitrification rate can be determined as discussed below (Fig. 2b), and [F.sub.O] may be partitioned to derive the gross rate of microbial immobilisation of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. [Figure 2 ILLUSTRATION OMITTED] Fig. 2b shows the fluxes of N through the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool. If atmospheric deposition is negligible and no nitrate fertiliser is applied, then [F.sub.I] will mainly represent the rate of nitrification. [F.sub.O], however, comprises the sum of denitrification and microbial immobilisation rates under laboratory conditions, plus plant uptake and leaching rates under field conditions. [F.sub.O] cannot be resolved into separate processes unless some of the processes are measured separately using other methods. Methodology The determination of N flux rates through the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool involves labelling the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool, usually with a highly enriched [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] salt [e.g. [[sup.15]NH.sub.4]Cl or [([[sup.15]NH.sub.4]).sub.2][SO.sub.4]], and determining the changes in the size of the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool and the atom% excess abundance of [sup.15]N in the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool, at 2 different times, after the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] tracer is added to the soil. The changes in the size of the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool at times [t.sub.1] and [t.sub.2] will yield [Q.sub.1] and [Q.sub.2], and the [sup.15]N atom% excess of the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool at times [t.sub.1] and [t.sub.2] will give [A.sub.1] and [A.sub.2]. These values can then be used to calculate [F.sub.I] and [F.sub.O] using Eqns 5 and 6 or 8. The determination of the flux rates through the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool is similar and involves labelling the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool with a [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] salt (e.g. [K.sup.15][NO.sub.3]) and monitoring the changes with time of the size of the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool and the [sup.15]N atom% excess of the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool. In practice, if the flux rates through both the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool and the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool are determined at the same time, 4 soil samples are usually labelled, 2 with a [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] salt and 2 with a [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] salt (see Barraclough 1991 for an alternative procedure where only the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool is labelled). The labelled soil samples are then left for a period (usually a few hours to a day) for the [sup.15]N to equilibrate in the soil system. The actual equilibration period needed varies, depending on the soil conditions, and may need to be investigated by a preliminary experiment (Davidson et al. 1991; Monaghan and Barraclough 1997). One sample from the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]labelled soil and one from the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]labelled soil is then taken out after the initial period of equilibration ([t.sub.1]) for analysis. The remaining 2 samples, one labelled with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and one with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], are used after a further period (e.g. 57 days) ([t.sub.2]) for analysis. The two [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]labelled soil samples are extracted with dilute (2 M) KCl solutions. After centrifuging and filtering of the KCI solutions, the [sup.15]N atom% excess of the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is usually determined using the diffusion method (Brookes et al. 1989), by trapping ammonia on an acid paper strip and analysing on an isotope ratio mass spectrometer. The concentration of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in the KCl solution is determined using flowinjection analysis. The total amounts of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] at the two different times give [Q.sub.1] and [Q.sub.2], whereas the [sup.15]N atom% excess values provide [A.sub.1] and [A.sub.2], from which the influx and outflux rates can be calculated. It is important to note that only the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] needs to be recovered for the calculation of gross transformation rates through the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool. Nitrate N need not be recovered. For the determination of gross transformation rates through the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool, the two [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]labelled soil samples are extracted with KCl solutions. The extracts are then diffused to determine the [sup.15]N atom% excess of the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (Brookes et al. 1989). This is achieved by first depleting [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] from the extracts and discarding it. The [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in the remaining extract is then converted into [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] by