Modelling approach to analyse the effects of nitrification inhibition on primary production

Authors


*Correspondence author. E-mail: boudsocq@bondy.ird.fr

Summary

  • 1Wet tropical savannas have high grass productivity despite the fact that nitrogen is generally limiting for primary production and soil nutrient content is typically very low. Nitrogen recycling, and especially nitrification, is supposed to be a strong determinant of the balance between conservation and loss of nutrients at the ecosystem level. The important primary production observed in wet tropical savannas might be due to a tight nutrient cycling and the fact that some grass species inhibit soil nitrification.
  • 2Using a general theoretical ecosystem model taking both nitrate and ammonium into account, we investigate analytically, using a four–compartment-differential-equation system the general conditions under which nitrification inhibition enhances primary production. We then estimate the quantitative impact of such a mechanism on the dynamics and budget of nitrogen in a well-documented ecosystem, the Lamto savanna (Ivory Coast). This ecosystem is dominated by the grass Hyparrhenia diplandra, which drastically reduces nitrification in the whole savanna except for a small zone. While this small zone supports a lower grass primary production, nitrification is higher, most likely due to the presence of another genotype of H. diplandra, which has no effect on nitrification processes. Ultimately, we test whether differences in nitrification fluxes can alone explain this variation in primary production.
  • 3Model analysis shows that nitrification inhibition enhances primary production only if the recycling efficiency – that is, the fraction of nitrogen passing through a compartment that stays inside the ecosystem – of ammonium is higher than the recycling efficiency of nitrate. This condition probably manifests itself in most soils as ammonium is less mobile than nitrate and is not touched by denitrification. It also depends partially on the relative affinity of plants for ammonium or nitrate. The numerical predictions for this model in the Lamto savanna show that variations in nitrification inhibition capacity may explain observed differences in primary production.
  • 4In conclusion we find that nitrification inhibition is a process which probably enhances ecosystem fertility in a sustainable way, particularly in situations of high nitrate leaching and denitrification fluxes. This mechanism could explain the ecological advantage exhibited by native African grasses over indigenous grasses in South-American pastures.

Introduction

Recent studies support the hypothesis that in nutrient-limited ecosystems, plant biomass and productivity at equilibrium are determined by the balance of ecosystem inputs and outputs of the limiting nutrient (de Mazancourt, Loreau & Abbadie 1998; Knops, Bradley & Wedin 2002; Barot, Ugolini & Brikci 2007). Conceivably, the higher the inputs and the lower the outputs of a limiting nutrient, the higher the stock of this nutrient an ecosystem will reach in the long term, that is, at equilibrium state. In turn, this should lead to an increase in plant biomass and production. In most terrestrial ecosystems, nitrogen is often among the principal limiting factors of primary production, and its availability can determine vegetal biomass and production (Vitousek & Howarth 1991). A good knowledge of the different processes controlling inputs and outputs of nitrogen is thus imperative to understand ecosystem functioning and to make quantitative predictions of primary production. Controlling these processes could lead to a better management of agro-ecosystem fertility. Moreover, if losses of nutrients are reduced, agriculture could require less fertilizer thus permitting a higher and more sustainable vegetal production. It has been shown that the amount of mineral nitrogen lost worldwide from fertilized agro-ecosystems through leaching and denitrification is higher than the total fertilizer input (Portejoie, Martinez & Landmann 2002). This suggests that an efficient decrease in nitrogen output could result in a lower need for fertilizers, which should furthermore permit to reduce the pollution of water by mineral nutrients and the emissions of NO and N2O (Howarth et al. 1996; Vitousek et al. 1997; Matson, Naylor & Monasterio, 1998).

Inputs and outputs of nutrients depend partially on abiotic conditions. As such, nutrient leaching is, for example, likely to increase in climates with heavy rains and to diminish in soils rich in clay (Brady & Weil 1999; van Es, Sogbedji & Schindelbeck 2006). However, it has also been proven that some organisms have the ability to partially control inputs and outputs of nutrients and can thus largely influence fertility and primary productivity in nutrient-limited ecosystems (Loreau 1998; Knops et al. 2002). This control involves both trophic and non-trophic processes which constitute ecosystem engineering activities (Jones, Lawton & Shachack 1994). Several models support this line of thought and confirm the importance of the openness of ecosystems on their own properties. The model conceived by de Mazancourt et al. (1998) and de Mazancourt, Loreau & Abbadie (1999), in particular, shows that grazing may increase primary production (‘grazing optimization’ mechanism) if the proportion of nutrients lost along the herbivore pathway is sufficiently smaller than the proportion of nutrient lost throughout the rest of the ecosystem at low grazing pressure. In a similar manner, earthworms should increase primary production if they increase the proportion of nutrients, which stays in the ecosystem along a complete recycling loop, that is, the recycling efficiency (Barot et al. 2007). In these two models, the long-term increase in production depends on an increase in nutrient recycling efficiency.

