Plant and Soil

, 348:29

Acquisition of phosphorus and other poorly mobile nutrients by roots. Where do plant nutrition models fail?


    • INRAUMR Eco&Sols
  • Alain Brauman
    • IRDUMR Eco&Sols
  • Nicolas Devau
    • INRAUMR Eco&Sols
  • Frédéric Gérard
    • INRAUMR Eco&Sols
  • Christophe Jourdan
    • CIRADUMR Eco&Sols
  • Jean-Paul Laclau
    • CIRADUMR Eco&Sols
  • Edith Le Cadre
    • Montpellier SupAgroUMR Eco&Sols
  • Benoît Jaillard
    • INRAUMR Eco&Sols
  • Claude Plassard
    • INRAUMR Eco&Sols
Marschner Review

DOI: 10.1007/s11104-011-0903-y

Cite this article as:
Hinsinger, P., Brauman, A., Devau, N. et al. Plant Soil (2011) 348: 29. doi:10.1007/s11104-011-0903-y



In the context of increasing global food demand, ecological intensification of agroecosystems is required to increase nutrient use efficiency in plants while decreasing fertilizer inputs. Better exploration and exploitation of soil resources is a major issue for phosphorus, given that rock phosphate ores are finite resources, which are going to be exhausted in decades from now on.


We review the processes governing the acquisition by plants of poorly mobile nutrients in soils, with a particular focus on processes at the root–soil interface. Rhizosphere processes are poorly accounted for in most plant nutrition models. This lack largely explains why present-day models fail at predicting the actual uptake of poorly mobile nutrients such as phosphorus under low input conditions. A first section is dedicated to biophysical processes and the spatial/temporal development of the rhizosphere. A second section concentrates on biochemical/biogeochemical processes, while a third section addresses biological/ecological processes operating in the rhizosphere.


New routes for improving soil nutrient efficiency are addressed, with a particular focus on breeding and ecological engineering options. Better mimicking natural ecosystems and exploiting plant diversity appears as an appealing way forward, on this long and winding road towards ecological intensification of agroecosystems.


Ecological intensificationMicroorganismModellingPhosphorus, potassiumRhizosphereFacilitation

Introduction—The roots of ecological intensification of agroecosystems

Over the last 50 years, human beings have modified the ecosystems to an unprecedented point in humankind history, in order to meet the increasing world demand for food, drinking water, wood, fibers and energy (Millenium Ecosystem Assessment 2005; Tilman 1999). Such changes have contributed to considerably improving humankind well-being, but also to global degradation of numerous essential ecosystem services (Rockström et al. 2009). Prediction models forecast further degradation of ecosystem services in the coming 50 years, if management strategies remain unchanged (Tilman et al. 2001, 2002). The scientific challenge is considerable though: how to feed the world and its increasing population in a context of limited changes of land use, i.e. limited increase in productive arable land surface area (Griffon 2006; Vance et al. 2003). In order to preserve ecosystem services, current levels of agroecosystem productivity thus need to be further increased in a sustainable way, both at an environmental and economic point of view. There is thus a need for an ecological intensification of agroecosystems, in order to cover global food demand while decreasing agricultural inputs such as fertilizers (Cassman 1999; Griffon 2006).

The Millennium Ecosystem Assessment underlined that the cycles of nutrients, especially nitrogen (N) and phosphate (P) were among the most affected ecosystem services, leading to a massive and fast-increasing eutrophication of aquatic ecosystems (Galloway et al. 2008; Gruber and Galloway 2008; Mackenzie et al. 2002), contamination of groundwaters by nitrate and emission of greenhouse gas (Vitousek et al. 1997). These are the consequence of the considerable increase in agricultural inputs and the steady decrease of N and P fertilizer efficiency (Hinsinger et al. 2011; Tilman et al. 2002), which occurred during the Green Revolution: from 1965 to 2000, the doubling of cereal production was accompanied by a 3.5- and 6.9-fold increase in the amounts of P and N fertilizers applied, respectively (Tilman 1999). Pursuing such an increase in N and P fertilizer applications is no longer an option. For P, the world reserves of high grade P ores are expected to be exhausted by the end of 21st century at current rate of consumption of P fertilizers (Herring and Fantel 1993; Runge-Metzger 1995; Stewart et al. 2005). This rather short deadline, which may be further extended by using lower quality resources and paying a greater cost, clearly challenges the sustainability of current P fertilizer use in developed and emerging countries (Cordell et al. 2009). For potassium (K), the situation is less dramatic, but Manning (2010) recently stressed that K also had to be considered as a finite resource. Increasing nutrient use efficiency in crops while decreasing nutrient inputs means that better exploration and exploitation of soil resources must be achieved in agroecosystems. For the purpose of this second Green Revolution, one needs to know what are the intimate processes and factors that govern the acquisition of soil nutrients by plants, with solutions pertaining to plant roots (Lynch 2007). These relate to both biophysical and biogeochemical/biochemical processes, which are influenced by root activities, either directly or through soil biota, including symbionts such as mycorrhizal fungi, free living microorganisms and soil fauna in the rhizosphere. The complexity of these belowground interactions is almost impossible to explore through only experimental approaches and direct measurements. Modelling is thus a powerful alternative approach to further our understanding of such processes, and how they ultimately determine plant nutrition. The aim of our review is to focus on these complex rhizosphere processes and on the lessons that should be drawn from modelling approaches. We ultimately stress the various directions to take to improve plant nutrition models, when used as tools to design more nutrient efficient plants or plant stands in the particular case of P and other poorly-mobile nutrients such K and micronutrients.

Why and which plant nutrition models, what for?

The term “model” has various meanings in life sciences, depending on the target organism, temporal and spatial scales or end users. Le Bot et al. (1998) reviewed the history of plant nutrition modelling, and their application to strategic and tactical crop management. In this review, we will not address how modelling can be used as a practical tool for crop management, e.g. fertilizer recommendation. We will rather address modelling as a unique approach to increase our understanding of how plants acquire poorly mobile nutrients. A challenge is to better take into account the complexity and nonlinearities of the soil-plant interactions that drive plant nutrition. Nonlinearity should be understood as the ability of one entity to express strategies depending on its neighbours but also as a consequence of its environmental conditions (Bellomo and Carbonaro 2011). Complexity is the law in nature. Living organisms obey to physics and chemistry laws but the number of variables required to describe them and their interaction with environmental conditions are huge. Only models can provide a quantitative description of processes and their many interactions, while experimental and empirical approaches are fundamentally inadequate because studying components in isolation (Crawford 2010), or combining only a limited number of factors. Crawford (2010) pointed the challenges of such mechanistic modelling as follows: (i) number of possible interactions and determination of a description limit, (ii) spatial heterogeneity of addressed processes, (iii) propagation of uncertainties across spatio-temporal scales and subsequent loss of predictive power. Determining the adequate level of model complexity is not an easy task, but models should be kept as simple as possible. Reducing solutions such as the “Model Reduction by Variable Replacement” proposed by Crout et al. (2009) are promising to obtain reduced models while preserving input-ouput behaviour. Briefly, the inter-nested calculations of mechanistic models can be simplified by constants set by Bayesian statistical methods based on the likehood. The comprehensive calculations of the likehood is performed by numerical methods such as Markov Chain Monte Carlo.This methodology has been successfully adopted by Tarsitano et al. (2011) for modelling radiocesium soil-plant uptake in which 18 variables (model input and variables) where reduced to 13. The simpler model was outperforming the more complex model because over-parametrization had occurred during the development of the latter. However, modelling is a reliable tool provided that realistic data can be obtained from experiments. Indeed, acquiring experimental data is still a major limitation for appropriately accounting for rhizosphere interactions (see review by Luster et al. 2009). For instance, it is hardly feasible to probe the local conditions (e.g. concentrations of nutrients and the numerous interacting solutes such as root exudates or microbial metabolites) that occur close to various portions of a root system for soil-grown plants in field conditions. At this point of view, the heuristic value of modelling makes no doubt. Making use of sensitivity analysis and pure simulation models are highly valuable to test a large number of scenarios and processes that would otherwise not be testable. In the context of the present review, we will therefore discuss all types of models, not only mechanistic (they are actually all empirical to some extent), but also stochastic. Providing more details about model requirements and conditions for each would have certainly been helpful to readers, but would have diluted the primary focus of our review: better understanding the processes of acquisition of poorly mobile nutrients by plants. Hence, the readers shall refer to the cited publications to now more about the various types of models we are addressing below.

