Soil phosphorus (P) leaks rapidly from newly formed land surfaces to upland rivers and lakes, surface water P concentrations peaking early before declining as soil apatite (Ca5(PO4)3(OH)) becomes depleted. We present lake sediment P profiles that record this leakage through the early Holocene. The results are entirely consistent with our re-analysis of published soil chronosequence data, but conflict with more recent quantitative interpretations of global soil P dynamics that identify far slower loss rates. P inherited from the bedrock on soil formation, long regarded as the major source for terrestrial ecosystems, only lasts ~104 years rather than the previously suggested 106 years, and thus is, globally, much less important in the long term than atmospheric supply. This changes the conceptualization of terrestrial P dynamics, with the “terminal steady state” of Walker and Syers (1976) being the norm not the exception, and with soil P export being little if at all controlled by biotic retention mechanisms. High early export of P from newly formed soil causes a peak in the productivity of terrestrial surface waters, before a decline as the soil P pool depletes. Globally, the 18 × 106 km2 of terrain exposed since the Last Glacial Maximum potentially produced a substantial surge in runoff P, with greatest impacts likely in high-latitude, restricted basin seas and maximal area of deglaciated terrain.
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 Many studies have argued that soils in noneroding settings acquire most, if not all, of their phosphorus (P) from bedrock or unweathered surface materials during initial soil formation [Ruttenberg, 2003; Smeck, 1973], a geological P dose that undergoes transformation from primary to secondary forms [Walker and Syers, 1976], but which leaks away so slowly that it remains the dominant ecosystem P source until soils are ~106 years in age [Chadwick et al., 1999; Crews et al., 1995; Hedin et al., 2003; Porder et al., 2007]. In this conceptual model, the atmospheric P flux plays a minor role except at extremely old and mechanically noneroding sites [Porder and Hilley, 2011; Porder et al., 2007] and even then serves only to minimize the state of P depletion, in what Walker and Syers  call the “terminal steady state.” The ecological consequences of this interpretation of long-term soil P dynamics have been examined at several sites [Chadwick et al., 1999; Hedin et al., 2003; Richardson et al., 2004], leading to the view that P export is bioregulated, leakage being initially high when primary productivity is nitrogen limited, and then progressively lower as P limitation becomes increasingly severe. Regardless of the ecological mechanism, there is good evidence that P limitation can impact terrestrial productivity [Birks and Birks, 2004; Chadwick et al., 1999; Richardson et al., 2004; Wardle et al., 2004], and the models of Porder et al.  and Porder and Hilley  allow us to predict where such limitation should occur.
 These model predictions are at their most reliable in rapidly eroding landscapes, where advective processes dominate. In stable landscapes, their predictions depend more on the decay rate of soil available P, and these are less well constrained, the analysis of Porder et al.  finding rate parameters for different sites that differ by more than an order of magnitude. Furthermore, the magnitude of the estimated decay parameters found for available P by Porder et al.  and for total P by Porder and Hilley  is incompatible with the global riverine dissolved P flux of 6.7 to 12.1 mg m−2 a−1 of Ruttenberg . Even if all the decayed P were exported to runoff (rather than partially retained in the soil in unavailable forms), the decay constant of 2.9 × 10−7 a−1 would imply a mean soil P content of 27–41 kg m−2, which is 2 orders of magnitude too large. In order to identify the source of this discrepancy and to better constrain long-term soil P dynamics in noneroding landscapes, we re-evaluate and develop the long-term, large-scale soil P model of Porder et al. . We do this by more explicitly assessing the dynamics of soil apatite and by supplementing the published soil chronosequence data with evidence from lake sediment records of runoff P, broadening the basis for parameterization and model validation. Such a refinement also allows us to consider the fate of P leaking from the soil; whether it is retained deeper in the soil or exported to runoff has profound implications for aquatic ecosystems.