Besides, different studies have shown that some plant species are able to control nitrification (Meiklejohn 1962; Basaraba 1964; Boughey et al. 1964; Munro 1966a, 1966b; Meiklejohn 1968; Melillo 1977). More recently, Lata et al. (2004) have highlighted the capacity of Hyparrhenia diplandra, a perennial Graminaceae (Poaceae) species growing in tufts, to control nitrification in the humid tropical savanna of Lamto (Abbadie et al. 2006). Two zones dominated by H. diplandra but with grass covers of very different densities have been identified in the Lamto savanna (Le Roux et al. 1995). In the first zone, the nitrification potential is very low and the vegetal cover is dense (low nitrification zone, hereafter LNZ). In the second zone, the nitrification potential is high and the vegetal cover is scattered (high nitrification zone, hereafter HNZ) (Lata et al. 1999). In an experiment where tufts from the LNZ were transplanted in the HNZ, Lata et al. found after 1 year a decrease in nitrification potential equivalent to the potential originally observed in the LNZ (Lata et al. 2004). They also observed that soil beneath plants from the HNZ transplanted in the LNZ showed after one year an increase in nitrification potential close to the one measured in the HNZ. This suggests that the nitrification is controlled by H. diplandra regardless of soil properties, and that the two ecotypes of grass studied here are genetically different. This control would lead to a reduction of the nitrate stock, and thus to a reduction of nitrate losses by denitrification and leaching. This mechanism would actually enable H. diplandra from LNZ to increase the availability of nitrogen and its own growth, and more generally helps to explain the high primary production observed in this type of wet savanna (20–30 Mg ha−1 year−1) in spite of the relatively low mineral nitrogen content of their soils (Lata et al. 2004).

It is not known exactly how nitrification is controlled. However, there is a negative correlation between the grass root density and the nitrification intensity in the LNZ and a positive one in the HNZ. This suggests the existence of a root exudation by plants from the LNZ of allelopathic compounds which have an inhibiting effect on the activity of soil nitrifying communities (Lata et al. 2000; Subbarao et al. 2006; Subbarao et al. 2007b). Another hypothesis which could explain this negative correlation would be a high capacity for H. diplandra from the LNZ in absorbing ammonium. Indeed, a very high absorption of ammonium would lead to a lower quantity of ammonium available for nitrification in the vicinity of the roots, thus reducing nitrifier populations and the nitrification potential. This also could explain the high biomass observed in the LNZ. However, we propose that this latter hypothesis is unlikely (see Appendix S1). Moreover, a recent study shows that nitrification inhibition is a very widespread phenomenon observed in different plant orders at variable intensities. This work also shows that the range of interspecific and intraspecific variations in inhibition intensity is determined genetically (Subbarao et al. 2007a). Subbarao et al. also identified the molecules responsible for nitrification inhibition in root exudates from another African grass (Subbarao et al. 2007b). Their recent work therefore gives the direct evidence that biological nitrification inhibition does exist and largely supports the allelopathic nitrification inhibition hypothesis for the Lamto savanna.

The control of nitrification by plants seems to be one of the processes through which organisms could improve the conservation of nutrients within ecosystems and to increase primary production. In this study, we aimed to give a theoretical support to these hypotheses. Three objectives were pursued. (i) We have determined the general condition needed to obtain an increase in primary production when nitrification is inhibited. To achieve this goal, we built a general compartment model based on a system of differential equations which can be applied to any ecosystem and that is simple enough to permit mathematical analyses. (ii) Next the quantitative impact of nitrification inhibition on nutrient dynamics and primary production in a whole ecosystem was estimated. We chose to parameterize the model for the Lamto ecosystem (Ivory Cost) (Abbadie et al. 2006), and a sensitivity analysis of the model was achieved. This enabled us to estimate the quantitative effect of nitrification inhibition on the nitrogen stocks and fluxes in the Lamto ecosystem, as well as the relative influence on primary production of the different parameters determining nitrogen fluxes within the ecosystem. (iii) Finally, we tested the hypothesis that the difference between the primary productions of the two zones can be explained by a difference in nitrification inhibition.

Materials and methods

model description

Our model (Fig. 1) describes the dynamics of nitrogen – the limiting nutrient – in four compartments: plants (p), dead organic matter (D), and two pools of inorganic nutrients, ammonium (Na) and nitrate (Nn), which constitute the two major sources of nitrogen for plants. Stocks are expressed in kg N ha−1 while fluxes are expressed in kg N ha−1 year−1, for a 30 cm soil depth. To assure mathematical tractability, this model was kept as simple as possible. All fluxes but symbiotic fixation and constant inputs (R0, Ra and Rn) are expressed with simple linear ‘donor-controlled’ functions (DC): that is, they are proportional to the size of the compartment they come from.