Rhizosphere biophysical processes and spatial/temporal dynamics

Nutrient transport processes at the single root scale

The acquisition of nutrients by plants requires for most of them their transfer towards the root surface, prior to uptake, as accounted for by conventional models of plant nutrition (Barber 1995). Transfer processes playing a key role in that respect are mass-flow and diffusion. The relative contributions of mass-flow and diffusion for the transport of nutrients to roots considerably vary amongst nutrients and indeed depend on plant requirements, soil moisture, and nutrient concentration in the soil solution (i.e. nutrient availability). This was first modelled by Nye and Marriott (1969) in the case of a single root model, assuming Michaelis-Menten formalism for nutrient absorption across the root surface. In most nutrient uptake models deriving from this, the central hypothesis is that the driving force of nutrient acquisition is the absorption of nutrients by the root, which shall result in a decrease in nutrient concentration at the surface of the root, leading to a diffusion gradient in the rhizosphere. Experimental evidence for nutrient depletion occurring in the rhizosphere is especially well documented for poorly mobile, major nutrients such as K and even more so for P (e.g. Claassen et al. 1986; Hendriks et al. 1981 ; Hinsinger 1998, 2001; Jungk and Claassen 1986, 1997; Jungk 2002; Kuchenbuch and Jungk 1982). The first evidence of this phenomenon was obtained by using radioactive isotope-labelled soils and autoradiography techniques (Bhat and Nye 1974; Lewis and Quirk 1967; Walker and Barber 1962) (Fig. 1a and b). The depletion in the rhizosphere is much less documented for micronutrients although most of them are assumed to be poorly mobile as well. There are however very few works reporting direct evidence of depletion of e.g. copper (Cu) and iron (Fe) in the rhizosphere (Bravin et al. 2009; Kirk and Bajita 1995) while there are a number of papers modelling diffusion gradients, e.g. Samal et al. (2003) for manganese (Mn), or Lehto et al. (2006) for zinc (Zn). For poorly mobile nutrients, mass-flow marginally contributes to their transfer towards the root surface as they usually occur at rather low concentrations in the soil solution (Barber 1995; Hinsinger 1998; Jungk 2002). Mass-flow can contribute to a larger proportion of the transfer towards the root surface for mobile nutrients such as nitrate, although depletion is still expected to occur because of large N requirements of plants (Barber 1995). Diffusion is thus assumed to be the prominent process of transfer of poorly mobile nutrients in the rhizosphere, occurring as a consequence of the uptake and subsequent depletion of such nutrients at the root surface (Barber 1995; Hinsinger 1998; Jungk 2002).
Fig. 1

a. Photograph of roots (left) and corresponding autoradiograph (right) showing 86Rb accumulation within root tips (black areas) and depletion zones (white areas) around 13-day old maize roots growing in a soil which was amended with 0.5 μCurie 86Rb g−1. 86Rb was used as a surrogate of K in this work (from Walker and Barber (1962), reprinted with permission from Springer-Verlag, Dordrecht). b. Autoradiographs showing 32P depletion zones around wheat roots growing in a soil which was amended with 100 μg 31P g−1 and 2.5 μCurie 32P g−1. Autoradiographs taken at various time intervals after sowing showed that the width of the 32P depletion zone was about one millimetre and only slightly influenced by time, due to slow diffusion (from Lewis and Quirk (1967), reprinted with permission from Springer-Verlag, Dordrecht)

Interestingly, Bravin et al. (2009) reported a steep Cu depletion occurring in the rhizosphere of durum wheat (Triticum turgidum durum L.) but they also showed that the observed Cu concentration gradient extended much farther away from the root surface than a diffusion model would predict. This work showed that the depletion of Cu was actually not due to Cu uptake per se, but rather the consequence of a dramatic pH change in the rhizosphere, in this case an alkalization, which extended up to several millimetres away from the root surface. In addition for some poorly mobile nutrients and especially for P, there has been some reports of more complex patterns of nutrient distribution in the rhizosphere, combining a depletion at the very root surface with nutrient accumulation occurring farther away from the root surface, relative to the bulk soil (Calvaruso et al. 2011; Hinsinger 1998, 2001; Hinsinger and Gilkes 1996; Hinsinger et al. 2009; Hübel and Beck 1993) (Fig. 2). Recent measurements obtained after sampling the rhizosphere in situ in various field-grown plant species including durum wheat and grain legumes have shown a systematic increase in available P in the rhizosphere (Betencourt et al., personal communication). A few authors observed the same trend for various plant species, although in controlled conditions in the laboratory, with rhizobox approaches (e.g. Hinsinger 2001; Hinsinger and Gilkes 1996; Kirk et al. 1999a). Such findings clearly invalidate classical models of nutrient acquisition in which the only driving force is the nutrient uptake by roots. More recently, Devau et al. (2010, 2011b) measured an increase in water-extractable P in the rhizosphere of durum wheat grown in controlled conditions in a rhizobox experiment. Interestingly, these authors successfully modelled the observed root-induced increase in P availability (see below). Their modelling approach, as few previous ones, was actually designed to account for biogeochemical processes which predict concentration patterns that cannot be explained by the sole nutrient uptake process (Geelhoed et al. 1999; Nowack et al. 2006). These modelling efforts will be further addressed in the section about rhizosphere biogeochemistry. It shall be noted that some of the above- and below-mentioned studies, either based on experimental or modelling approaches, explicitly account for gradients of nutrients occurring in the rhizosphere, while others only distinguish between two compartments, the rhizosphere and the bulk soil, which average rhizosphere properties such as nutrient concentrations. The latter is easier to implement, but represents a simplified representation of the rhizosphere, which is subject to much debate about how and where one positions the rhizosphere/bulk soil borderline, as discussed in the review by Luster et al. (2009).
Fig. 2

Autoradiographs showing cross-sections of the standard teflon tubing (T) and root (R) of maize grown in a soil which had been labelled with 44 kBq 33P g−1, showing distinct accumulation (A, darker grey) and depletion (D) zones around the root (a) and the corresponding P concentration profile as determined experimentally (b): this was obtained after applying a correction function for the 33P crossfire effect obtained for the standard teflon tube of similar section as the root (from Hübel and Beck (1993), reprinted with permission from Springer-Verlag, Dordrecht)

Upscaling nutrient transport to the whole root system scale

Further refinements of the Nye and Marriott (1969) derived models consisted to upscale from the root segment to the whole root system, and accounted for root growth (Baldwin et al. 1973; Claassen and Barber 1976; De Willigen et al. 2002), and Roose et al. (2001) showed that the method used to upscale may lead to substantial differences (up to 30%) in the predicted uptake of nutrients. When applied to nutrients such as K and P, such models have generally proved quite efficient at predicting the acquisition over time scales of days or weeks in the case of soils receiving high K or P inputs, but almost systematically failed in low input conditions (Brewster et al. 1976; Claassen et al. 1986; Lu and Miller 1994; Mollier et al. 2008; Samal et al. 2010; Schenk and Barber 1980). Under such conditions, those models actually underestimate the observed uptake flux (Fig. 3), which suggests that other processes than those accounted for by the models are operating, and ultimately driving nutrient acquisition. Sensitivity analyses conducted with these models (Barber 1995) showed for poorly mobile nutrients such as P that the major parameters were (i) root elongation rate and (ii) nutrient availability, i.e. soil solution concentration and soil buffering capacity, while the least important parameters were those describing the nutrient absorption capacities of the roots (Michaelis-Menten parameters). Rengel (1993) underlined that the uptake was thus not the limiting step of nutrient acquisition for poorly mobile nutrients such as K and P, contrary to water or more mobile nutrients such as nitrate. In spite of this, it is quite astonishing to see so much excellent work concentrating on the identification of P and K transporters in plants, while other acquisition processes have received little interest from the plant molecular physiology community, although being more relevant to P acquisition as early stressed by Clarkson (1985). Most of the above-mentioned works stand for annual crops. Nutrient uptake models developed in forest ecosystems since the 1960s have shown similar evolutions, but no revolutions, over the last decades (Kelly and Ericsson 2003; Smethurst and Comerford 1993; Williams and Yanai 1996). Recent versions started to take into account the effects of fertilizer inputs and nutrient uptake by mycorrhizae (Comerford et al. 2006; Lin and Kelly 2010). However, a comparison of nutrient uptake predictions against experimentally measured values showed that the last version of three process-based models (NST 3.0, SSAND, and PCATS) largely underestimated P uptake for three woody plant species, except under large P fertilizer additions for the transient state model NST 3.0 developped by Classen and co-workers (e.g. Claassen et al. 1986; Steingrobe et al. 2000). The behaviour of the three models was more contrasted for nitrate and potassium uptake, which were underestimated in most of the simulations. This pattern showed that including mycorrhizal uptake in the simulations was not sufficient to predict accurately nutrient uptake under the low nutrient concentrations typically occurring in forest soils. This study suggested that rhizospheric effects, not yet taken into account in these models, should be implemented to improve their predictive ability (Lin and Kelly 2010).
Fig. 3

Measured (symbols) and calculated (lines) P uptake by maize as a function of the time (thermal days) duration of growth in field conditions at two levels of P supply, according to the model developped by Mollier et al. (2008). Vertical bars stand for the 95% confidence interval around the mean value. The model efficiency amounted to 0.66 for the low P treatment and 0.97 for the high P treatment, showing substantial underestimation of the observed P uptake at low P supply (from Mollier et al. (2008), reprinted with permission from Elsevier BV)