reducing it with Devarda's alloy, and analysed as above. Nitrate concentrations in the KCl extracts are analysed using flow injection analysis. Six days of diffusion are usually required to recover the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] from the KCl extract, although the actual length of time required may vary depending on the room temperature, volume of solution, and size and shape of the container. A daily swirling of the solution speeds up the diffusion process. The right length of time needs to be established for all laboratory conditions before the start of the experiment. Although the diffusion method of using acidified filter disks suspended on a stainless steel wire above the solution has been the commonly used method to recover N from the KCl extract (Brookes et al. 1989; Liu and Mulvaney 1992; Herman et al. 1995), one of the limitations with this method is that the volume of solution that can be diffused may be limited (usually 4050 mL) to avoid contamination of the filter disk by the solution during the diffusion operation. This can be a limiting factor if the solution to be diffused has a low N concentration, as the amount of N required by the mass spectrometer (usually 1520 [micro]g N) may not be obtained by a single diffusion. In addition, moisture may accumulate on the stainless wire and, upon contact with the acidified disk, may result in N loss (Stark and Hart 1996). A new method has been developed to avoid these complications where an acidified glass fibre filter is sealed between 2 strips of PTFE (polytetrafluoroethylene) sealing tape, and this PTFEencased acid trap is placed inside the container, floating on the surface of the alkaline solution (Sorensen and Jensen 1991; Stark and Hart 1996). PTFE is permeable to gases but not to liquids, thus allowing the trapping of [NH.sub.3] without the acid trap inside being contaminated by the solution. Stark and Hart (1996) carried out a detailed assessment of this method and found nearly complete recovery ([is greater than] 96%) after 6 days of diffusion. The solution can be mixed freely during diffusion without the risk of contaminating the acid trap. This method has also been adapted to determine [sup.15]N in marine estuarine and fresh waters where the N concentrations are low (Sigman et al. 1997; Holmes et al. 1998). Stevens and Laughlin (1994) and Laughlin et al. (1997) developed a method for determining [sup.15]N content in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] forms in KCl extracts by converting [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] or [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] into [N.sub.2]O gas, and analysing the [sup.15]N content of the [N.sub.2]O on a mass spectrometer equipped with a gasphase autosampler system. The use of these methods will probably depend on the setup of the mass spectrometer, i.e. the availability of a gas sampler system. If the ammonium concentration in the KCl extract is determined using flow injection analysis, then complete recovery of N in the KCl extract in not necessary to determine the [sup.15]N enrichment as there is usually little fractionation of [sup.15]N and [sup.14]N during diffusion (Stark and Hart 1996). However, this should be experimentally confirmed under specific laboratory conditions. In addition, errors can be introduced by blank correction when recovery is [is less than] 100%. Under such circumstances, the blank correction should be based on the amount of isotope dilution that occurs in diffused standards compared with nondiffused standards (Stark and Hart 1996). Different methods have been used to label the soil. If the experiment is carried out under laboratory incubation conditions, the labelling is usually done by mixing soil samples with [sup.15]N solutions. For field studies using intact soil cores, [sup.15]N solutions are usually injected into intact soil cores with purposebuilt injectors with multiinjection points (Davidson et al. 1991; Monaghan and Barraclough 1995; Sparling et al. 1995; Zaman et al. 1999b). A minimum amount of N (both [14]N and [15]N) tracers should be added to the soil to minimise the disruption of the existing soil nitrogen dynamics, while at the same time providing enough [sup.15]N for reliable detection. Highly enriched (e.g. 99 atom% [sup.15]N) sources of [sup.15]Nlabelled [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] or [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are therefore desirable to minimise the amount of total N applied. The total amount of [sub.15]N required varies, depending on the amount of soil mineral N present and the transformation rates. An amount equivalent to about 2 [micro]g [sup.15]N/g soil has been used in grassland soils (Davidson et al. 1991; Zaman et al. 1999a). An amount of [sup.15]N added that gives a 510% initial [sup.15]N enrichment in the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] or [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool would, in many cases, be appropriate. If the soil mineral N concentration is very low and the amount of N recovered in the extracts is too small for reliable analysis on the mass spectrometer, the sample may be spiked with the same form of mineral N at the background [sup.15]N enrichment for analysis, with the final result corrected for N added in the spike. Example calculation The following example illustrates the correct use of the equations to calculate the transformation rates. Assume