Figure 1.

Model of the nitrogen cycle in an ecosystem. Arrow labels indicate the formula used for the corresponding flux. Definitions of parameters can be found in Table 1.

Plants build up their biomass absorbing nitrogen which comes from the two pools of inorganic nutrients with the respective rates uNa and uNn for ammonium and nitrate stocks. In turn, plant biomass mortality leads to a flux of nitrogen from the plant compartment to the dead organic matter compartment (D), following a death rate dP. The D compartment includes humus, litter and dead roots biomass. This dead organic matter is mineralized, leading to a flux of nutrients to the ammonium compartment, with a rate mD. Ammonium is then absorbed by plants (uΝa), or transformed into nitrate with a rate nNa. Nitrification can be inhibited by plants with an inhibition rate iP, leading to the nitrification flux nNaNa–iPP.

In natural ecosystems, there are many losses from these four compartments. For example, fire can cause losses for plant and dead organic matter compartments which can lead to important fluxes in tropical ecosystems (César 1971; Raison 1979). Erosion and leaching lead to losses of dead organic matter and the nitrogen it contains. Ammonium can be subject to volatilization while nitrate can be subject to leaching and denitrification. We integrated these losses, that is, nutrients going out of the ecosystem, with the respective rates lP, lD, lNa and lNn for plant, dead organic matter, ammonium and nitrate compartments.

There are three sources of nitrogen inputs to the ecosystem: atmospheric deposits of inorganic and organic nitrogen brought by winds and rains, as well as the fixation of atmospheric nitrogen by rhizospheric and non-rhizospheric (free) bacteria. The former two provide constant nitrogen inputs to the dead organic matter, ammonium and nitrate compartments (Ro, Ra and Rn respectively); the latter provides a nutrient input to the plant compartment, following a nitrogen symbiotic fixation rate fP, which is considered to be proportional to that of the receiver compartment. Non-symbiotic nitrogen fixation here is included in Ro. Nitrification inhibition is considered to be proportional to plant biomass and is opposed to the nitrification flux.

To ensure that using ‘donor-recipient-controlled’ (DRC) functions for ammonium and nitrate uptake fluxes (proportional to the plant and ammonium/nitrate compartments) instead of DC functions would not change qualitatively the effect of nitrification inhibition on primary production, we made simulations with a modified version of this model which was analytically much less tractable. This version uses DRC functions instead of DC functions for nutrient uptakes. This permitted us to estimate the primary production in the LNZ in function of nitrification inhibition (iP) with DRC functions.

The evolution of the compartment stocks is thus expressed by the following system of differential equations:

image(eqn 1)
image(eqn 2)
image(eqn 3)
image( eqn 4)

Each equation represents the sum of inputs and outputs of nitrogen in a given compartment during one time step (1 year). At equilibrium, stocks and fluxes can be obtained by setting all derivatives to 0 and solving the corresponding system of equations.

The solutions obtained provide the size of each compartment in function of the model parameters. In order to make our results more concise and easier to understand, four lumped parameters are used and can be interpreted as representative of the recycling efficiencies of the four model compartments. These expressions result from the calculations that have been done to resolve the system of differential equations. For each compartment, the recycling efficiency corresponds to the fraction of nutrients that leaves a given compartment and which stays in the ecosystem (Barot et al. 2007). αP, αD, αNa and αNn represent the recycling efficiencies of plant, dead organic mater, ammonium and nitrate compartments respectively:

image(eqn 5)
image(eqn 6)
image(eqn 7)
image(eqn 8)

From our calculations we derived the formula for the recycling efficiency of the whole ecosystem:

image(eqn 9)

Finally, primary production reads as follows:

φ=uNaNa +uNnNn eqn(10)

parameterization

The Lamto ecosystem

The Lamto savanna (5°02′W, 6°13′N; 200 km north of Abidjan, Ivory Coast) has been studied for more than 40 years and is one of the best documented tropical ecosystems in the world (see Part 1 in Abbadie et al. 2006). This savanna is subject to large losses of nitrogen caused by the annual fires, and has low organic matter decomposition rates, low N and C soils, as well as a general lack of nutrients. Paradoxically however, this ecosystem shows one of the highest vegetal productivity ever observed (Villecourt & Roose 1978; Villecourt, Schmidt & Cesar 1979; Bate 1981). This suggests that nutrient conservation plays a very important role in Lamto savanna productivity (Abbadie & Lensi 1990; Abbadie, Mariotti & Menaut 1992; Lata et al. 1999; Abbadie et al. 2006).