Major challenges are in front of us for improving current models of plant nutrition and upscaling rhizosphere knowledge at the whole plant and agroecosystem scales (Darrah et al. 2005; Dunbabin et al. 2006; Hinsinger et al. 2005, 2009; Jones and Hinsinger 2008) given that reducing fertilizer inputs will require a better prediction of nutrient acquisition. From the biophysical standpoint, two major improvements are needed. First of all, we need a better description of what is the actual surface of uptake to account for (Rewald et al. 2011). So far, most models rely on a very poor description of root growth, and do not explicitly account for root architecture, in spite of its importance in resource exploitation efficiency (Fitter et al. 1991). In particular, the contribution of very deep roots on water and nutrient uptake in natural and agroecosystems established on highly weathered tropical soils is still poorly known (Battie-Laclau and Laclau 2009; Christina et al. 2011; Jackson et al. 2000; Schenk and Jackson 2002; Silva et al. 2011). Nevertheless, root architecture models have proved useful for predicting water uptake (Doussan et al. 1998, 1999, 2003, 2006; Pagès et al. 2004; Pierret et al. 2007), localizing nutrient uptake zones or describing situations of heterogeneous distribution of nutrients in the soil profile (Ge et al. 2000; Liao et al. 2001; Lynch and Brown 2001; Rubio et al. 2003). These can be either based on explicit, detailed representation of the architecture (e.g. Jourdan and Rey 1997a,b; Jourdan et al. 1995; Ge et al. 2000; Pagès et al. 2004), or on simplified representations (Dupuy et al. 2010) that bear more promises for coupling with a number of complex soil-based processes. The linking of coarse roots and fine root distribution has always been a hard task in root modelling because of the different scales at which each distribution is measured (Tobin et al. 2007). However, linkage appears feasible in architectural models where topological relationships among different root types make it possible (Collet et al. 2006; Jourdan and Rey 1997a; Vercambre et al. 2003). Accounting for architecture is especially needed for the most mobile nutrients such as nitrate, as root-root competition and consequent overlapping of nutrient depletion zones is increasing with increasing diffusion coefficient (Ge et al. 2000 ; Hinsinger et al. 2005). Such finding was recently confirmed by Pagès (2011) who accounted for some stochasticity in his model to explore the considerable plasticity of root system architecture. This issue of overlapping uptake zones certainly explains why root system architecture models have been developed in the first place for modelling water uptake (Doussan et al. 1998, 1999, 2003, 2006; Javaux et al. 2008), and much progress is needed there as well (Draye et al. 2010). In contrast, very few models of nutrient acquisition have been explicitly accounting for root system architecture, a notable exception being the work of Dunbabin and co-workers, which applied mostly to nitrate, and P too (Dunbabin et al. 2003, 2004, 2006), and the recent work of Leitner et al. (2010a) dealing with spatial heterogeneity of P distribution and root system plasticity. In their work on P acquisition, Dunbabin et al. (2006) clearly demonstrated that upscaling from the root segment to the whole root system scale led to a more realistic description of the whole plant functioning, enabling feedback effects of rhizosphere processes on root growth to be accounted for (Fig. 4). At the whole root system scale, it is indeed possible to take into account that rhizosphere processes occurring at the root segment scale, e.g. the exudation of a P-solubilizing compound, improve P acquisition by the plant, and ultimately plant growth, which can have a positive feedback on P acquisition as a consequence of improved root growth and access to new soil zones (Dunbabin et al. 2006). Such positive feedback processes are not accounted for in most plant nutrition models which derive from a root segment approach of nutrient acquisition. Considerable progress has been made in the modelling of root system architecture over the recent years, thanks to computation facilities that open new avenues, with potential applications for assisting the design of best performing crop genotypes (de Dorlodot et al. 2007). Alternative approaches to explicitly accounting for root system architecture, e.g. continuous (Dupuy et al. 2010) or voxel automata (Mulia et al. 2010) approaches, also bear promises, especially when aiming at coupling such models with models of root functioning, integrating root-soil interactions occurring in the rhizosphere.
Fig. 4

Phosphorus acquisition benefit in wheat as a response to the exudation of a P-solubilizing exudate (a phospholipid surfactant, as expressed as % of P acquired compared with roots exhibiting no not such exudation) according to either a root segment (a) or root system model (b and c) developed by Dunbabin et al. (2006). While only P uptake is computed in the root segment model (root growth not being accounted for), for the root system model, three variables are computed: P uptake (black bar), root surface area (white bar) and P uptake per unit of root surface area (grey bar). In this case, simulations have been achieved both (b) in high P input conditions, and (c) low P input conditions, which are more prone for a significant benefit of the exudation (from Dunbabin et al. (2006), reprinted with permission from Springer-Verlag, Dordrecht)

The surface of uptake of a root is not only depending on root system architecture, whatever the level of accuracy of its representation in plant nutrition models. Fine features that evolved a long time ago in higher plants such as root hairs (Dolan 2001; Menand et al. 2007) and mycorrhizal hyphae (Brundrett 2002; Lambers et al 2009) are indeed of crucial importance for the acquisition of poorly mobile nutrients such as P (Hodge et al. 2010; Jakobsen et al. 1922a and b; Plassard and Dell 2010; Smith and Read 2008) and micronutrients (Clark and Zeto 2000; Hildebrandt et al., 2007). The models of nutrient acquisition have been improved decades ago to account for root hairs (Bhat et al. 1976; Bouldin 1961; Itoh and Barber 1983a,b; Leitner et al. 2010b; Nye 1966; Passioura 1963), which play a prominent role in extending the volume of the depletion zone in the rhizosphere, as clearly demonstrated for P (Gahoonia and Nielsen 2004a,b; Gahoonia et al. 2001). In contrast with root hairs, very little progress has been made to quantitatively account for the contribution of mycorrhizal hyphae, in spite of their much greater ability to expand the volume of the rhizosphere, compared with root hairs, due to their greater spread, which can reach several centimeters away from the root surface (Jakobsen et al. 1992a,b) and result in a network of mycorrhizal hyphae amounting to 100 cm of hypha per mm of root length (Allen 2007). In addition, an important feature of mycorrhizal fungi is their capacity to penetrate smaller soil pores than roots or root hairs. Indeed, most roots penetrate macropores that are larger than 80 μm, while root hairs can penetrate mesopores down to a diameter of 30 μm. Finest root hairs, such as those of Poaceae can even penetrate the largest micropores. But neither the roots nor the root hairs can penetrate the smaller micropores, contrary to mycorrhizal fungal hyphal tips that are as small as 2 μm (Drew et al. 2003) and thus capable of growing into the largest ultramicropores (Allen 2007). This very small hyphal diameter thus enable the roots mycorrhizal plants to access to poorly mobile nutrients located in portions of the soil solution that would otherwise not be accessible. It is therefore a pity that we do not have more quantitative insight into the respective contribution of the mycorrhizal symbiosis in the acquisition of P and other poorly mobile micronutrients such as Cu and Zn, although it is largely admitted that this contribution is significant in most plant species (Jakobsen et al. 1992a,b; Plassard and Dell 2010; Ryan and Angus 2003; Smith and Read 2008; Smith et al. 2003, 2004; Tatry et al. 2009), especially in low input conditions (Janos 2007). In addition, recent results demonstrate that the mycorrhizal pathway contributed from 20 to 100% to plant P uptake, depending both on the plant and the fungal species and independently of the effect of the fungal association on plant biomass (Facelli et al. 2010; Smith et al. 2004). These results emphasize that some plant species could therefore rely completely on the mycorrhizal pathway for P acquisition, which further justifies accounting for the fungal component in plant nutrition models. Schnepf and Roose (2006) and Schnepf et al. (2008a,b) have recently made first steps forward to account for P depletion zones around mycorrhizal hyphae in a root segment model (Fig. 5), which occurred to agree fairly well with results obtained in compartmented rhizobox experiments by Jakobsen et al. (1992a,b). This shall now be done at the more realistic scale of a whole root system model. However, the main difficulty is to understand and to predict what are the factors responsible for the variability of fungal growth (Thonar et al. 2011) together with the variable contribution of the mycorrhizal pathway for plant P uptake (compare Smith et al. 2004 and Facelli et al. 2010). Interestingly, numerical modelling proposed by Schnepf et al. (2008a) based upon different patterns of mycelial growth—linear or non linear branching or anastomosis (Schnepf and Roose 2006)—was able to fit reasonably well the measured values of hyphal length densities of three arbuscular mycorrhizal fungal (AMF) species with contrasting traits of growth (Thonar et al. 2011). Therefore, such numerical modelling appears as a promising approach to generate testable hypotheses on the mechanisms underlying the observed patterns in hyphal network dynamics and P acquisition by the AMF hyphae in soils, and the differences between AMF species in terms of soil prospection (Jakobsen et al. 1992b; Jansa et al. 2005; Thonar et al. 2011). Given the importance of the extension of the rhizosphere volume that may be explored by mycorrhizal fungi (Jakobsen et al. 1992a,b), models enabling us to calculate the rates of fungal nutrient uptake and nutrient delivery to the plants would greatly enhance our capacity to model plant nutrition in soil-grown plants, especially so in the context of low input agroecosystems.
Fig. 5