the following data have been obtained after an isotopic dilution experiment to determine the gross flux rates of N through the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool: [t.sub.1] is 1 day (i.e. 1 day after the labelling of the soil); [t.sub.2] is 5 days (i.e. 5 days after the labelling of the soil); [Q.sub.1] is 10 [micro]g [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] soil; [Q.sub.2] is 6 [micro]g [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] soil; [A.sub.1] is 3% [sup.15]N (excess atom%) in the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool; [A.sub.2] is 1% [sup.15]N (excess atom%) in the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool. [F.sub.I] and [F.sub.O] are calculated using Eqns 5 and 6 as follows: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Phosphate transformation rates Conceptual model Although isotope techniques have been used to study P cycling in the soilplant system in the past (e.g. Fried 1964; McLaughlin et al. 1986; Fardeau et al. 1996; Frossard et al. 1996; Di et al. 1997) (see the review article by Di et al. 1997 for other applications), to the authors' knowledge, the isotopic dilution theory, as outlined above, has not been widely used to determine the gross transformation rates of P in the soil. Di (1991) developed an isotopic dilution technique, based on the theory described above, to determine the rates at which phosphate was released from slowly dissolving P fertilisers, and compared the results with those from chemical extraction methods (DJ et al. 1994b, 1994c, 1994d). This isotopic dilution technique was based on the conceptual model of P dynamics in the soilplant system as shown in Fig. 3. The isotopically exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool refers to the fraction of phosphate that undergoes rapid exchange with the radioisotope [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] introduced into the soil. [Figure 3 ILLUSTRATION OMITTED] The processes which release [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] into the readily exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool, and thus dilute the radioisotopes introduced, include the dissolution of P fertilisers applied, the desorption of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] from soil surfaces, and mineralisation of organic P. The dissolution of P fertilisers becomes particularly important when slowrelease fertilisers are applied, where the dissolution and thus release of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] occurs over an extended period of time (Di et al. 1994b). Watersoluble P fertilisers such as triple superphosphate or ammonium phosphates dissolve rapidly after their application, and the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] released becomes part of the exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool shortly after the application. The release of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] from soil surfaces may also be significant when the concentration of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in the soil solution is reduced by plant uptake. In soils with high organic matter content, the mineralisation of organic P will be an important factor releasing [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to the exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool. The processes that remove [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] from the readily exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool include P sorption or precipitation, microbial immobilisation, and plant uptake. The magnitude of these processes will depend on the soil P retention capacity, microbial activities, and the presence or absence of plants. In a soil that has recently received P fertilisers, the dissolution of fertiliser P and sorption may constitute large proportions of the [F.sub.I] and [F.sub.O] values (Di et al. 1994b). In a soil with a P status at a steady state, the microbially mediated processes of mineralisation and immobilisation may make up major proportions of the influx and outflux rates. Methodology Similar to determining the gross N transformation rates, the determination of P flux rates through the readily exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool requires the quantification of the sizes of the exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool ([Q.sub.1] and [Q.sub.2]) and the specific activities ([A.sub.1] and [A.sub.2]) of the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool at [t.sub.1] and [t.sub.2] after the addition of the isotopic tracer. The approach that Di et al. (1994b) developed for studying the P fertiliser dissolution rates involved uniformly mixing the soil with a solution containing radioactive [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The soil was then packed in a pot and plants (Lolium perenne) were grown to sample the specific activity in the soil. The plants were harvested regularly and the samples were digested for the analysis of P concentration and the counting of radioactivity. The specific activity thus derived provided a curve (A v. t) from which the specific activity immediately after labelling was extrapolated. This instantaneous specific activity was used to calculate the quantity of the readily exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] using Eqn 9: (9) Q=q/A where q is the total radioactivity added, and A the specific activity. A series