In our study we consider the open shrub savanna which is dominated by the herbaceous H. diplandra and is the most studied type of vegetation in Lamto (Menaut & Cesar 1979). In this part of the savanna two different zones, can be identified according to their nitrification rates (see introduction). Our model has been parameterized for the two zones, that is, the one with a very low nitrification rate (LNZ) and the one with a much higher rate of nitrification (HNZ). In this article we examine whether the observed difference between the primary productions of the two zones, 68·7 kg N ha−1 year−1 in the HNZ vs. 88·8 kg N ha−1 year−1 (Lata, pers. commun.) in the LNZ, can be explained solely by a difference in nitrification rates.

Value of the parameters

The parameters of our model were calculated using nitrogen stocks and fluxes documented in relevant literature (Table 1). Calculations of parameters were typically obtained by dividing nitrogen fluxes by nitrogen stocks. For example, the mineralization rate (mD) is equal to the ratio ‘flux of ammonium created through the mineralization of dead organic matter’/‘dead organic matter stock’. However, because of the lack of precise or appropriate information in the studied literature, we encountered difficulties in evaluating four parameters: the uptake rates (uNa and uNn), the nitrification rate (nNa) and the nitrate loss rate (lNn). The uptake rates in the HNZ were chosen using the optimal nutrition conditions for H. diplandra. In her thesis, Tavernier (2003) found that these optimal conditions are met with a nutritive solution composed of 25%inline image and 75%inline image Knowing the values for primary production as well as nitrate and ammonium stocks in the HNZ, the uptake rates were calculated so that the fluxes of absorbed ammonium and nitrate verify this proportion. It is possible for H. diplandra to grow well in a nutritive solution composed of 100%inline image though it grows slightly better in a solution of 75% of ammonium. This suggests that the actual optimal proportion for ammonium is between 100 and 75%, with 100% ammonium probably leading to toxicity. Concerning nitrification and nitrate loss rates, we tried different combinations of realistic values which lead to the observed primary production flux in the HNZ, and ultimately chose those that give the more realistic fluxes. Results obtained with combinations of values comprised in the 0·5 < nNa/lNn < 2 interval were the closest to field observations. After verifying that other values maintaining the ratio nNa/lNn within the [0·5, 2] interval do not change the model properties, we chose equal rates for these two parameters as the simplest hypothesis. Leaching of nitrate is here considered as negligible as suggested by the cited literature (Abbadie et al. 2006), so that nitrate losses are here considered to be solely due to denitrification.

Table 1.  Parameters of the model
ParameterValueDimensionDefinitionReference
fP0·01year−1Annual symbiotic nitrogen fixation rate(Lata 1999)
dP0·6year−1Annual plant recycling rate(Lata 1999)
lP0·4year−1Annual plant loss rate(Lata 1999)
iP0·445year−1Annual nitrification inhibition rateEstimated
Ro16·5kg N ha−1 year−1Annual organic input(Villecourt & Roose 1978)
mD0·025year−1Annual dead organic matter recycling rate(Abbadie et al. 2006)
lD0·0027year−1Annual dead organic matter loss rate(Abbadie et al. 2006)
Ra23kg N ha−1 year−1Annual ammonium input(Villecourt & Roose 1978)
uNa5·835year−1Annual ammonium uptake rateTavernier 2003, Lata, pers. commun.
nNa2·7year−1Annual nitrification rateEstimated
lNa0·0133year−1Annual ammonium loss rate(Villecourt & Roose, 1978)
Rn4·1kg N ha−1 year−1Annual nitrate input(Villecourt & Roose, 1978)
uNn4·315year−1Annual nitrate uptake rateTavernier 2003, Lata, pers. commun.
lNn2·7year−1Annual nitrate loss rateEstimated

Finally, the nitrification inhibition rate was estimated. We consider that its value is null in HNZ. For the LNZ, we chose the value which leads to the observed primary production (Lata 1999), supposing that nitrification inhibition is the only parameter that changes between the two zones.

Results

feasibility and biological meaning of the equilibrium

By solving the differential equation system, all compartments and primary production at equilibrium (noted by *) can be expressed as functions of the model parameters (Table 2). For each compartment the equilibrium stock is the product of three terms. The first term corresponds to the time a nutrient spends in the considered compartment. The second term (1/(1 –β)) is the recycling efficiency of the nutrient along an entire recycling loop. The last term corresponds to the inputs of nutrients that do not depend on compartment stocks, in a given compartment during one time step.

Table 2.  Algebraic expressions of the four model compartments and of the primary production at equilibrium
ParameterDimensionEquation
Equilibrium plant stockkg N ha−1
image
Equilibrium dead organic matter stockkg N ha−1
image
Equilibrium ammonium stockkg N ha−1
image
Equilibrium nitrate stockkg N ha−1
image
Equilibrium primary productionkg N ha−1 year−1
image

After determining the cases for which equilibrium exists, we identified the equilibrium properties of the model. It is important to note that if β > 1 the nitrogen recycling of the whole system is so efficient that the total nitrogen quantity always increases and the system can never reach equilibrium. Four different cases resulting from the analysis of β and plant compartment dynamics can be distinguished:

(1) When fPlP < 0, the plant compartment leads to a net loss of nutrients, all compartments are bounded and equilibrium can be reached (β < 1).