 Previous models of soil P evolution over time have not incorporated data from lake sediments, which in some cases can preserve information about the evolution of soil P in the landscape over time. Mackereth  observed that for three sites in the English Lake District, concentrations of P in lake sediments showed an early post-glacial maximum and subsequent decline. He argued that changing P supply from the catchment soil was the most likely cause, post-glacial warming bringing about an initial increase in weathering, and subsequent depletion of the soil P pool leading to an eventual decline. This interpretation in terms of fluxes was confirmed for Lake Trummen in southern Sweden by Digerfeldt  who showed a maximum flux to the lake bed of 290–330 mg P m−2 a−1 in the early Holocene, falling rapidly to 15–25 mg m−2 a−1 within 3000 years. Higher-resolution Holocene P flux studies at Plešné Lake in the Czech Republic [Kopacek et al., 2007] and Sargent Mountain Pond in Maine, USA [Norton et al., 2011], provide greater detail, showing a rapidly increasing flux to the lake bed through the first 500–1000 years of the Holocene, followed by an exponential decrease up to the time of modern landscape disturbance. As observed by Filippelli and Souch  based on low-resolution lake sediment records from North America, the decline stage of these curves shows striking similarity to the total soil P depletion trajectories of the Walker and Syers  conceptual model, suggesting that lake sediments and soil chronosequences may share a common controlling mechanism. Crucially, lake sediment records provide a means of answering the question posed by Walker and Syers  of where P leaked from soils ends up. Furthermore, lake sediments capture not only the soil P leakage but also eroded soil primary minerals from which the changing soil composition may be inferred (secondary soil minerals are also captured, though often less effectively owing to the small particle size). Thus, Filippelli and Souch , Norton et al. , and Kopacek et al.  have used lake sediment records to reconstruct the history of soil apatite variation, and it is the dual function of providing records of both P export flux and soil apatite loss that we use lake sediment data for here.
2.1 Conceptual Model
 Our long-term soil P model comprises a simple numerical representation of the Walker and Syers  conceptual model. It broadly follows the treatment of Porder et al. , though simplified to a vertically integrated form. The long-term dynamic model of soil available P (here designated as PS, mg g−1) presented by Porder et al.  explores the balance between loss of available P due to a combination of leaching and immobilization and its supply from dissolution of apatite P (here designated as PCa, mg g−1) either inherited from the original substrate or released via erosion-driven bedrock exhumation. Rates of release from apatite to the available P pool, and loss from it, are handled by the first-order rate constants (year−1), with symbols k and λ, respectively. The model of Porder et al.  assesses the role of exhumation relative to substrate inheritance in controlling the availability of P to ecosystems, quantifying the coefficients by the inverse method using noneroding chronosequences sites. Porder and Hilley , in contrast, explore the relative importance of dust flux and exhumation the long-term regulation of soil total P (here designated as PT, mg g−1). They apply a similar model, but one in which the time scale makes it unnecessary to separate PCa from PS, allowing the k term to be ignored. Again, this is calibrated using noneroding soil chronosequences data.
 For our investigation, which places greater emphasis on the early dynamics, we cannot ignore k, and in this sense, our model is close to that of Porder et al. . However, we differ from this study in ignoring the exhumation component which is done for two reasons. First, our focus on the early stages makes it less reasonable to adopt an assumption of steady state between erosion and exhumation [Porder et al., 2007], which would require instead the use of a more complex but untestable dynamic erosion model. Second, the sites we use to parameterize our model (lake sediment records and the soil chronosequences) are from minimally eroding sites which therefore provide no guidance on parameterization of an erosion term. Consequently, our model is applicable only to sites with low exhumation rates. We estimate soil erosion at both lake study sites to be no more than 3 mm kyr−1 (bedrock equivalent). We assume that the soil chronosequence sites have experienced no soil erosion.
 We differ in one further way from both Porder et al.  and Porder and Hilley . Because of our emphasis on absolute rather than relative fluxes, we express our model in terms of P density rather than concentration. Thus, our three concentration terms, PT, PCa, and PS, (in mg g−1) have corresponding density terms DPT, DPCa, and DPS (in g P m−2). Fluxes associated with these P densities can be calculated directly using first-order rate constants. These terms and their units are listed in Table 1.