of these experiments was carried out to determine the changes in the quantity of exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] with time (Q v. t). The [F.sub.I] and [F.sub.O] values were then calculated using the specific activity values (A) at [t.sub.1] and [t.sub.2], both from the same labelling experiment, and the quantities of exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] corresponding to [t.sub.1] and [t.sub.2] derived from the series of experiments which provided the Q v. t curve (Di et al. 1994b). The advantage of this method was that plants were used to sample the soil to measure the specific activity; any effects that the growing plants may have had on the dissolution rates of the P fertiliser would have been taken into account by the method. However, the method was labour intensive and required a series of labelling experiments. An alternative to using plants to sample the specific activity is to measure directly the specific activity in the readily exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool by measuring that in the soil solution. This assumes that the soil solution [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is part of the exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool, and thus has the same specific activity. This involves labelling the soil with a radioactive [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] isotope and, at [t.sub.1] and [t.sub.2], shaking the labelled soil sample with a volume of water for 124 h. The solution to soil ratio may vary depending on specific circumstances but a ratio of about 10 is often convenient (Di et al. 1997). The period of shaking is arbitrarily determined, as the exchange reaction may not reach an equilibrium for many days, depending on the soil. After centrifuging and filtering, the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] concentration in the supernatant is analysed using colourimetric methods, and the radioactivity counted on a liquid scintillation counter (L'Annunziata 1987). This will provide the specific activities, [A.sub.1] and [A.sub.2], at [t.sub.1] and [t.sub.2], respectively. At the same time as the labelled soil samples are shaken with water, soil samples that are not labelled with the radioisotope, but are kept under conditions identical to the labelled samples, are shaken with a radioisotope [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] solution (the same volume as the water above and for the same period). After centrifuging and filtering, the supematant is then analysed for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] concentration and radioactivity as above. The quantities of the readily exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pools ([Q.sub.1] and [Q.sub.2]), corresponding to [t.sub.1] and [t.sub.2], can then be calculated using Eqn 9. [F.sub.I] and [F.sub.O] can be calculated using Eqns 5 and 6 or 8. Water is preferred to other chemical extractants for determining the specific activity in the exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool, because stronger chemical (alkaline or acidic) extractants may release soil inorganic and organic phosphates that are not part of the readily exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool. The labelling of soil with radioactive isotopes may also be achieved by injecting [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] solutions into intact soil cores either in the field or in the glasshouse. Di et al. (1995) showed that when [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] solutions were injected into intact soil cores (150 mm diameter and 150 mm height) with an injector consisting of 20 syringe needles, the specific activity as sampled by plants was the same as that from pots in which the tracer was uniformly mixed with the soil. This indicated that the distribution of the injected tracer was reasonably uniform. Both [sup.32]P and [sup.33]P radioisotopes can be used as a tracer for the isotope dilution technique. [sup.32]P has a shorter halflife of 14.3 days than [sup.33]P, which has a halflife of 24.4 days, but both halflives are long enough for the technique. The radioactivity of [sup.32]P can be counted by Cerenkov counting directly on the aqueous phase, whereas that of [sup.33]P needs to be counted by scintillation counting involving the addition of fluorescent reagents (L'Annunziata 1987). Example calculation Assume that the following data have been obtained after an isotopic dilution experiment to determine the gross flux rates of P through the exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool. The specific activities in the exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool were determined using the water extraction method as described above; [t.sub.1] is 3 days (i.e. 3 days after the labelling of the soil); [t.sub.2] is 10 days (10 days after the labelling of the soil); [Q.sub.1] is 60 [micro]g [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] soil; [Q.sub.2] is 52 [micro]g [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] soil; [A.sub.1] is 300 Bq/[micro]g [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; [A.sub.2] is 260 Bq/[micro]g [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (both [A.sub.1] and [A.sub.2] have been corrected to the same reference time to account for radioactive decay). Then, using Eqns 5 and 6: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Sulfate transformation rates Conceptual