(2) When,

image

the plant compartment leads to a net gain of nutrients, compensated by losses from other compartments so that an equilibrium exists (β < 1).

(3) When,

image

the plant compartment leads to a net gain of nutrients, which is not compensated by losses from other compartments so that no equilibrium can be reached (β > 1).

(4) When dP < fPlP, the plant compartment can never reach equilibrium, because plants fix more nutrients than they can lose and consequently the system can never reach equilibrium (β > 1).

iPP ≤ nNaNa represents another necessary condition in which plants cannot inhibit more nitrification than is possible. We can thus determine the expression of the maximum iP value as a function of other parameters at equilibrium:

image(eqn 11)

Using the Routh-Hurwitz criterion, we tested whether or not the equilibrium found for the system is stable (all coefficients of the characteristic equation of the Jacobian matrix are positive) (May, 1974). It was not possible to show algebraically that conditions for stability were always met. However, we showed using numerical simulations made with randomized parameters and the Routh-Hurwitz criterion that the equilibrium is always stable when equilibrium conditions are fulfilled.

Finally, at equilibrium, all compartments of the model must be positive to be biologically meaningful. If the equilibrium conditions mentioned above are met and at least one of the constant inputs of nutrients is not null, then all compartments are positive. Otherwise there are no inputs into the system that are independent of compartment stocks and all compartments are null at equilibrium.

effects of nitrification inhibition on the ecosystem

At equilibrium, we looked for the condition in which nitrification inhibition enhances primary production. We found that:

image( eqn 12)

so that

image(eqn 13)

This condition is true for all iP values and it means that the recycling efficiency of the ammonium compartment must be higher than the recycling efficiency of the nitrate compartment to obtain an increase in primary production when nitrification inhibition increases. This general condition depends only on the two uptake rates of plants and on the loss rates of these two compartments.

This condition is implemented in Lamto savanna so that primary production increases with iP (Fig. 2a, DC curve). The determination of the parameter of nitrification inhibition in the LNZ leads to a value very close to iPmax (Fig. 2a). Quantitative estimations of nitrogen stocks and fluxes for the two zones of Lamto savanna were calculated using estimated parameters (Fig. 3). At equilibrium, we found that with the exception of nitrate stocks, nitrate losses and nitrification fluxes, all nitrogen stocks and fluxes, increase when nitrification is inhibited: a 67% increase in ammonium stock is obtained, while an 85% decrease in nitrate stock is observed. Because the inhibition parameter value is close to iPmax, nitrification inhibition causes a total absence of nitrification flux in LNZ.

Figure 2.

Sensitivity analysis. (a) Effect of rate of nitrification inhibition on primary production at equilibrium. (b) Effect of rate of nitrate uptake on primary production at equilibrium. (c) Effect of rate of nitrate loss on primary production at equilibrium. For (a), (b) & (c), the thin dashed lines represent the parameter values corresponding to the observed primary production in Lamto. For (a), the thick solid curve represents the primary production expressed as a function of nitrification inhibition with donor-controlled fluxes for nutrient uptake (DC), and the thick dotted curve represents the primary production in function of nitrification inhibition with donor-recipient-controlled fluxes for nutrient uptake (DCR). For (b) and (c), the thick dotted curve represents the primary production in the high nitrification zone (HNZ, iP = 0), while the thick solid curve represents the primary production in the low nitrification zone (LNZ, iP = 0·445). Primary production is expressed in kg of nitrogen N ha−1 year−1, whereas nitrification inhibition, nitrate uptake and nitrate loss rates are expressed in year−1.

Figure 3.

Estimates of the nitrogen fluxes (kg N ha−1 year−1) and stocks (kg N ha−1). (a) High nitrification zone (iP = 0). (b) Low nitrification zone (iP = 0·445).