Simulated soil solution phosphate concentration in the rhizosphere of a mycorrhizal root as a function of the distance to root surface, according to two hypothetical scenarios of uptake by fungal hyphae of an arbuscular mycorrhizal fungus (accounting for anastomosis of the hyphal network over the 21 days of simulation). A first scenario assumes that P uptake occurs only at the tip of the mycorrhizal hyphae, which results in a small depletion zone. In contrast, the second scenario assumes that P uptake occurs along the whole length of mycorrhizal hyphae, thereby resulting in a considerably extended P depletion zone (from Schnepf et al. (2008b), reprinted with permission from Springer-Verlag, Dordrecht)

The biophysics of the rhizosphere: spatial and temporal issues

As stressed by Walter et al. (2009), «the rhizosphere can be thought of almost as a living structure, which is “born” at the time the growing root first influences the soil particles and develops as the soil particles are influenced by the adjacent root tissue, which is becoming progressively older». Silk and co-workers have developed an innovative theoretical framework to adress the spatial/temporal development of root-soil interactions (Walter et al. 2009; Watt et al. 2006). In particular, Kim et al. (1999) and Nichol and Silk (2001) included both spatial variability in proton flux along the root axis and temporal displacement of root tips caused by root growth inside the convection-diffusion equation commonly used in plant nutrition model. These authors calculated that the root elongation zone, which is assumed as a ‘non-active’ root zone, was in contact with the pH gradient induced by root tips (‘active’ root zone) in the rhizosphere if root growth was faster than proton diffusivity. This model thus showed that the rhizosphere can be assumed as a steady-state medium from the standpoint of ‘active’ root zones while the rhizosphere is a non steady-state medium from the standpoint of stationary soil particles as their properties evolve according to their period of contact with roots. Such results raise the question of using either Eulerian or Lagrangian standpoint to model rhizosphere processes, as recently stressed by Walter et al. (2009). These authors pointed that on the one hand, plant scientists use a moving reference frame, i.e. a reference frame attached to the moving apex (placing the origin of the distance coordinate at the root tip), which enable them to study root development without specifying the precise length of the root. Following soil or cellular particle through time corresponds to the Lagrangian viewpoint. On the other hand, soil scientists use a stationary reference frame to study soil processes, for which the origin is generally located at the soil surface. This corresponds to the more conventional Eulerian standpoint. Confronting these two contrasting standpoints may be fruitful, and actually, combining Eulerian and Lagrangian approaches is certainly needed to gain an indepth understanding of root-soil interactions (Walter et al. 2009).

Relatively little attention has been placed on the spatial/temporal development of root-soil interactions in plant nutrition models. Doussan and co-workers (Doussan et al. 1998, 1999, 2003, 2006) have made major progress in modelling water uptake at the rhizosphere up to whole root system scales by explicitly accounting for the spatial heterogeneity of water uptake capacities along root axes. This, combined with the temporal and especially diurnal patterns of water uptake generates complicated water gradients around roots, which should be accounted for as they ultimately govern the fluxes of nutrients as well. When it comes to nutrient uptake, little is known about what are the relative contributions of the various parts of a root system to the acquisition of nutrients by the whole plant (e.g. Silva et al. 2011). Most models implicitly assume that the uptake capacity (i.e. parameters of the Michaelis-Menten kinetics for instance) is evenly distributed over the whole root length, while experimental evidence of nutrient uptake not being uniform along growing roots has accumulated since the early work of Clarkson and co-workers. Harrison-Murray and Clarkson (1973) and Ferguson and Clarkson (1975) first showed that calcium (Ca) uptake mostly took place at the root tip because of the suberised endodermis restricting the radial flow of those nutrients which preferentially use the apoplastic pathway. Clarkson and co-workers showed that other nutrients, which are known to be taken up via the symplasmic pathway, such as P and K, occurred to be evenly taken up along the root length (see also for P the work of Rubio et al. 2004). However, Ernst et al. (1989) reported highest P uptake in 1-day old root zones and P uptake declining to 25 to 30% in 26-day old zones of maize (Zea mays L.) roots. A similar pattern of uptake was observed for nitrate by Reidenbach and Horst (1997). These authors suggested that such differences in nutrient uptake along the root system should be reflected in uptake models by forming root age classes with different uptake rates, as achieved for P by Wissuwa (2003, 2005). However, these models did not take into account the modifications arising from mycorrhizal symbiosis. As an example, the ectomycorrhizal status of roots strongly affected the rates of P uptake measured in pine seedlings (Tatry et al. 2009). These authors showed that the uptake capacity of the growing root apex, although never forming ectomycorrhizae, was much lower in ectomycorrhizal than in non mycorrhizal plants. Conversely, P uptake rates measured in root parts with ectomycorrhizae were 2- to 3-fold greater, compared to root parts without ectomycorrhizae (Tatry et al. 2009). Generally speaking, a strong heterogeneity of uptake rates of poorly mobile ions such as K and ammonium (but also more mobile nitrate ions) has been reported along the root of a range of forest species, whether ectomycorrhizal or not, with root tips exhibiting much greater uptake activities than the more basal parts of roots (e.g. Hawkins et al. 2008; Plassard et al. 2002). Regarding the variability of P uptake capacity along the hyphae of mycorrhizal fungi, little data are available. Building up on the approach designed by Jakobsen et al. (1992b) and supplying 33P available only to the hyphae of AMF and localised at known distances from the root compartment, Thonar et al. (2011) showed that the hyphae were able to take up and to deliver P to the plants from different maximal distances of 1–10 cm from the roots, according to the fungal species and its ability to develop in the root-free compartment, which further confirmed the results of Jakobsen et al. (1992b). In addition, the ratio between the amount of 33P in plant and the hyphal length densities did not vary much with the distance of P supply, except at the maximal distance where they are the lowest. These calculations suggest that the hyphae were able to take up and translocate 33P all along the hyphae, therefore supporting the ‘full length uptake scenario’ more than the ‘hyphal tip scenario’ (Fig. 5) proposed by Schnepf et al. (2008b). The low efficiency of 33P translocation to the plant at the maximal distances reported by Thonar et al. (2011) could be due to a delay of P transfer along the hyphae. Alternatively, it could be due to a low P uptake efficiency of growing tips of the AMF. Following the pattern of fungal P transporter identified so far in AMF (reviewed by Javot et al. 2007) or in ectomycorrhizal fungi (reviewed by Plassard and Dell 2010) as a function of the distance from the roots could bring valuable data to the actual contribution of the tips versus mature parts of the mycorrhizal hyphae associated with plant roots. These data would, in turn, contribute to a better modelling of P uptake by the mycorrhizal fungi. A major challenge would be to get quantitative insight on the relative contribution of mycorrhizal hyphae to nutrient acquisition by soil-grown plants under field conditions. However, the relative contribution of various portions of the root system to whole plant nutrition is little documented in situ, because of methodological difficulties. Recent studies under standardized conditions and using tracers in situ have suggested large differences in root uptake potentials between superficial and deep roots for various temperate tree species (Göransson et al. 2006, 2007 and 2008) as well as for eucalypts (Eucalyptus grandis Hill ex Maid.) under tropical conditions (Silva et al. 2011). Beside nutrient uptake, many rhizosphere processes that drive nutrient acquisition (see below) are not homogeneously distributed along root axes. Apical root zones have been repeatedly shown to be responsible for larger fluxes of exudates or protons (Calba and Jaillard 1997; Hinsinger et al. 2003; Lambers et al. 2006; Neumann et al. 1999; Plassard et al 1999; Vansuyt et al. 2003). Nevertheless, most models of plant nutrition do not account for such spatial heterogeneity of root functioning, which are difficult to quantify, and therefore assume that the acquisition of nutrients is uniform along the root system. This is likely to be of greater concern for perennial plant species, which exhibit more differentiated anatomy and morphology along root length, with direct implications on nutrient uptake properties (e.g. Hawkins et al. 2008; Plassard et al. 2002).

Since their development in the 1960s, plant nutrition models have been applied to simulate nutrient uptake of a range of species exhibiting a large range of ecological and physiological properties, including annual and perennial Monocotyledonous or Dicotyledonous species (Barber 1995; Jonard et al. 2010; Kelly et al. 1992; Nye 1983; Schenk and Barber 1980). Nevertheless, plant nutrition models have been originally designed to simulate nutrient uptake of annual crop species (e.g. Claassen and Barber 1976). Indeed, some assumptions in such models can be considered only valid for plant species with a rather short lifespan. For instance, root properties such as root growth rate or nutrient uptake capacity are considered as stable, regardless of the plant’s physiological status. Such hypotheses have been made following the work of Barber and co-workers on nutrient uptake capacity of crops at several developmental stages (Anghinoni et al. 1981; Baligar and Barber 1979; Barber 1995; Edwards and Barber 1976). These authors measured in hydroponics that P uptake capacity of maize remained stable during its vegetative growth stages (Baligar and Barber 1979). At the field scale, Edwards and Barber (1976) also demonstrated for several poorly mobile nutrients (P, K and micronutrients) that soybean (Glycine max L.) takes up nutrients at a constant rate during its vegetative growth stages. However, several studies measured a steep decrease in nutrient uptake capacity for several annual crop species at the reproductive growth stage (Barber 1995; Claassen and Barber 1976; Jungk and Barber 1975; Mengel and Barber 1974).