model Although [sup.35]S has been used to trace the transformations of sulfur in the soil (e.g. Freney et al. 1971; McLaren et al. 1985; Ghani et al. 1993a), there have been no studies reported in the literature, involving the use of the tracer dilution theory described above, to determine the gross S transformation rates through the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool. This is surprising in view of the fact that a significant amount of the S taken up by plants is released from mineralisation (McLaren et al. 1985). The tracer dilution technique described above can be used to determine the gross transformation rates through the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool in a similar way to that for phosphate, using [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] as the tracer. The conceptual model of S transformations through the mineral [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool in the soil is shown in Fig. 4 (McLaren and Cameron 1996). The dissolution of S fertilisers, mineralisation of organic S, and desorption of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] sorbed on soil surfaces all contribute to [F.sub.I] (Fig. 4). Microbial immobilisation, reduction, sorption, leaching, and plant uptake are the processes that remove [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] from the labelled [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool. In a soil that has not received fresh S fertilisers, [F.sub.I] is probably dominated by the release of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] from the mineralisation of organic S (Stevenson 1986). [Figure 4 ILLUSTRATION OMITTED] Under aerobic incubation conditions, microbial immobilisation is probably the dominant process removing [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] from the labelled exchangeable pool. Reduction of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] only becomes significant when the soil is under anaerobic conditions. The values of [F.sub.I] and [F.sub.O] under these conditions would thus give a good indication of the gross mineralisation and immobilisation rates. Under field conditions with growing plants, however, leaching and plant uptake will become important, contributing to [F.sub.O]. Methodology [F.sub.1] and [F.sub.0] for the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool can be determined in a similar way to those for the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool, by using [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (halflife = 86.7 days) as the tracer. After the soil exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool is labelled with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], the specific activities at [t.sub.1] and [t.sub.2] in the exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pool can be determined by shaking the soil sample with a volume of water, and analysing the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] concentration and radioactivity in the supernatant (McLaren et al. 1985; L'Annunziata 1987). Similarly, the quantities of exchangeable [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] ([Q.sub.1] and [Q.sub.2]) corresponding to [t.sub.1] and [t.sub.2] can be determined by shaking [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] solutions with unlabelled soils that were treated in the same way as the labelled soils, and determining the specific activity in the supematants. The Q val ues are calculated using Eqn 9. Alternatively, after the soil is labelled with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], soil samples are taken at [t.sub.1] and [t.sub.2] and are extracted with a phosphate solution (Blakemore et al. 1 987). After centrifugation and filtering, the concentrations of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and the radioactivity in the extracts are determined. The specific activities of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] ([A.sub.1] and [A.sub.2]) in the extracts are then calculated from these analyses. The [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] concentrations extracted by the phosphate solution are used to calculate the mineral [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] pools ([Q.sub.1] and [Q.sub.2]). The two methods may not yield identical results, because the Q and A values measured by the two methods may not be the same due to the different extraction solutions used. The labelling of the soil, again, may be by uniform mixing or, if intact soil cores are used, by injecting [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] solutions into the soil cores. Example calculations See the example for calculating P transformation rates in the previous section. Limiting factors Interpretation of [F.sub.I] and [F.sub.O] values Figs 24 show that the values of [F.sub.I] and [F.sub.O] may comprise more than one influx or outflux process. Therefore the influx and outflux rates cannot simply be regarded as mineralisation or immobilisation rates, respectively. The relative significance of the different processes that contribute to [F.sub.I] and [F.sub.O] depends on the conditions under which the experiment is conducted. Under certain conditions, however, the values of [F.sub.I] and [F.sub.O] can be good indicators of transformation rates for specific processes when the transformation rates of other processes are either negligible or determined independently. A number of