Table 1. Model Parameters and Coefficients
PT, PCa, PS
Soil concentrations of total (T), apatite (Ca), and secondary (S) P
DPT, DPCa, DPS
Soil areal density of total (T), apatite (Ca), and secondary (S) P
g P m−2 a−1
Supply to the soil surface of atmospherically derived P
g P m−2 a−1
Supply of P to the soil from PCa dissolution and Qatm
g P m−2 a−1
Total P export rate from the soil
g P m−2 a−1
Mass accumulation rate (MAR) of non-apatite P in the lake sediment normalized to lake area
Rate coefficient for apatite dissolution
Rate coefficient for release of PS
Fraction of P released directly to runoff on dissolution of apatite
 Other differences are addressed in the text below. The field and laboratory data used to parameterize the model are obtained largely from published studies. The most important methodological issues concern characterization of the soil and sediment P fractions, which differ somewhat among the various studies. Of the many operationally defined soil P fractions, two measured concentrations are both reproducible and useful to this study: acid-extractable P (PCa) which is assumed to be predominantly from apatite (Ca5(PO4)3(OH)) [Walker and Syers, 1976] and total P (PT) from which changes in soil profile P content can be calculated. Secondary soil P (PS) is calculated as the difference between these two concentrations. Here PCa is the fraction removable by 0.5 M H2SO4 [Walker and Syers, 1976] or 1 M HCl [Crews et al., 1995; Norton et al., 2011] from the soil or sediment residue following extractions with 0.1 M NaOH and Na bicarbonate/dithionite [Psenner et al., 1988]. PT is normally calculated from the sum of all fractions including boiling concentrated H2SO4 [Crews et al., 1995], 1 M NaOH at 85°C [Norton et al., 2011], or NaCO3 fusion followed by extraction with H2SO4 [Walker and Syers, 1976]. For the Kråkenes Lake sediment (site described below), PT was measured by X-ray fluorescence analysis. The soil P fractions and model parameters used in this study are defined in Table 1.
2.2 Lake Study Sites
 Two lakes sites were used for this research. Kråkenes Lake, situated 38 m above sea level on the island of Vågsøy, Western Norway, a small (0.055 km2) lake with a catchment mainly of mixed granitic and amphibolitic rocks, was formed by deglaciation approximately 14 ka B.P. (see Boyle et al.  for details). Sargent Mountain Pond, situated at 336 m above sea level in Acadia National Park, Maine, USA, a very small (0.0038 km2) lake with a granitic catchment, was formed by deglaciation approximately 16 ka B.P. (data from Perry ).
2.2.1 Coring, Chronology, and Elemental Analysis
18.104.22.168 Kråkenes Lake
 Full details on the procedures summarized here are given in Boyle et al. . A sediment core (8.96 m) was collected from the terrestrialized southwestern lake arm (lake level was lowered in the nineteenth century) using a 1 m long 70 mm diameter Russian corer in 10 overlapping drives in May 2007. Meter-long sections were stored at 4°C in plastic guttering, wrapped in polythene sleeves. Within 2 weeks, the core drives were sliced at 1 cm intervals and freeze dried. Loss on ignition at 450°C was measured relative to the dry weight at 105°C. The total element concentrations were determined by X-ray fluorescence (XRF) analysis using a Bruker S2 Ranger energy dispersive instrument. Loose powders were pressed lightly in sample cups with 6 µm polypropylene film and were measured for 250 s under helium at three different tube settings. Variable alpha mass attenuation corrections were applied taking measured organic matter concentrations into account. Calibration used a set of 15 certified reference materials, and processing the reference materials as unknowns generated root mean square differences for P of better than 5% of the mean. The allogenic phosphorus fraction was measured by XRF analysis after chemical treatment to remove loosely bound and organic fractions, using 1 M NaOH, based on the modified Williams method of Pardo et al. . Core chronology was established using tephra layers (Vedde 11.97–12.25 ka, Saksunarvatn 10.11–10.25 ka, and Hekla-4 ~4.4 ka) and cross correlation with the radiocarbon-dated master core for Kråkenes [Birks et al., 2000].
22.214.171.124 Sargent Mountain Pond
 Full details are given in Perry . A 5.3 m long core was taken from the center of the lake (5 m water depth) using a 1 m long, 50 mm diameter square-rod piston corer in six overlapping drives in March 2007. The core was sectioned in the field at 20 mm intervals. The sediment was stored at 4°C. Phosphorus was fractionated using the method of Lukkari et al. . Only the apatite (HCl extractable) and available (NaOH extractable) fractions are reported here. Twelve AMS (Accelerator Mass Spectrometry) 14C measurements (primarily plant macrofossils) ranging 2900 to 13,300 14C years were used to develop an age-depth model.