In perennial plant species, in spite of the evidence for changes in root physiological properties (Escamilla and Comerford 2000; Kelly et al. 2001), most studies used similar models as those developed for annual plants to simulate nutrient acquisition (Cropper and Comerford 2005; Gregory 2006; Kabba et al. 2009; Kelly et al. 1992; Lin and Kelly 2010). To satisfy the hypothesis of stability of plant physiological properties, most of these works on perennial plant species were conducted in controlled conditions, i.e. mesocosm, for short time periods ranging from several weeks to months. Under these conditions, adequate simulations of nutrient uptake for several perennial species such as loblolly pine (Pinus taeda, Kelly et al. 2001), maritime pine (Pinus pinaster, Jonard et al. 2010) or poplar (Populus tremula, Kelly and Ericsson 2003) were performed when soil nutrient availability was high. However, such results obtained over short time periods can hardly be used to estimate nutrient acquisition over longer study periods. Kelly et al. (2001) clearly demonstrated for red maple (Acer rubrum) and red oak (Quercus rubra) that plant nutrition models successfully predict Ca acquisition at two months of age, but consistently overestimate, in average by 99%, Ca acquisition at 18 months of age. These authors suggested that such discrepancy between measured and simulated values of Ca acquisition was caused by the inability of plant nutrition models to account for the decrease in Ca uptake capacity of older roots, which is due to the suberisation of the endodermis. In order to account for such changes in the nutrient uptake capacity of roots with plant age, several authors have attempted to include slight refinements in standard plant nutrition models (Blanco et al. 2005; Cropper and Comerford 2005; Jonard et al. 2010; Yanai et al. 2003). The major refinement achieved in these models concerned the simulation of the nutrient uptake capacity by means of a concentration-dependent function. Indeed, such function makes it possible to simulate implicitly contrasted nutrient uptake capacity of young and old roots. Based on such approach, Jonard et al. (2010) were able to correctly simulate nutrient acquisition in maritime pine over a five-month period. In contrast, Yanai et al. (2003) showed that the amounts of K and Ca taken up by Norway spruce (Picea abies) during three years at the field scale were underestimated by such a plant nutrition model. The results obtained by Yanai et al. (2003) may stem from the fact that only surface roots (roots present in the upper 30-cm thick layer of soil) were taken into account in this study. Indeed, deep roots must be accounted for to correctly estimate nutrient acquisition by perenial plants, especially for Ca and K (Buxbaum et al. 2005; Göransson et al. 2007, 2008). Plant nutrition models shall thus account for (i) the temporal heterogeneity of root activity pattern, (ii) the spatial distribution of roots in soil and (iii) the root growth and its interactions with nutrient availability to correctly simulate nutrient acquisition for perennial species (Gobran et al. 1998; Lin and Kelly 2010; Middelhoff and Breckling 2005).

On top of the spatial/temporal heterogeneity that is inherent to root function and structure, one shall also account for the heterogeneity of distribution and availability of nutrients in the soil, and how roots adapt to such pre-existing heterogeneity. In many soils including fertilized soils, there is at least a strong vertical gradient of nutrient availability, which decreases from the topsoil to the subsoil. Lynch and co-workers have been using root system modelling to address the nutrient uptake efficiency of various types of root architectures in soils exhibiting a more or less steep gradient of P availability (Ge et al. 2000). In addition, root system architecture is characterized by a tremendous plasticity (e.g. Hodge 2009; Hodge et al. 2009; Mulia et al. 2010; Pagès 2011). At a biophysical point of view, excess water (actually limited aeration) and mechanical constraints such as hard pans, rock fragments, etc. can physically stop root growth, or alter the direction of root growth and ultimately the total volume of soil that can be exploited for resource acquisition (Hodge et al. 2009; Stokes et al. 2009). Roots can also sense and respond to heterogeneity of nutrient concentration, and this dimension of root plasticity will thus be addressed in the next section on rhizosphere biogeochemistry and biochemistry. Although soil heterogeneity is a rule rather than the exception, heterogeneities of either biophysical or biogeochemical properties of soils, and how roots respond to these are little accounted for in most plant nutrition models. Finally other biophysical processes shall also be implemented into plant nutrition models, such as those processes that are related to mechanical effects of root growth (both axial and radial) or the production of mucilage by either roots or rhizosphere microorganisms, and the subsequent formation of rhizosheaths (Hinsinger et al. 2009). Veen et al. (1992) discussed the functional role of contact between the root surface and surrounding soil for the uptake of water and nutrients, and a number of authors have addressed the role of mucilage on the maintenance of such contact when soil dries out, as typically occurs over a diurnal rhythm as a consequence of water uptake (Hinsinger et al. 2009). By means of analytical calculation of water flow, Carminati et al. (2010) recently demonstrated the role of mucilage in altering soil water retention properties at the benefit of plant uptake when the soil dries out. In addition, the group of Bengough in Scotland has been making major progress in understanding how roots grow and anchor into the soil, root tip, including root cap cells, and root hairs playing a key role in such processes (Bengough et al. 2006, 2011). They have been showing how roots actually need to displace soil particles to create biopores in densely packed soils (Vollsnes et al. 2010). How these biophysical processes may interplay with root growth, root-soil contact, and water and nutrient transfer in the rhizosphere shall be estimated and ultimately incorporated in advanced plant nutrition models.

Rhizosphere biogeochemical and biochemical processes

Nutrient uptake and empirical modelling of soil nutrient buffering capacity

Plant nutrition models developed by Nye and co-workers in UK, and Barber and co-workers in USA share in common a rather simple representation of soil-root interactions which is based on an equilibrium description of the availability of the considered nutrient through basically two variables: (i) the concentration of the nutrient in the soil solution and (ii) the so-called buffering capacity of the soil solid phase which accounts for the ability of the soil to replenish the soil solution when the nutrient concentration decreases. These models, as stressed above, assume that nutrient acquisition is only driven by the absorption (uptake) into the root, and thereafter by the depletion of the nutrient of concern in the rhizosphere (decrease of its concentration in the soil solution close to the root surface). The buffering capacity is usually deduced from sorption isotherms, and most often from adsorption isotherms although desorption isotherms (e.g. Sato and Comerford 2006) would be more relevant in the domain of nutrient depletion. As stressed above for poorly mobile nutrients such as K and P, these types of models successfully predict their acquisition in nutrient-rich conditions, but consistently underestimate the actual acquisition in nutrient-poor conditions (Brewster et al. 1976; Lu and Miller 1994; Mollier et al. 2008; Schenk and Barber 1980). For P, a number of authors pointed that such models failed due to the inability of sorption isotherms to account for changes of P availability arising from the range of biogeochemical and biochemical processes that occur in the rhizosphere, on top of P uptake (Geelhoed et al. 1997a; Silberbush and Barber 1983).

Indeed, evidence has accumulated that plant roots use a number of ‘tricks’ to increase the availability of nutrients when encountering adverse conditions (e.g. nutrient deficiency), as pointed by Darrah (1993) and Marschner (1995) and reviewed by Hinsinger (1998, 2001) and more recently by Richardson et al. (2009). In the case of P, roots and associated rhizosphere microbial communities alter the pH, exude organic ligands (carboxylates especially) and other P-solubilizing compounds which trigger a range of biogeochemical (ligand exchange, ligand- or proton-promoted dissolution of minerals, etc.) and biochemical (enzymatic hydrolysis of organic P compounds by phosphatases) processes in the rhizosphere (Hinsinger et al. 2011). Only the combination of at least one of these processes and nutrient uptake can actually explain the observed increase of the concentration of a poorly mobile nutrient, as repeatedly observed in the rhizosphere for P, K, ammonium and micronutrients such as Cu, Fe, Mn and Zn (Cloutier-Hurteau et al. 2008; Courchesne and Gobran 1997; Devau et al. 2010, 2011b; Hinsinger et al. 2009; Pankhurst et al. 2002; Schöttelndreier and Falkengren-Grerup 1999; Séguin et al. 2004; Turpault et al. 2005). In addition, as already stressed above, conventional plant nutrition models which assume that roots affect their surrounding environment solely via the depletion of nutrients in the soil solution cannot account for (i) either the complex patterns combining depletion close to the root surface, and accumulation at greater distance as sometimes observed for P (Hinsinger 1998, 2001; Hinsinger and Gilkes 1996; Hinsinger et al. 2009; Hübel and Beck 1993) (Fig. 2), or (ii) the depletion of poorly-mobile micronutrients at greater distances from root surface than diffusion would predict, as found for Cu by Bravin et al. (2009). In this study, the observed profile of Cu concentration was shown to be actually the consequence of root-induced pH change instead of Cu uptake. In his review on plant nutrition models, Rengel (1993) also stressed that no available models were actually accounting for chemical interactions between ions (e.g. competition between major cations such as K and Ca or Ca and Mg, or among metal micronutrients), even the so-called multi-ion uptake model proposed by Bouldin (1989). This is the reason why, many years later, Nowack et al. (2006) pledged for the development of a multi-component approach based on a thorough description of soil geochemistry in the next generation of plant nutrition models (see below).