studies which have been cited in the preceding sections have applied the techniques to gain quantitative understanding of nutrient dynamics under different soil or sediment conditions. Another process which is not shown in Figs 24 but affects the nutrient dynamics in the soil is the slow diffusion of the isotope into soil microsites (e.g. into the fine pores of stable soil aggregates). This equilibration process affects the ratio of the tracer to tracee in the labelled nutrient pool and may take many days or weeks to reach equilibrium, particularly for slowmoving nutrients such as phosphate or ammonium. However, the significance of this process in affecting the calculated nutrient transformation rates is unknown. Uniformity of tracer distributions in the soil Ideally, the stable or radioactive tracers added to the soil should be uniformly mixed with the mineral nutrient in the soil. This can be assumed to have been achieved when the tracer solution is thoroughly mixed with the soil. However, complete mixing is difficult when intact soil cores are labelled. When tracer solutions are injected into soil cores, even with multiple injections, the tracer solutions are only distributed in several columns around the injection holes. This nonuniform distribution of the tracer in the soil could result in errors in the calculated [F.sub.I] and [F.sub.O] values. However, the errors only become significantly large ([is greater than]10%) when there is a biased tracer distribution that is concurrent with a nonuniform distribution of microbial processes, e.g. changes with soil depth (Davidson et al. 1991). Monaghan (1995) showed that large errors may also arise when the FO values are high in combination with poor tracer distributions. Additionally, where growing plants are present, the nutrient transformations are likely to be more rapid in the rhizosphere than in the bulk soil. If tracers are not present in the rhizosphere, then the transformation rates determined would not reflect the rhizosphere activities. The recommendation is that the tracer solution should be delivered to as many points in the soil as possible without causing excessive disruption to the `intactness' of the soil cores, or causing significant soil moisture changes. Multiplepoint injectors with sideport needles are recommended. Changes in soil conditions as a result of labelling Adding tracer solutions to soil can change the soil moisture content, and this might significantly affect microbial activities and nutrient transformation rates, particularly in dry soils or soils with a low water retention capacity. However, if the volume of solution applied is kept intentionally small to reduce this problem, the tracer label applied may not be uniformly distributed in the soil. The challenge is thus to balance the needs for minimum moisture changes on the one hand, and uniform tracer distributions in the soil on the other. Attempts have recently been made to apply [sup.15]N tracers as a dry powder (Willison et al. 1998), or in a gas form in the case of ammonium (Murphy et al. 1998). It is generally accepted that for moist, finetextured soils, the effect by moisture changes brought about by the addition of the tracer solution is probably limited. Nevertheless, for dry soils and soils with a low water retention capacity, the results obtained by the isotopic dilution method, involving the addition of tracer solution, should be interpreted with caution. Davidson et al. (1991) suggested that the technique should not be applied to soils with a matric potential below 1.5 MPa. The isotopic tracer added to the soil may also disturb the existing nutrient dynamics in the soil. This effect, however, is negligible if carrierfree (i.e. no stable nutrient carrier in the tracer solution) radioactive tracers are used, because the amounts of tracer nutrients added are very small. With the [sup.15]N stable isotope, the main concern occurs when the amount of tracer added is significant compared with the soil mineral N concentration. Highly enriched [sup.15]N sources (e.g. 99 atom% [sup.15]N) are thus recommended, so that less N needs to be applied to obtain suitable [sup.15]N enrichment in the mineral N pool. Injecting tracer solutions into soil cores creates holes in the soil, and this may change the soil aeration status, and thus the nutrient transformation rates. The effect of this, however, is largely unknown. Losses of [sup.15]N labels If the tracer labels injected into the soil are lost shortly after addition before reaching an equilibrium with the native soil nutrient, e.g. by leaching and denitrification of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], or volatilisation of [NH.sub.3], then these tracer losses can lead to an overestimation of the transformation rates (Barraclough 1991). The leaching is mainly significant in soils with a low water retention capacity, e.g. in sandy soils (Sparling et al. 1995). The use of sideport needles, limiting the volume of tracer solution injected, and sealing the base of the soil core will minimise the impact by leaching. The effect of initial volatilisation and denitrification losses on calculated transformation rates has not been quantified, and is probably of a minor magnitude in most cases. Spatial variability In field experiments where the isotopic tracer is injected into intact soil cores, spatial variability in the concentration of the nutrient in question can result in errors in the estimated nutrient transformation rates. The