2.3 Lake Sediment Record of Soil P Export
 Our model assumes (a) that P leaked from soil is exported in runoff and (b) if a lake intercepts such runoff, then it captures a proportion of the leaked P. Thus, lake sediment records of P flux can be used to investigate soil P leakage, provided corrections can be made for incomplete P retention by the lake, and for the magnification effect of a larger catchment feeding into a smaller lake. Equation ((1)) provides a simple procedure for linking the non-apatite P sedimentation flux (PMAR, g m−2 a−1) at a coring site in the lake centre to the catchment soil P leakage flux (Qleakage).
F is a lake P retention factor that can be estimated from the empirical equation of Kirchner and Dillon  (which predicts 1/F from water flux data), SAA (sediment accumulation area) is the area of lake bed within the mud limit [Rowan et al., 1995] on which fine lake sediments accumulate (and across which P is assumed to accumulate evenly), and CA is the terrestrial catchment area. The data needed for these calculations are provided in Table 2.
Table 2. Lake Catchment Physical and Soil Properties Data
 The scaling achieved by equation ((1)) has the effect of expressing the lake sediment flux record in a metric comparable to the soil P density. If Qleakage calculated this way is expressed cumulatively (forward in time), and is normalized to the soil initial PCa density (DPCa,0), then we obtain a measure changing soil P loss through time, starting at zero and increasing as the soil depletes. Thus, the percentage soil P loss at time t is given by
 The calculations in equations ((1)) and ((2)) are based on the sediment record of non-apatite P. However, there is an additional sediment P signal resulting from the presence of in-washed (allogenic) primary apatite [Boyle et al., 2013]. As weathering depletes the soil of its apatite, the concentration of apatite present in the sediment allogenic fraction (as measured by sediment PCa normalized to the proportion of the sediment comprising allogenic matter) falls proportionately. The percentage apatite loss from the parent soil for time t is then estimated by
3 Results and Discussion
3.1 Lake Sediment Records of Long-Term Terrestrial P Fluxes
 The lake sediment records of Sargent Mountain Pond and Kråkenes Lake (Figure 1a) show broadly exponential declines in both apatite concentration (corrected for dilution by organic matter and biogenic silica using immobile elements [Boyle et al., 2013]) and non-apatite P flux values. Both signals postdate the rapid early Holocene reduction in erosion rate and therefore are not driven simply by landscape stabilization. To assess the rates of decline, it is convenient to reverse the time axis, establishing a zero point after which weathering is assumed to be active. In both cases, we have zeroed time at the start of the Holocene on the basis that any pre-Holocene weathering was at a substantially lower rate. At Kråkenes Lake, glacial ice covered a large part of the catchment to within a few decades of this date, and non-ice-covered ground experienced very low summer temperatures and precipitation [Birks et al., 2000]. At Sargent Mountain Pond, the catchment had been ice free for some thousands of years, but remained cold during the Younger Dryas [Borns et al., 2004]. The first-order rate coefficients calculated on this basis (Figure 1a) are similar for both lakes and for both phosphorus forms. This result is fully consistent with the soil P model of Walker and Syers  in finding that leakage of P from the soil closely parallels depletion of apatite from the soil. To test this association, we calculate for the two sites both the rate of apatite loss from soil as inferred from PCa in the lake sediment (equation ((3))) and the rate of decline in soil P leakage as inferred from the declining P flux to the sediment (equation ((2))).
 The calculated percent loss of apatite (Figure 1b) follows a saturation exponential form. The percent total loss curves mirror the apatite loss closely in form, but lower in value reflecting partial retention of P in the soil. Several curves are shown for each lake representing the range of values estimated for the soil initial DPCa,0. These curves suggest very substantial loss of soil P by the end of the Holocene, ranging 35–75% at Kråkenes Lake. At Sargent Mountain Pond, both curves suggest near-complete loss of initial soil P within the Holocene, a result which likely reflects either underestimation of DPCa,0, or overestimation of the P flux to the lake. The two measured P values for the granite of the Sargent Mount Pond catchment are very low compared with average granite, and may possibly under-represent the average condition. A curve based on average granite P concentrations [Krauskopf, 1982] implies a loss of 40% by the end of the Holocene, a value that should be regarded as a minimum estimate.
 To simulate this loss of apatite P to runoff, we introduce a leakage parameter, α, representing the fraction of PCa dissolution that is immediately exported from the soil. To find values for α, we calculate the percentage soil P loss curves (equation ((2))) and fit equation ((4)) to these. The value of k is taken from the apatite depletion curves (also shown in Figure 1b), leaving only α to be adjusted:
 The curves provide reasonable fits to the calculated P loss data for both sites. The α values found this way range between 0.3 and 0.9 indicating not only substantial soil leakage rates but also considerable uncertainty.