As the occurrence of these many interactive processes that can alter the concentrations of nutrients in the soil solution was already recognised by then, some authors such as Nye (1983, 1984) and, later, Kirk and co-workers (Kirk et al. 1999b; Kirk 2002; Kirk and Saleque 1995) tried to integrate the possible interactions between the uptake-driven diffusion of P ions towards the root surface and the exudation of a P-solubilizing compound (e.g. protons) diffusing away from the root surface. The interaction was based on the experimental evidence of an alteration of the P sorption isotherm by the considered solute (e.g. proton or citrate in the groups of Nye and Kirk, or a surfactant in the work of Dunbabin et al. 2006). This approach successfully predicted complex P concentration patterns combining depletion at the very surface of the root and some accumulation farther away (Kirk 1999; Kirk and Saleque 1995; Kirk et al. 1999a,b; Nye 1983, 1984). However, the drawback of such an approach lies in its empirical basis, requiring the calibration of the value of the interaction factor (i.e. an empirical function describing how for instance a P-solubilizing compound alters soil solution P concentration, as shown for protons by Nye in 1983) for every soil to be studied. A more mechanistic approach of rhizosphere biogeochemistry was thus clearly needed, as stressed by Nowack et al. (2006). Beyond the rhizosphere, Goldberg et al. (2007) stressed the limitation of empirical models of ion adsorption/desorption (e.g. Langmuir or Freundlich formalisms usually applied to anions such as P), which cannot adequately account for the many parameters that affect sorbing surfaces across large ranges of soil types, while mechanistic surface complexation models are designed to do so. The following section summarizes the few studies that have been attempting to achieve this for improving nutrient uptake models.

Acquisition of nutrients explicitly accounting for rhizosphere biogeochemistry and biochemistry

Plant nutrition is not just about plant physiology, especially for the acquisition of poorly mobile nutrients for which the limiting process is not the absorption by the roots, but rather the transport and biogeochemical and biochemical processes that occur in the rhizosphere, prior to the uptake (Clarkson 1985; Hinsinger 1998). This should be considered as a major lesson to be drawn from conventional plant nutrition models: for instance, Barber (1995) clearly stressed via sensitivity analysis that P uptake parameters were the least sensible for P acquisition. In spite of this, no major change of paradigm has occurred in the focus of research in plant nutrition and in plant nutrition models. A major change of paradigm—still to be achieved—would be to develop mechanistic models that truly account for the considerable amount of knowledge accumulated over the last decades in the identification of biogeochemical and biochemical processes occurring in the rhizosphere (Hinsinger et al. 2009). This would provide a more quantitative approach of the driving processes of acquisition of poorly mobile nutrients and help design new strategies to tackle the challenge of an ecological intensification of agroecosystems.

A pioneer work in this respect is that done by Geelhoed and co-workers in Van Riemsdijk’s group in the Netherlands (Geelhoed et al. 1997a,b, 1999) on the impact of citrate exuded by roots on the fate of P in the rhizosphere at the root segment scale. These authors used a modelling approach which accounted for competitive desorption of P by citrate in the model situation of a substrate made of a goethite-quartz mixture. Their work showed that in terms of simulated P uptake, little benefit of citrate exudation was achieved at low exudation rate (in the order of what would be occurring for most plant species) and high P conditions, while a 75% increase would occur at a 10-fold larger exudation rate, in the order of that achieved in cluster roots of white lupin (Lupinus albus L.), assuming no microbial degradation of citrate occurs in the rhizosphere (Fig. 6). When accounting for a citrate decay rate of 50 day−1, the benefit of exudation was reduced to about 30% (Geelhoed et al. 1999). In contrast, when making similar calculations for low P conditions (lower P coverage of goethite surface and equilibrium solution P concentration), the extra benefit of citrate exudation was considerably larger: a 7-fold increase in P uptake at low exudation rate and 28-fold increase at large exudation rate, assuming no decay (Fig. 6). Even when accounting for a rapid decay of citrate, the benefit was still large, up to 21-fold at high exudation rate. This work conducted with the CD-MUSIC model (Hiemstra and Van Riemsdijk 1996), and a subsequent similar work conducted with ORCHESTRA (Nowack et al. 2006) consistently showed that while depletion of soil solution P occurred without exudation, a complex pattern combining depletion and accumulation of soil solution P was modelled when citrate exudation was accounted for (Fig. 7). In contrast with the work of Kirk et al. (1999b) that was based on the empirical approach initiated by Nye (1983, 1984), those models are truly mechanistic and can thus be applied to other situations than those for which they have been calibrated. In addition, they can account for even more complex biogeochemical interactions, as e.g. the role of root-induced acidification of the rhizosphere combined with citrate exudation and P uptake (Geelhoed et al. 1999). It is a pity though that such models have been essentially applied to simplified substrates, mostly goethite-quartz sand mixtures (Geelhoed et al. 1999; Nowack et al. 2006; Szegedi et al. 2008) where the number of sorbing surfaces and P pools (most often only two: soluble P and adsorbed P) have nothing to compare with the complexity of real soils.
Fig. 6

Effect of citrate exudation and decay rates on simulated P uptake by maize from P adsorbed onto goethite-coated quartz sand at two levels of phosphate loading: (a) 20 μM P initial concentration resulting in a P loading of goethite of 1.9 μmol m−2 and (b) 0.1 μM P initial concentration resulting in a P loading of goethite of 1.3 μmol m−2 (drawn from data taken from Geelhoed et al. (1999), reprinted with permission from Blackwell Publishing Ltd. / British Society of Soil Science)
Fig. 7

Rhizosphere concentration profiles of (a) phosphate in solution and (b) phosphate adsorbed on goethite with and without exudation of citrate, as predicted by the ORCHESTRA model. Calculations were made for maize growing in goethite-coated quartz sand (Geelhoed et al. 1999) with the following conditions : 95 m2 goethite per kg sand, 1.9 mmol m−2 phosphate initially bound on the goethite surface, 0.5 mmol m−1 day−1 citrate exudation and t = 1 day diffusion (from Nowack et al. (2006), reprinted with permission from Springer-Verlag, Dordrecht)

We recently developed a similar mechanistic model and an additive approach to account for the various mineral and organic constituents of soils that can be implied in surface complexation processes controlling P concentrations (Devau et al. 2009, 2010, 2011a,b). This modelling effort proved successful at predicting the pH-driven changes of P availability in low P soils, and showed a substantial contribution of clay minerals to the control of P availability (Devau et al. 2009, 2011a). More interestingly, we showed with this approach that calculated P uptake well matched with the measured P uptake by a cereal, provided that root-induced changes of pH and Ca concentration were also accounted for (Devau et al. 2010, 2011b). The actual increase in water extractable P that we measured in the rhizosphere was obviously not predicted when accounting only for P uptake, or P uptake combined with rhizosphere pH change (Fig. 8). A third biogeochemical process had to be considered for obtaining a good match between measured and calculated P acquisition: the root-induced decrease in Ca concentration, which occurred in the rhizosphere as a consequence of Ca uptake. Here, it is important to stress that the dependency of P to Ca is not related to the dissolution or precipitation of Ca-phosphate minerals but stems from electrostatic interactions between negatively-charged phosphate ions and positively-charged Ca ions. It is worth to mention that without such a mechanistic modelling approach, we would never have considered that such a process would come into play, based on the existing knowledge of the key parameters and processes controlling soil P availability (Hinsinger 2001). A posteriori, the importance of Ca occurred to be related to the major role of soil clays in the control of P adsorption and its impact on surface charges and surface complexation processes (Devau et al. 2010, 2011b). These works demonstrate that mechanistic biogeochemical models stand as unique tools to further our understanding of plant nutrition. For instance, such models could be used to better account of the reality of carboxylate exudation in the rhizosphere. While most former models have only addressed the interaction of a single carboxylate (most often citrate) with P nutrition, roots always exude a complex mixtures of carboxylates, which considerably differ in their affinity for sorbing surfaces and ability to desorb phosphate ions, on top of their varying, relative concentrations (Jones 1998). Mechanistic models such as those used by Van Riemsdijk’s group in the Netherlands (Geelhoed et al. 1997a,b, 1999), and our group (Devau et al. 2009, 2010, 2011a,b) offer this potential to account for such complex interactions amongst a range of carboxylates. Their development is opening new avenues to quantify the relative contribution of various, possibly interacting processes triggered by roots or the associated rhizosphere microorganisms. The results obtained by Devau et al. (2009, 2010, 2011a,b) suggest that such mechanistic models should be used to perform in silico experiments; i.e. exploring a broad range of simulation scenarios, to study for instance how soil types (with contrasting mineralogy and/or fertilisation history) determine the hierarchy of rhizosphere processes affecting P availability. The heuristic value of such models makes no doubt, and becomes even more valuable for approaching processes that are hardly accessible to direct measurements. For instance, Devau et al. (2010) showed how rhizosphere processes alter the distribution of adsorbed phosphate ions on the various soil minerals that are responsible for adsorption, which is the clue of rhizosphere P availability.
Fig. 8