variations in nutrient (e.g. [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] or [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) concentration from location to location make it difficult to find identical pairs of soil cores for the isotopic labelling. If fertilisers or other nutrient sources are applied to the soil, the spatial variability can be minimised by inserting the paired soil cores into the ground first, and then applying known amounts of the nutrient source to each soil core. This is a preferred approach to broadcasting the nutrient source to field plots first and then inserting the soil cores, because it is difficult to spread the nutrient source evenly onto the soil surface. Optimum duration of experiment The optimum time period between the two samplings, [t.sub.1] and [t.sub.2], during which the assumptions remain valid is dictated by the following 4 factors. (1) The time period beyond which significant amounts of the tracer immobilised may be recycled back to the labelled mineral pool. (2) The time period beyond which the [sup.15]N content or specific activity in the labelled mineral nutrient pool becomes too low for reliable detection. (3) The time period during which the rates of influx ([F.sub.I]) and outflux ([F.sub.O]) remain constant. (4) The minimum time period during which significant nutrient transformations have taken place and thus resulted in significant changes in tracer abundance or specific activity in the labelled nutrient pool. Large errors may occur if the experimental period is too short without significant transformations occurring to the labelled nutrient pool. The relative length of the 4 time limits varies in different soilplant systems. The main concern in the past has been the possible recycling of the immobilised tracer back to the labelled mineral nutrient pool. Some studies have shown that recently incorporated organic nutrients such as S are more readily mobilised than the bulk of the organic S in the soil (e.g. Freney et al. 1975; McLaren et al. 1985; Ghani et al. 1993b). However, there have been no detailed studies reported where the optimum durations of experiments for determining the gross transformation rates of N, P, or S are determined. It has been assumed in N transformation studies that a period of 57 days between [t.sub.1] and [t.sub.2] is acceptable (Barraclough 1995). Although equations have been formulated to suit conditions where remineralisation might occur (Kirkham and Bartholomew 1955), they have rarely been used, probably because of the complex nature of the work required and restrictive assumptions. Numerical solutions, however, have been used to take into account the recycling of immobilised [sup.15]N in the calculations (Bjarnason 1988; Wessel and Tietema 1992; Smith et al. 1994). The duration of the experiment will also depend on the objective of the study. If, for instance, the aim is to determine the rate at which a nutrient is released from a fertiliser applied, then the recycling of the immobilised tracer is, in fact, an advantage, because it essentially cancels or reduces the contribution by mineralisation to [F.sub.I]. The influx rate will thus be more indicative of the fertiliser dissolution rate. However, if the recycling rate changes with time, it will still compound the determination of the fertiliser dissolution rate. There is clearly a need to investigate some of the factors discussed above that may compound the determination or interpretation of the flux rates derived from the isotopic dilution method. Despite this, if the user is aware of these factors and takes due precautions in conducting the experiment, the isotopic dilution technique can serve as a valuable tool to provide quantitative insights into the nutrient dynamics in the soil. Acknowledgments We thank the Foundation for Research, Science and Technology of New Zealand for funding, and Dr Tim Clough for reviewing the manuscript. References Barraclough D (1991) The use of mean pool abundances to interpret [sup.15]N tracer experiments. I. Theory. Plant and Soil 131, 8996. Barraclough D (1995) [sup.15]N isotope dilution techniques to study soil nitrogen transformations and plant uptake. Fertiliser Research 42, 185192. Barraclough D, Geens EL, Davies GB, Maggs JM (1985) Fate of fertiliser nitrogen. III. The use of single and double labelled [sup.15]N ammonium nitrate to study nitrogen uptake by ryegrass. Journal of Soil Science 36, 593603. 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Cameron KC, Rate AW, Noonan MJ, Moore S, Smith NS, Kerr LE (1996) Lysimeter study of the fate of nutrients following subsurface injection and surface application of dairy pond sludge to pasture. Agriculture Ecosystems and Environment 58, 187197. Chalk PM, Victoria RL, Muraoka T, Piccolo MC (1990) Effect of a nitrification inhibitor on immobilisation and mineralisation of soil and fertiliser nitrogen. Soil Biology and Biochemistry 22, 533538. Condron LM, Di HJ, Goh KM, Campbell AS, Harrison R (1995) Agronomic effectiveness of partially acidulated phosphate rock fertilisers in selected New Zealand soils. Australian Journal of Experimental Agriculture 35, 387393. Davidson EA, Hart SC, Shanks CS, Firestone MK (1991) Measuring gross mineralisation, immobilisation, and nitrification by [sup.15]N isotopic pool dilution in intact soil cores. Journal of Soil Science 42, 335349. Di HJ (1991) Application of isotopic dilution methods to the study of the dissolution of phosphate fertilisers of differing solubility in the soil. PhD Thesis, Lincoln University, New Zealand. Di H J, Cameron KC, Moore S, Smith NP (1998a) Nitrate leaching from dairy shed effluent and ammonium fertiliser applied to a freedraining pasture soil under spray or flood irrigation. New Zealand Journal of Agricultural Research 41,263270. Di HJ, Cameron KC, Moore S, Smith NP (1998b) Nitrate leaching and pasture yields following the application of dairy shed effluent or ammonium fertiliser under spray or flood irrigation: results of a lysimeter study. Soil Use and Management 14, 209214. Di HJ, Cameron KC, Moore S, Smith NP (1999) Contributions to nitrogen leaching and pasture uptake by autumnapplied dairy effluent and ammonium fertiliser labelled with [sup.15]N isotope. Plant and Soil (in press). 