Finally, we found that using DRC functions for uptake fluxes instead of DC functions leads qualitatively to the same result: primary production increases in Lamto savanna with iP (Fig 2a, DRC curve). Changing the values for nitrate and ammonium uptake and losses suggests again that αNa > αNn is a necessary and sufficient condition for nitrification inhibition to increase primary production with DRC nutrient uptakes (results not shown).

sensitivity analysis

To determine the key-processes governing nitrogen cycling in the Lamto savanna, a sensitivity analysis was carried to evaluate the relative impact of each parameter on primary production. Using the parameter values estimated for this ecosystem, one parameter was changed at a time. Figure 4 displays the sensitivity of primary production to a 10% change in the 14 model parameters. Conceivably, the vegetal production at equilibrium depends on all parameters, that is, both on internal recycling rates (including nitrification inhibition) and on inputs and outputs of nutrients in the ecosystem. In the LNZ, the parameters which have the highest influence on vegetal production are the loss of nutrients from plant stock (lP) and the constant input of atmospheric ammonium (Ra). Other parameters have a significant influence on primary production: the recycling rates of plant nutrients (dP) and ammonium (uNa and nNa) stocks, the constant input of organic nitrogen (Ro) and the rate of nitrification inhibition (iP). The influence of this rate is large enough to explain the difference observed between the two studied zones (Fig. 3). However, this influence becomes negligible when fluxes controlled by the plant compartment (the sum: dP, +lPfP) increase (see formula for β, eqn 9). Overall, it cannot be determined whether primary production depends more on internal recycling rates or on inputs and outputs of nutrients. On the other hand, the input of plant nutrients by symbiotic fixation of nitrogen (fP), recycling rate of nutrients from nitrate pool (uNn), and nutrient losses from both mineral pools (lNa and lNn) have a weak influence on primary production. Nevertheless, the influence of each model parameter is relative to their starting value in the studied ecosystem and thus oher values corresponding to other ecosystems could lead to very different conclusions about the relative influence of the 14 model parameters on primary production. For example, the sensitivity to a fixed change in the rate of nitrate uptake or losses decreases when the starting value for this rate increases (see Fig. 2b,c, decrease in the slopes of the primary production as a function of nitrate uptake or losses in both the LNZ and the HNZ). In effect, when nitrate uptake increases (Fig. 2b) and/or nitrate losses decrease (Fig. 2c), the recycling efficiency of the nitrate compartment (αNn) increases leading to a positive effect of nitrification inhibition (iP) on primary production decreases (eqns 12 and 13). It also becomes evident that primary production at equilibrium reaches a plateau when nitrate uptake and/or nitrate losses increase. This occurs due to the fact that as plants absorb more nitrate, and/or as the nitrate pool is subject to more losses, the stock of nitrate diminishes, and thus the parameters relative to this compartment become less influential on vegetal production (Fig. 2b,c).

Figure 4.

Sensitivity analysis. Variations in equilibrium primary production after a 10% increase and decrease of each parameter of the model.

Discussion

necessary conditions for a positive effect of nitrification inhibition on primary production

Our primary results demonstrate that plants can enhance their own primary production if they inhibit nitrification. This mechanism can induce a better nutrient conservation and thus, increase the size of all compartments of the ecosystem: plants, dead organic matter and mineral nutrient pools (with ammonium and nitrate compartments considered together). Most importantly we show that the increase in plant production depends on the relative efficiency of the different recycling pathways of nutrients. In other words, the ammonium pathway must be more efficient than the nitrate pathway to observe an increase in primary production. The recycling efficiencies of these two pathways (αNa and αNn ) increase when losses from both compartments decrease and when uptakes of nitrate or ammonium by plants increase.

The general condition we have found is probably applicable to many ecosystems. Indeed, nitrates are more subject to losses than ammonium. Due to their electronegative charge, nitrates are more labile than ammonium and are thus more easily leached. Furthermore, important nitrate losses result from denitrification (Brady & Weil 1999). In addition, ammonium can affix itself to organo-mineral complexes (Brady & Weil 1999) and in soils with a pH of about 6 (as in Lamto), ammonium volatilization is considered null. As such, the nitrate pathway is probably less efficient than the ammonium pathway (Salsac et al. 1987). However, recycling efficiencies also depend on nutrient uptake and this is an important aspect of the general condition for an increase in primary production. A plant which ‘prefers’ ammonium to nitrate, that is it absorbs more ammonium than nitrate, increases ammonium recycling efficiency. Thus, nitrification inhibition is more likely to increase primary production if plants prefer ammonium to nitrate. It should also be noticed that because of the energetic cost of reduction of nitrate into ammonium, the assimilation of 1 mol of nitrate requires about 20 mol of ATP compared to only about 5 mol of ATP for 1 mol of ammonium (Salsac et al. 1987). This difference in energy requirements associated with the assimilation of nitrogen forms can be considered as a driving force for the evolution of mechanisms to inhibit nitrification in natural systems, which can increase further the competitive advantage of nitrification inhibiting plants.

limitations of the model

The model presented here is largely applicable and its results should pertain to all ecosystems in which primary production is limited by nitrogen. However, certain limits exist. The functions used to describe nutrient uptake by plants are simple linear DC functions: nutrient uptake fluxes increase proportionally with the size of the two mineral nitrogen pools. This is not biologically realistic, particularly in young ecosystems (at the start of vegetal succession with a low plant biomass). Nevertheless, this should not be a problem when the ecosystem is considered to be at equilibrium, with a fully developed vegetal cover. Moreover, using realistic functions should change transitory dynamics of the system more than its equilibrium properties (de Mazancourt et al. 1998; Barot et al. 2007). This was verified numerically using DRC functions for nutrients uptakes (fluxes are proportional to plant biomass and nutrients pool size). We found that with Lamto savanna parameters, DRC functions do not change the qualitative properties of the model. Additionally, it would be more realistic to express nitrification inhibition as a function of both the plant and the ammonium compartments. While, choosing more realistic functions could be useful, it would be detrimental to the model simplicity and mathematical tractability.