 From the preceding discussion, based on the data presented in Figure 1, two conclusions arise. First, leakage of P from the soils is also substantially greater than the decay rate for available P (an upper limiting estimate for the leakage rate) suggested by Porder et al. . Second, the soil P leakage covaries with the inferred soil apatite concentration, suggesting that the soils only partially capture the P released by apatite weathering. This picture of rapid P leakage appears at odds with the soil chronosequence evidence. We now look more closely at this.
3.2 Re-evaluating Chronosequence Data in Long-Term Soil P Modeling
 Here we evaluate the data from four published soil chronosequence studies, Hawaii, USA [Crews et al., 1995; Hedin et al., 2003], and Franz Josef, Reefton, and Manawatu in New Zealand [Walker and Syers, 1976], to see whether the discrepancy can be reconciled. The Hawaii and Franz Josef data sets are identical to those investigated by Porder et al. , though our treatment of these is different, particularly in our direct assessment of both apatite depletion and loss of the soil P pool. We treat the chronosequence data exactly as we have treated the lake sediment records, determining rate coefficients for the P depletion. The data for both apatite and total P concentration (Figure 2a) produce curves that are very similar to the lake records, though in some cases covering a very much longer time period. Again, exponential curves have been fitted to the apatite concentrations, the best fit first order decay coefficients ranging from log k = −3.4 at Manawatu to log k = −3.8 at Reefton, values that bracket our results for the two lake sediment records. Our value at Franz Josef is similar to that found by Porder et al.  (log k = −3.5). Differences between sites are likely impacted by climate or other factors, but because of the small sample size, this has not been explored.
 The percent loss of apatite (Figure 2b), calculated directly from the published data, follows a saturation exponential form just as for the lake sediment records. Ninety percent loss is reached at 6 ka (Franz Josef) and 15 ka (Reefton), bracketing the values for the lake sediment data. Loss of P from the soil, calculated from the declining soil P pool (DPT), follows a similar shape to the apatite loss curve and, just as for the lake sediment records, can be predicted from the apatite loss curve using the leakage coefficient, α. The shape of the predicted loss curves is, in all cases, similar to the observed data. The best fit values for α, ranging between 0.23 (Hawaii) and 0.9 (Franz Josef), bracket the estimates from the lake sediment records. It should be noted that the high α value at the Franz Josef Glacier site is due to an exceptionally high P content in the youngest soil. If this value is disregarded (Figure 2b, Franz Josef, dashed line), then a much lower α value of just 0.37 is obtained.
 Thus far, the lake sediment and soil chronosequence data tell us the same thing. However, we have neglected to consider the release of secondary soil P, a process inherent in the Walker and Syers  conceptual model and addressed in detail by Porder et al. . The possible impact of secondary soil P decay can be tested using the approach of Porder et al.  by exploring the extent to which a decay parameter (λ) allows us to better explain the observed data. Equation ((5)), by predicting changes in soil secondary P density (DPS) through time, allows us to predict the variation in soil total P density (DPT, where DPT = DPCa + DPS):
 In the relatively short time intervals represented by the data in Figure 2, reasonable values for λ make little difference to the curve shapes. However, if we apply the model to the older soil chronosequence sites (Figure 3), the model fit becomes increasingly poor after approximately 104 years if λ is set at zero. For all sites except Hawaii, this can be solved simply by giving λ a value of 1.0 × 10−5 a−1. To improve the fit for Hawaii, it is necessary to include atmospheric P supply in the model, a flux known to be substantial. Thus, using an atmospheric deposition rate of 0.001 g P m−2 a−1 for Hawaii [Chadwick et al., 1999] and the other chronosequence sites [Mahowald et al., 2008], we get a far better fit for Hawaii and similar degree of fit at the three younger sites, though the value of λ must be raised to 2.0 × 10−5. After we have incorporated both atmospheric supply and loss of secondary P into the model, it is no longer possible to use degree of fit for parameterization; higher atmospheric flux values can be made to fit by selecting higher λ values. At Hawaii, the fit shown uses 0.002 g m−2 a−1 [Hedin et al., 2003] and λ = 6.0 × 10−6, but no reliability should be placed on these parameter values; instead, the analysis serves to show two important things. First, for very ancient noneroding soils, interpretation depends critically on the chosen dust flux value, something which will always be poorly constrained for the distant past and is known to vary by orders of magnitude in the Northern Hemisphere through glacial cycles [Mcgee et al., 2010]. Second, at reasonable values for the dust flux, the decay coefficient for secondary soil P is very low, suggesting that this process contributes little to total soil P leakage for soils younger than 104 years. Though low in value, this decay constant is very important in long-term modeling; if λ is set at zero for the Hawaii chronosequence, then by 4 Ma, the soils would contain an additional 4000 g P m−2, or some 10 times the initial soil content at even the lower of the two atmospheric flux estimates.