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The relationship between rate of dissolution and plant response. Fertiliser Research 38, 1927. Di HJ, Harrison R, Campbell AS (1995) An isotope injection technique to measure agronomic effectiveness of different phosphate sources in undisturbed soils. Australian Journal of Experimental Agriculture 35, 489493. Fardeau JC, Guiraud G, Marol C (1996) The role of isotopic techniques on the evaluation of the agronomic effectiveness of P fertilisers. Fertiliser Research 45, 101109. Freney JR, Melville GE, Williams CH (1971) Organic sulfur fractions labelled by addition of [sup.35]Ssulphate to soil. Soil Biology and Biochemistry 3, 133141. Freney JR, Melville GE, Williams CH (1975) Soil organic matter fractions as a source of plantavailable sulfur. Soil Biology and Biochemistry 7, 217221. Fried M (1964) `E', `L' and `A' values. In `Eighth international congress of soil science transactions IV'. pp. 2939. Bucharest, Romania. (International Society of Soil Science.) Frossard E, LopezHernandez D, Brossard M (1996) Can isotopic exchange kinetics give valuable information on the rate of mineralisation of organic phosphorus in soil? Soil Biology and Biochemistry 28, 857864. Ghani A, McLaren RG, Swift RS (1993a) The incorporation and transformations of 35S in soil: effects of soil conditioning and glucose or sulphate additions. Soil Biology and Biochemistry 25, 327335. Ghani A, McLaren RG, Swift RS (1993b) Mobilisation of recentlyformed soil organic sulfur. Soil Biology and Biochemistry 25, 17391744. Guiraud G, Marol C, Thibaud M (1989) Mineralisation of nitrogen in the presence of a nitrification inhibitor. Soil Biology and Biochemistry 21, 2934. Herman DJ, Brookes PD, Ashraf M, Azam F, Mulvaney RL (1995) Evaluation of methods for nitrogen15 analysis of inorganic nitrogen in soil extracts. II. Diffusion methods. Communications in Soil Science and Plant Analysis 26, 16751685. Holmes RM, McClelland JW, Sigman DM, Fry B, Peterson BJ (1998) Measuring [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in marine, estuarine and fresh waters: an adaptation of the ammonia diffusion method for samples with low ammonium concentrations. Marine Chemistry 60, 235243. Kirkham D, Bartholomew WV (1954) Equations for following nutrient transformations in soil, utilizing tracer data. Soil Science Society of America Proceedings 18, 3334. Kirkham D, Bartholomew WV (1955) Equations for following nutrient transformations in soil, utilizing tracer data: II. Soil Science Society of America Proceedings 19, 189192. L'Annunziata MF (1987) `Radionuclide tracers, their detection and measurement.' (Academic Press: London) Laughlin R J, Stevens RJ, Zhuo S (1997) Determining nitrogen15 ammonium by producing nitrous oxide. Soil Science Society of America Journal 61,462465. Ledgard SF, Sprosen MS, Brier G J, Nemaia EKK, Clark DA (1996) Nitrogen inputs and losses from New Zealand dairy farmlets, as affected by nitrogen fertiliser application: year one. Plant and Soil 181, 6569. Liu YP, Mulvaney RL (1992) Use of diffusion for automated nitrogen15 analysis of soil extracts. Communications in Soil Science and Plant Analysis 23, 613625. Mayrold DD, Tiedje JM (1986) Simultaneous estimation of several nitrogen cycle rates using [sup.15]N: theory and application. Soil Biology and Biochemistry 18, 559568. McLaren RG, Cameron KC (1996) `Soil science: sustainable production and environmental protection.' 2nd Edn. (Oxford University Press: Auckland, NZ) McLaren RG, Keer JI, Swift RS (1985) Sulfur transformations in soils using sulfur35 labelling. Soil Biology and Biochemistry 17, 7379. McLaughlin MJ, Alston AM, Martin JK (1986) The relative contribution of plant residues and fertiliser to the phosphorus nutrition of wheat in a pasture/cereal system. Australian Journal of Soil Research 24, 517526. Monaghan R (1995) Errors in estimates of gross rates of nitrogen mineralisation due to nonuniform distributions of [sup.15]N label. Soil Biology and Biochemistry 27, 855859. Monaghan R, Barraclough D (1995) Contributions to gross N mineralisation from [sup.15]Nlabelled soil macroorganic matter fractions during laboratory incubation. Soil Biology and Biochemistry 27, 16231628. Monaghan R, Barraclough D (1997) Contributions to N mineralisation from soil macroorganic matter fractions incorporated into two field soils. Soil Biology and Biochemistry 29, 12151223. Murphy DV, Fillery IRP, Sparling GP (1997) Method to label soil cores with [[sup.15]NH.sub.3] gas as a prerequisite for [sup.15]N isotopic dilution and measurement of gross N mineralisation. Soil Biology and Biochemistry 29, 17311741. 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