Measured and calculated P availability in the bulk soil and in the rhizosphere of durum wheat for three simulation scenarios of increasing complexity (Devau et al. 2010): scenario 1 accounts only for P uptake, scenario 2 also accounts for rhizosphere alkalization and scenario 3 takes these two processes into account as well as Ca uptake. Only this third scenario adequately matched with the measured increase in P availability in the rhizosphere (from Devau et al. (2010), reprinted with permission from Oxford University Press)

The set of mechanistic adsorption models used in Devau et al. (2009) and subsequent works can be viewed as being complicated to handle, notably because of the large number of parameters required for an application. It is therefore important to stress that most of these parameters, such as the equilibrium constants, are generic, i.e. their values should be independent of the soil and should correspond to pure mineral systems. These values can be found in the literature, directly or indirectly (i.e. from the reinterpretation of published experimental data), and other ions can be used as a surrogate for phosphate ions (i.e. arsenate) and Ca ions (i.e. cadmium). Most parameters involved in the adsorption model for soil organic matter were also described by means of the generic values proposed by Milne et al. (2001, 2003). This approach can thus be easily achieved by anyone without further efforts than those made in order to determine the soil specific parameters; i.e. the model parameters that are expected to vary in each soil, or at least from a soil type to another soil type. However, a limitation of these works based on surface complexation modelling is that they only consider equilibrium relationships between solutes and sorbed species, which imply that P-controlling soil reactions are instantaneous. Future biogeochemical models should therefore also cope with the kinetic dimension observed for decades in the case of P sorption by soils. Various kinetic formalisms or models have been proposed (see review by McGechan and Lewis 2002), but they all seem quite empirical notably because of the absence of provisions for surface complexation process. The nature of the processes controlling the slow sorption component of the overall P sorption reaction is also a matter of further researches, as it could be due to diffusion within micropores (Van Riemsdijk et al. 1984a), precipitation/dissolution of P-containing minerals such as Ca-phosphates (e.g. Murrmann and Peech 1969), or more probably some combinations of these two processes (Van Riemsdijk et al. 1984b).

Besides the case of P, which has been a major focus in the above-mentioned works, mechanistic biogeochemical models should be especially powerful for addressing the acquisition of metal micronutrients. The complexation of metals by a range of root and microbial exudates is likely to play a key role, which shall however depend on the pH, and the potential competition with other metal cations (including major cations such as Ca), of which concentrations can tremendously vary in the rhizosphere. Obviously, only reactive transport, multi-component models as developed in geochemistry appear as suitable tools to better predict the fate of very reactive nutrients such as P and micronutrients, or potentially toxic elements such as Al and trace contaminants at the soil-root interface in a broad range of soil types and substrates (Anoua et al. 1997; Calba et al. 2004; Devau et al. 2009, 2010, 2011a,b; Nowack et al. 2006; Szegedi et al. 2008).

The biogeochemistry and biochemistry of the rhizosphere: plant physiology feedbacks

A number of the rhizosphere processes that have been cited above as key players in nutrient acquisition are regulated by the whole plant, and depend in particular on plant nutritional status. Such feedback processes would need to be accounted for in future attempts to model nutrient acquisition. Indeed, the root-induced release of protons or the exudation of carboxylic anions as well as enzymes such as phosphatases have been shown to be stimulated under P deficient conditions (Hinsinger 2001; Neumann and Römheld 1999; Raghothama 1999; Raghothama and Karthikeyan 2005; Richardson et al. 2001; Tang et al. 2004; Vance et al. 2003). This is especially documented for protons in strategy I plant species (i.e. non Poaceae species), which exhibit enhanced proton efflux behind root apices as a response to Fe deficiency (Hinsinger et al. 2003; Marschner 1995; Vansuyt et al. 2003). The enhanced secretion of phytosiderophores in strategy II plant species (Poaceae) as a response to Fe (and Zn) deficiency is another well-known nutrition feedback process (Marschner 1995; Robin et al. 2008). To the best of our knowledge, very few plant nutrition models take such physiological feedback loops into account. The work of Dunbabin et al. (2006), which accounted for the increased availability of rhizosphere P as a consequence of the exudation of surfactants (phospholipids), may be considered as an exception in this respect. It showed that it is worth upscaling to the whole root system scale in order to account for the feedback effects of improved plant P nutrition on root growth and further extension of the prospected soil volume, ultimately increasing P acquisition. Indeed, as shown in Fig. 4, Dunbabin et al. (2006) calculated in a high P soil that the extra benefit of the exudation of surfactants on P acquisition was rather negligible at the root segment scale (only 4% increase), while it became significant at the whole root system scale (about 13%). In a low P soil, the extra benefit was obviously much larger, close to 50% increase in P acquisition, at the whole root system scale (Fig. 4). This model however did not account for a feedback effect of the P status of the plant on the exudation rate of the considered P-solubilizing compound.

Another plant physiological feedback loop based on the nitrogen status of the plant was also simulated by Kirk and co-workers for lowland rice (Oryza sativa L.) growing in a flooded soil, i.e. in reduced conditions (Kirk 2002; Kirk et al. 1999b; Saleque and Kirk 1995). Under such conditions, these authors simulated that NH4+ nutrition led to enhanced P availability, and hence improved P nutrition, compared to NO3 nutrition, despite the negative effect of rhizosphere acidification on plant growth (Kirk et al. 1999b). The promoting influence of NH4+ nutrition on P acquisition was supported by the release of protons from roots in order to balance the excess intake of cations over anions, which increased P availability by 30% in the rhizosphere. These results stress that plant nutrition model can be adequately used to understand nutrition of a plant in situations where experimental data are particularly difficult to interpret. In order to properly integrate such physiological feedback loops into plant nutrition models, physiological responses to nutrient deficiencies would also need to be to be accounted for. Formalisms which have been developed to simulate how nutrient deficiency affects plant growth (Chiera et al. 2002; Halsted and Lynch 1996), shoot-root allocation of the biomass and root growth (Mollier et al. 2008; Pellerin et al. 2000; Wissuwa et al. 2005) could be advantageously implemented into plant nutrition models.

Feedback loops to be accounted for are not only those related to the whole plant functioning, as there is accumulating evidence that local processes also play a key role in what Hodge (2009) called ‘root decisions’. Roots can sense their environment, and respond to this by altering their growth and physiology, e.g. foraging for nutrient-rich patches. The seminal work of Drew (1975) showed that such plasticity could occur for P and ammonium or nitrate, but not for K. Molecular physiology then provided some clues about (i) how roots can sense nutrient concentrations in their environment and (ii) the cascade of events leading to the proliferation of roots in nutrient-rich zones (e.g. Forde and Lorenzo 2001; Lima et al. 2010; Remans et al. 2006), but only few plant nutrition models have accounted for such root plasticity. Recently though, Leitner et al. (2010a) have introduced some degree of root architecture plasticity in their model of P uptake. Doing so they have shown the potential benefit for the plant in terms of P acquisition: their model indeed showed that when chemotropism occurred, i.e. root foraging in the nutrient-rich patch, the uptake of P by the whole plant was increased by as much as 82% compared with the case of a root system that would not exhibit such plasticity. This modelling work thus opens new avenue for integrating such feedback processes that have been shown to play an important role in resource acquisition in ecosystems, and possibly agroecosystems as well, although these processes have been little studied in this context. Root foraging is especially crucial when nutrients are not homogeneously distributed as may occur in the case of fertilizer placement for instance (Jing et al. 2010; Zhang et al. 2010).