A four-compartment model was built to keep it as simple and general as possible. It would certainly be more realistic to represent microbial biomass or to distinguish humus from litter for the dead organic matter compartment. However, since the conditions for the existence of equilibrium and for an increase in primary production by the inhibition of nitrification are independent from organic matter dynamics, adding other compartments would not qualitatively modify the general properties of the model at equilibrium. Nevertheless, the precision of quantitative estimations could be improved by adding more compartments, or by using more realistic functions. For example, we did not represent losses from N2O emissions during nitrification process, neither the N2O emissions from plant leaves when they assimilate nitrate (Bremner & Blackmer 1978; Smart & Bloom 2001). Indeed, these losses are estimated to represent a very small fraction of the nitrified nitrogen in the first case, and of the nitrate absorbed by plants in the second case. Once again, we have chosen to favour the simplicity and the general aspect of the model instead of its quantitative precision.

In the basic version of our model, we do not take heterotrophic nitrification into account. This shortcoming was overcome as detailed in Appendix S2. Our results show that (i) heterotrophic nitrification leads to a decrease in primary production because it increases the nitrate pool size and thus the losses of nitrate, (ii) heterotrophic nitrification hardly influences the sensitivity of primary production to nitrification inhibition, and (iii) for a likely small rate of heterotrophic nitrification our results on the two zones of Lamto savanna still hold.

Nitrogen immobilization in microbial biomass is another process that is not taken into account in the basic version of our model. Such a mechanism could explain the difference in primary production between the HNZ and the LNZ of Lamto savanna. Indeed, the soil of the LNZ could contain a higher microbial biomass that could in turn immobilize more nitrogen than in the HNZ. This would decrease leaching and denitrification in the LNZ (Bengtsson, Bengtson & Mansson 2003; Burger & Jackson 2003), which would finally increase primary production in this zone. However, studies conducted by Degrange show that microbial biomasses (measured with an adapted fumigation-extraction method as described by Amato & Ladd (1988)) are not significantly different between these two zones (Degrange 1996) so that a difference in the mean level of nitrogen immobilization is unlikely to explain the observed difference in primary production between the LNZ and HNZ. Moreover, in Appendix S3, we show that nitrogen immobilization could affect the different compartment recycling efficiencies as well as primary production, but only if the parameters of nitrogen cycling vary in time, for example due to seasonality. In this case, the degree of synchronisation between the different processes controlling nitrogen fluxes would be determinant (Hodge, Robinson & Fitter 2000; Chapman et al. 2006). It is so far impossible to exclude the possibility that differences between the two zones in the temporal dynamics of nitrogen immobilization could explain their difference in primary production. Nevertheless, no data support this possibility and modelling such a temporal dynamics goes beyond the objectives of our model and would require assessing many new parameters.

case of lamto savanna

Our results show that the differences in primary productions and nitrification potentials between the two zones can be solely due to nitrification inhibition. However, as presented in the introduction, another hypothesis could explain theses observed differences: H. diplandra could show a higher capacity in absorbing ammonium in the LNZ than in the HNZ, leading to a lower quantity of ammonium available for nitrification in the vicinity of the roots and then reducing nitrifier populations. We show (see Appendix S1) that this hypothesis (super-absorption hypothesis) is unlikely because our model estimates that the necessary ammonium uptake rate in the LNZ must be 10–100 times higher than in the HNZ. Given the mean root biomass of H. diplandra is equal in the two zones (Lata et al. 2000), such an increase in ammonium uptake capacity would have to be due to a much higher quantity/efficiency of ammonium transporters of the LNZ H. diplandra roots. Furthermore, such an increase in ammonium uptake would quickly lead to an important impoverishment of the poorly mobile inline image ions in the neighbourhood of the roots, which renders this hypothesis very improbable. This result supports the conclusion of the empirical study of the two nitrification zones of Lamto savanna (Lata et al. 2000, 2004), and strengthens Subbarao et al.'s conclusion that nitrification inhibition is a quantitatively important mechanism of ecosystem functioning (Subbarao et al. 2006). Parameterizing our model for other ecosystem types would help determining more generally for which ecosystems nitrification inhibition and super-absorption on ammonium should be more influential.