3.3 A Leaky Model of Long-Term Soil P Dynamics
 The parameters identified from the preceding analysis of lake sediment records and soil chronosequence data can be used to quantify a model of long-term soil P dynamics, similar to Porder et al.  but including an apatite dissolution leakage term. Good agreement between the lake sediments and the soil chronosequences for the rate of soil apatite loss, and the relatively restricted range in best fit parameter values across a wide range of climates and soil types, suggests that the model can be applied in a generalized way at least in broadly temperate regions. There is no consistent association between parameter values and either climate or geology (Table 3). We must, however, expect that rates would be lower at more arid locations [Selmants and Hart, 2010] and also where soils are frozen for much of the year.
Table 3. Study Site Parameters and Environmental Properties
 The basic premise of the model is that for a newly formed land surface, P is made available to the soil through dissolution of primary apatite and from any atmospheric inputs. The supply of P (Qsupply) to the available (including dissolved) soil pool can be expressed in terms of the atmospheric deposition (Qatm) and partial dissolution of primary soil apatite P (DPCa):
 Whether the atmospheric supply is largely apatite or more available P forms is unimportant owing to the rapid rate of apatite dissolution relative to the timescales at which dust fluxes greatly contribute. Less soluble phases such as monazite are neglected.
 The P made available in this way is partially retained in the soil as secondary phases and partially exported to runoff. Slow decay of the secondary soil P contributes to the export and depletes the secondary P pool, the leakage flux (Qleakage) being given by
 These expressions fully describe the long-term dynamics for noneroding sites. In the short term, for time periods less than approximately 104 years, both Qatm and the decay of DPS are very minor, and export of P to runoff is well described by αkDPCa, a simple fraction of the apatite dissolution rate.
 To apply this model in a generalized way, it is necessary to find global values for k, α, DPCa,0 (DPCa at time = 0), and for longer time periods, λ and Qatm. For the first three of these, we propose using the mean values for our six sites, yielding log k = −3.61, α = 0.40, and DPCa,0 = 540 g m−2, and for λ, we suggest a value of 2.0 × 10−5. However, the atmospheric flux cannot be generalized in this way owing to its great geographic and temporal variability. Values taken from Mahowald et al.  provide a starting point.
3.4 Phosphorus Leakage, Atmospheric Supply, and the Geological Dose Concept
 Our analysis suggests that P leaks from soil far more rapidly than has been proposed in other recent studies [Porder and Hilley, 2011; Porder et al., 2007]. This difference in interpretation arises partly from our inclusion of an apatite P leakage term and partly from our very much higher estimate for λ, differences that require justification if our findings are to be accepted. In the case of λ, Porder and Hilley  find a value of 2.9 × 10−7 a−1, 2 orders of magnitude lower than our estimate, obtained in part from the same data. We attribute this to the way in which the atmospheric flux is treated; if we set the atmospheric flux at zero, then we too get a very low best fit value for λ. Two observations give us confidence that our estimate is approximately correct. First, all four soil chronosequences yield best fit values of the same order for λ (6 × 10−6 a−1 for Hawaii and 2 × 10−5 a−1 for the other sites). Second, the lysimeter data of Hedin et al.  and the soil data of Crews et al.  give us a direct estimate for λ of 0.8–0.9 × 10−5 a−1, essentially identical to our values but 30 times that of Porder et al. . Furthermore, if we use stream water P budget data as an alternative source of information, we also find values close to our estimate. For example, using the P budget at the Hubbard Brook Experimental Forest [Yanai, 1992], we obtain a value of 2.2 × 10−5 a−1 (likely an overestimate as a consequence of acidification over the last 100 years [Reinhardt et al., 2004; Roy et al., 1999]). The global runoff and soil data of Ruttenberg  (for pre-modern values) yield a value of 0.94 × 10−5 a−1 (range 0.5–1.9 × 10−5 a−1).