At equilibrium, except for the stock of nitrate, the losses of nitrate and the flux of nitrification, all nitrogen stocks and fluxes increase when nitrification is inhibited. Nevertheless, an increase of the total mineral pool (ammonium and nitrate) was observed. These trends fully support our predictions. However, some of the nitrogen fluxes, like nitrification and nitrate losses, may appear overestimated in the model in comparison to empirical estimations achieved in the field (Pochon & Bacvarov 1973; Le Roux et al. 1995). These fluxes, however, are significantly lower than values estimated using potentials obtained in incubation, or in optimal conditions (Abbadie & Lensi 1990; Lata et al. 2004). Furthermore, only denitrification potentials were measured in the HNZ and no data have been gathered on a one year period. Moreover, some studies support the existence of important denitrification fluxes (c. 20 kg N ha−1 year−1) in the same geographic zone as Lamto (Hofstra & Bouwman 2005; Seitzinger et al. 2006). This points to a lack of in situ data estimations, at relevant temporal and spatial scales, of parameters critical to ecosystem functioning.

At equilibrium, nitrogen inputs are equal to nitrogen outputs. With the exception of the weak symbiotic dinitrogen fixation (fP) due to the small density in leguminous plants in Lamto savannas, all inputs are in this case constant (do not depend on compartment sizes) and are in the form of atmospheric depositions. In Lamto savanna, this input is equivalent to 43·6 kg N ha−1 year−1 (including organic, ammonium and nitrate deposition). Thus, the total nitrogen output should be of the same quantitative order. In studies losses due to fire are estimated to range between 10 and 30 kg N ha−1 year−1 (Abbadie et al. 2006), while other nitrogen losses estimated are low: about 5 kg N ha−1 year−1 are lost by animal consumption and 5–7 kg N ha−1 year−1 are lost by erosion, lixiviation and leaching (Abbadie et al. 2006). Thus, considering Lamto savanna as an ecosystem at equilibrium, there is a non-negligible amount of nitrogen that must leave the ecosystem by another way. In particular, this should be the case in the HNZ, where primary production and thus, nutrient losses by fire, are lower than in LNZ. Our model suggests that these losses could be explained by denitrification, and that inhibition of nitrification can lead to a consequent decrease in nitrification and denitrification fluxes. Furthermore, this study points out the lack of precise data which are needed to obtain an exhaustive and equilibrated nitrogen budget in Lamto savanna as well as in natural ecosystems in general.

Conclusion

In the present context, where modern practices in agriculture are generally focused on nitrogen inputs, the question of nutrient conservation efficiency is pertinent. Indeed, a reduction in nitrogen losses could lead to a diminution in the use of fertilizers. For agro-ecosystems, which are subject to high nitrifying and denitrifying activities, our model predicts that nitrification inhibition by plants is a process that could lead to a better nutrient conservation, and then induce an increase in primary production if the ammonium pathway is more efficient than the nitrate pathway. It would be interesting to apply our conclusions in the field, using nitrification inhibiting plants, or the inhibiting molecule itself in agro-ecosystems subject to large amounts of nitrate losses (Subbarao et al. 2006).

It is important to note that many African grasses are grown in South America in mono-specific pastures for cattle ranching (D’Antonio & Vitousek 1992). As these grasses out-compete native grasses, they can be considered as species invasive to South America (with a bit of human intervention) (D’Antonio & Vitousek 1992). While reasons for their success are herein not clear, many of these African grasses have the capacity to inhibit nitrification (Ishikawa et al. 2003; Subbarao et al. 2007b). Our results suggest that this could lead to a strong competitive advantage. Applying our model using parameters from South American pastures with African and native grasses and allowing the two types of grass to compete could prove pertinent to test this hypothesis. More generally, this raises the question of the evolution of mechanisms enabling plants to inhibit nitrification. It is probable that nitrification inhibition occurs at a cost for plants and as such that it does not necessarily lead to a direct benefit for them. This cost could be counterbalanced by a higher availability of nitrogen and a resulting decrease in the cost paid to reduce nitrates (via the Nitrate Reductase enzyme) by plants absorbing large quantities of nitrates. Studying the conditions in which mechanisms of nitrification inhibition are likely to evolve is an important theoretical issue linked to the whole field of evolution of niche construction and activities of ecosystem engineers (Jones et al. 1994; Odling-Smee, Laland & Feldman 2003).

In conclusion, our model allows a better understanding of the functional consequences of nitrification inhibition by plants. Two issues remained largely unexplored and could be tackled developing further our model: the consequences of nitrification inhibition on plant competition and communities and the evolutionary dynamics of nitrification inhibition.

Acknowledgements

Authors are very grateful to Marta Rozmyslowicz for her help in English improvement. Our work has been supported by the ‘programme jeune chercheur 2005’ of the ANR (SolEcoEvo project, JC05-52230).

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