 Of potentially greater significance is the observation that P leaks very rapidly from a soil during its early development. How reliable is this? In fact the existence of such leakage is well established and has long been attributed to poor retention of apatite P [Walker and Syers, 1976]. It is clearly seen in declining total soil P content in chronosequences [Crews et al., 1995; Walker and Syers, 1976], lake sediment records [Filippelli and Souch, 1999], and ecosystem soil budget calculations [Kaňa and Kopáček, 2006; Yanai, 1992]. Direct evidence for leakage from the soil, if not to runoff, and one that allows a simple test of our model output, is provided by the lysimeter data of Hedin et al. . This shows 6–8 mg P m−2 a−1 of export for the two youngest sites (Figure 4), or about one third of our predicted value. The discrepancy in reality may be smaller than this as the lysimeters, which measured only the filterable dissolved P, yielded flux values lower than in the associated stream water by a factor of >2 (older site only as the two youngest surfaces had no streams) [Hedin et al., 2003]. Consequently, we are confident that P does indeed leach rapidly during early soil development.
 A high soil P leakage rate throughout soil development has important implications for our understanding of long-term ecosystem P dynamics. For example, global modeling by Porder and Hilley  shows that with a λ value of 0.29 × 10−5 a−1, slightly less than our best estimate value, the initial geological P dose gives way to atmospheric supply as the main predictor of soil P status. The powerful effect of differences in atmospheric supply is illustrated in Figure 5. At atmospheric flux values below 5 mg P m−2 a−1 the total P curve shapes are recognizable as the generalized Walker and Syers  conceptual model. However, at higher atmospheric deposition rates such as might be expected in southern Europe or during glacial periods, the shapes are wholly different, with increases in the soil total P pool through time heading toward a high steady state after approximately 105 years. The relative importance of atmospheric supply increases rapidly through time as the bedrock inheritance is lost (Figure 5b), and at even the lowest atmospheric flux values, atmospheric supply dominates after approximately 104–105 years.
 Our analysis therefore opposes the orthodox view that parent bedrock dominates P in soils, such that complete depletion of the geological dose occurs only on rare ancient soils [Ruttenberg, 2003]. Furthermore, it follows that this late stage in soil P development, during which atmospheric P feeds the ecosystem, though functionally similar to a “terminal steady state” is conceptually different in as far as it should not be seen as terminal. Indeed, except following glaciations or volcanic activity, or in rapidly eroding landscapes, it is the normal state in which soils are found. In short, the “atmospheric stage” is the norm, and geological dominance is found only in soils on the youngest surfaces (≪105 years), or in regions with erosion greater than 0.02 mm yr−1 [Porder and Hilley, 2011].
3.5 Ecological Implications of Rapid Soil P Leakage
Hedin et al. , based on their analysis of the Hawaii soil chronosequence and lysimeter data, conclude that the export of inorganic P forms is subject to traditional mechanisms of biotic retention. Specifically, they conclude that high P export rates during the early development of the soil are due to N limitation and that declining rates during later development are due to enhanced biotic retention. Our analysis offers an alternative interpretation. In the absence of systematic variations in either the dissolution or leakage coefficients for apatite across the soil chronosequences and lake sediment records, there is no sign of biotic regulation of leakage during early soil development. In the longer term, during the atmosphere-dominated stage on older soils in Hawaii, where ecosystem productivity is P limited, total P loss from soil is equal to the atmospheric flux [Hedin et al., 2003] and is thus independent of the state of P limitation. This suggests that whatever the role of biotic mechanisms in regulating the availability of P to plants, soil P leakage throughout soil development appears to be regulated primarily by physical rather than biological constraints.
 In the very short term, annual P uptake requirement of an ecosystem is largely supplied by biological recycling [Chapin et al., 1978; Yanai, 1992], and even during the earliest stage of soil development, the flux of newly released P from apatite dissolution is minor compared with the annual P uptake of 960 mg m−2 a−1 [Yanai, 1992] at Hubbard Brook. Our high leakage rate of apatite P does not therefore challenge the accepted view that ecosystem P availability will increase through the early stages of soil development as the soil pool of available P grows [Walker and Syers, 1976]. However, the higher P leakage rates we propose will lead to control of soil P supply by atmospheric deposition, at soil chronosequence sites or other noneroding settings, much sooner than suggested by Crews et al.  and subsequent studies in Hawaii. At sites where the atmospheric contribution is small, our results agree with the view of Walker and Syers  that available secondary P concentrations will start to significantly decline after the primary apatite is depleted. That this also leads to P limitation of ecosystem productivity is demonstrably the case at the Franz Josef [Richardson et al., 2004] and Hawaii [Hedin et al., 2003] chronosequences.
 Whatever its impact on terrestrial ecosystems, rapid leakage of soil P from newly formed land surfaces will profoundly impact the ecology of upland streams and lakes, systems that derive most of their water from shallow flow paths. Immediately after exposure of the new land, surface water P concentrations will be very high. Indeed, the P flux curves of Figure 1 suggest a peak runoff concentration for total P (allowing for lake retention and focusing effects) in the order of 100 µg L−1 at 10–11 ka, falling to 15 µg L−1 prior to modern disturbance. These lakes, and others on deglaciated land, should have been most productive in the early post-glacial. Paleoecological evidence at Kråkenes Lake is consistent with this interpretation; productivity increased at the start of the Holocene, before declining after 10.7–10.8 ka ([Birks et al., 2000]. At Sargent Mountain Pond, paleoproductivity has not been examined at high resolution but diatom assemblages prior to the Holocene are consistent with a pH close to 8 and high P availability [Norton et al., 2011]; diatom analysis of other sites in Britain [Haworth, 1969], Sweden [Digerfeldt, 1972, 1975], and Finland [Sarmaja-Korjonen et al., 2006] also shows an oligotrophication through the early Holocene.
 The early post-glacial high P supply rate to these lakes also implies a high rate of supply to coastal ecosystems. To consider the possible magnitude of this effect, let us suppose that all deglaciated land experienced an enhanced release of P to runoff of 42 mg P m−2 a−1 (mean initial rate calculated for our six sites) at the start of the Holocene. Then the 18 × 106 km2 would supply 8 × 1011 g a−1 of additional P, or 4% of the current total estimated riverine supply to the oceans [Ruttenberg, 2003]. Could this be sufficient to drive the long-term ocean core P cycles identified by Filippelli et al. ? Given the long residence time of P in the oceans, and the relatively short-lived nature of this P pulse, it seems unlikely there would be a detectable global impact. However, most of riverine P is delivered in low latitudes; if we repeat the calculation at high latitudes, then a far greater effect is expected. This situation is probably best represented by the Baltic Sea due to its high degree of isolation from the open ocean and exceptionally large proportion of land deglaciated since the Last Glacial Maximum. Could the early Holocene episode of hypoxia in the Baltic [Zillén et al., 2008] be a response to a transient P supply surge?
 Our analysis of new and existing lake sediment and soil chronosequence data yields a coherent picture of long-term soil P dynamics at noneroding sites that differs markedly from the prevailing view. This is particularly import in three aspects.
 First, it is clear that P leaks from soil profiles far more rapidly than is generally thought, with the consequence that relative to any inherited geological dose, the atmospheric delivery of P is of far greater importance in the long term. The “terminal steady state” stage in soil development, when any P inherited from the bedrock and surficial material has been depleted, will typically be reached after some 104 to 105 years, and must be regarded as the norm outside areas of recent glaciation or other disturbances, rather than the rare exception.
 Second, particularly rapid leakage of P from soils during their early development greatly limits the scope for terrestrial ecosystems to self-regulate the leakage of P from soil. Taken together with the observation that during the atmospheric stage, leakage must also be physically not biologically constrained, we conclude that loss of P from soil profiles owes little to biotic retention.
 Third, leakage of P during the early apatite rich stage of a soil's development means that in young landscapes, streams and lakes fed by soil water experience high P loadings, a matter of profound significance for the interpretation of post-glacial ecosystems.
 This work was funded in part by a Natural Environment Research Council grant, NE/F020732/1. Studies at Sargent Mountain Pond were funded by the U.S. National Science Foundation through a grant to S. A. Norton et al. (DEB-0533142). We thank Stephen Porder and an anonymous reviewer for their positive and constructive comments.