Rhizosphere biological and ecological processes

Rhizodeposition and rhizosphere microorganisms

Only root-borne processes have been discussed so far, except for the role of mycorrhizal hyphae in the uptake of poorly mobile nutrients. The potential roles of rhizosphere microorganisms are however many-fold. Rhizodeposition, which is comprising the release of a broad range of plant-derived compounds, beyond root exudates, is a key biogeochemical process occurring in the rhizosphere (Dennis et al. 2010; Hinsinger et al. 2005, 2009; Jones et al. 2009). Higher plants are thereby known to act as energy and substrate suppliers for the microbial rhizospheric communities, while getting positive/negative feedbacks from these, via an enhancement/alteration of both plant health and nutrition. However, the situation could be much more complicated than this “simplified” view for several reasons. First, as pointed out by Dennis et al (2010), the importance of C-rich exudates from roots should be re-evaluated compared to other rhizodeposits and microbial exudates for understanding how rhizosphere microbial communities are ultimately structured. The plant-derived, belowground C economy is subject to controversy due to the artificial conditions (often axenic hydroponic conditions), simplified experimental devices and limited insight in plant developmental stages beyond the early stages of growth in most of the studies conducted so far (Dennis et al. 2010). The lack of reliable quantitative information on how the release of root and microbial exudates vary over space and time constitutes a bottleneck for further implementation into plant nutrition models. Dennis et al. (2010) conceptualized the spatial/temporal heterogeneity and origins of C-compounds structuring the microbial communities along the root system. But one needs more than just a conceptual model. In this respect, the modelling work of Darrah (1991) showed that the production of root exudates at a localized, high efflux rate over a short period of time, increases their potential role for enhancing nutrient acquisition by plants. Indeed, this model showed that the microbially-mediated decay of root exudates was less than if the same amount of exudates was released continuously all along the root length. Interestingly, phytosiderophores are secreted by roots of Poaceae over a restricted temporal/spatial window, their secretion peaking from 3 to 6 h after the onset of daylight, and in the zone behind the root tip (Marschner 1995; Robin et al. 2008). This definitely contributes increasing the effectiveness of strategy II for Fe acquisition in plants (Robin et al. 2008). Second, beyond the amount of C released in the rhizosphere, the nature of these C compounds and their C/N/P stoichiometry may play a major role in the microbial control of the fate of plant nutrients such as N and P, building on the views of Cleveland and Liptzin (2007) about the role of C/N/P stoichiometry in soils in the biogeochemical cycles of C, N and P in terrestrial ecosystems. The priming effect can occur in the rhizosphere as a consequence of rhizodeposition (Cheng 2009) as microorganisms use the energy from these fresh C compounds to breakdown soil organic matter. Fontaine et al. (2011) suggested that microorganisms may do this especially under inorganic N-limitation in order to release organic N, and Hinsinger et al. (2011) hypothesised that this might occur in a similar manner for P. Third, the soil organic C content may not be the primary driver of microbial composition and activities, as shown by a number of recent studies on microbial biogeography at different scales, from the field plot to global scales (e.g. Bru et al. 2010; Fierer and Jackson 2006; Philippot et al. 2009; Rousk et al. 2010). These studies indeed revealed that soil pH was the main driver of microbial biogeography, while soil organic C content was not. Therefore, given the major changes of pH occurring in the rhizosphere (Hinsinger et al. 2003), one may hypothesize that root-induced pH change may be equally or more important than rhizodeposition in structuring rhizosphere microbial communities (Hinsinger et al. 2009). A weak effect of rhizodeposition on the structure of rhizosphere microbial communities has been previously reported by Henry et al. (2008). However, prediction of rhizosphere pH is a difficult task, given its implication in numerous chemical reactions in soils and the need to model both rhizosphere proton budget and pH buffering capacity. As reviewed by Hinsinger et al. (2003), the cation/anion balance (including ions taken up by roots and the release of carboxylates) plays a key role in determining root-borne sources of protons/hydroxyls. In addition, Schaller (1987) stated that the pH buffering capacity of the rhizosphere could be explained by short term buffering reactions but these had not been explicitly described yet. Recently, Devau et al. (personal communication) attributed the measured changes of pH buffering capacity between rhizosphere and bulk soil after two hours of soil/root contact to changes of organic matter quality as measured by Excitation Emission Matrix Fluorescence Spectrophotometry. Finally, the role of fungi (sensu lato, beyond mycorrhizal fungi) in plant nutrition remains poorly understood despite their ecological importance (between 20 to 66% of the microbial biomass in the rhizosphere of pasture species; Joergensen 2000). Isotope-based studies in grassland (Denef et al. 2007) suggest that the first step of C delivery from roots to the soil is mediated by fungi (both mycorrhizal and saprotrophic). This result reinforces the view of the rhizosphere as a mycorrhizosphere (Timonen and Marschner 2005) where rhizosphere bacteria would feed on fungal rather than root exudates. In the field, rhizosphere ecology and plant efficiency to take up nutrients will thus depend upon multiple interactions between plants and rhizosphere microorganisms. Regarding P nutrition, except in the most extremely impoverished situations (e.g. in ancient, highly weathered soils of some regions of the world—see Lambers et al. 2008) the contribution of mycorrhizal fungi appears as a key determinant through the operation of the mycorrhizal pathway. Finally, Bonkowski (2004) and Bonkowski et al. (2000, 2009) have highlighted the importance of diverse signalling pathways between roots and soil fauna which ultimately impact the acquisition of nutrients by plants, via altered root architecture and growth, host defence regulation, or the selective stimulation/inhibition of specific microbial populations. This suggests that other interactions than trophic relationships need to be accounted for, as largely documented for the case of plant-growth promoting microorganisms (Richardson et al. 2009). Accounting for these in plant nutrition models has not been attempted so far. Finally, one should account for root-induced changes of the abiotic factors that are susceptible to modify microbial communities and activities. For instance, Raynaud (2010) modelled that variations of soil water content at short time scales as occur in the rhizosphere modulate the interactions between roots and microorganisms.

Exudates of microbial origin in the rhizosphere

Jones et al. (2003) pointed out the diversity of root exudates, such as organic anions but also other plant metabolites which comprise a broad spectrum of water soluble low molecular weight organic molecules which are potential C sources for rhizosphere microorganisms. Besides the release of exudates by plant roots, rhizosphere microorganisms may contribute to the mobilization of poorly available nutrients via the release of microbial metabolites, which is largely documented for P and Fe (Marschner et al. 2011). In the case of Fe, siderophores released by rhizosphere bacteria and fungi are known to play a pivotal role in the fate of Fe, with potential consequences on microbial communities and, ultimately plant health on the one hand, and plant nutrition on the other hand, as reviewed by Robin et al. (2008). While the effect on plant health has some applications in biological control, the effect of microbial siderophores on Fe nutrition of plants is still a matter for debate. Besides siderophores, the capacity of fungi, whether saprotrophic or symbiotic, to release low molecular weight organic acids is well known despite the high degree of diversity among fungal species (Plassard and Fransson 2009; Plassard et al. 2011). Although plant P nutrition could benefit from carboxylic acids released by saprotrophic fungi when used as inoculants (Harvey et al. 2009), the effect might be even more important with mycorrhizal fungi. This is especially true for some ectomycorrhizal fungi as significant release of carboxylates by AMF has not been documented so far. Such a positive effect was shown for instance in young pine seedlings associated with an ectomycorrhizal species producing huge amounts of oxalic acid in a chromic cambisol (Casarin et al. 2004). Interestingly the hyphae were covered with Ca oxalate crystals (Casarin et al. 2003). Given the importance of Ca in determining P availability as modelled by Devau et al. (2009, 2010, 2011a), this additional sink of Ca should be taken in consideration. In addition, rhizosphere microorganisms may strongly modify the fate of P through the release of exoenzymes such as e.g. phosphatases of bacterial or fungal origin (Courty et al. 2010; George et al. 2002; Hinsinger et al. 2011; Koranda et al. 2011; Renella et al 2007; Richardson and Hadobas 1997).

In addition, regarding the role of microorganisms in the rhizosphere, one aspect that is difficult to deal with is the role of biological complexity. Only a few studies addressed this question. As an example, the work carried out in mesocosms by Van der Heijden et al. (1998) demonstrated clearly that increasing the diversity of AMF from 1 to 14 species isolated from the field increased by 70% the plant shoot biomass of 15 species of host-plant, following a logarithmic trend. This effect was concomitant with an increase of hyphal length density by two orders of magnitude. However, P accumulation in plants increased linearly with the number of fungal species, indicating that the relationship between the efficiency of mycorrhizal symbiosis and P uptake and delivery from the hyphae towards the plants may be more complicated than expected. Indeed, species of AMF can differ widely regarding (i) their growth pattern resulting in different extension of hyphae in the medium that in turn will determine the exploitation of the soil, and (ii) also in their efficiency to transport and to deliver P taken up by the fungal cells (Jakobsen et al. 1992b; Jansa et al. 2005; Thonar et al. 2011). A major challenge would be to ‘classify’ the species of AMF according to their ability to develop in the soil and to deliver P (and micronutrients) to the plant. Accounting for the diversity of rhizosphere microorganisms (and their predators, see below) possibly implied in mobilizing poorly mobile nutrients is even more challenging.

Implementing such microbially-mediated processes in plant nutrition models is not straightforward, as it would require accurate knowledge of C release rates, composition of root exudates, dynamics of microbial communities and associated activities, e.g. enzymatic activities and the fate of exoenzymes at the rhizosphere scale. As reviewed by Toal et al. (2000) several models of carbon flow are available which integrate at various levels (i) microbial growth, (ii) rhizodeposited C consumption and (iii) physiological state of soil microorganisms. Within such models, the bacterial population declines monotonously from the root surface whereas, according to Zelenev et al. (2005), modelling as a wave-like distribution would be more realistic. Moreover, such models should account for microbial dynamics along roots, when attempting to upscale such processes at the whole plant scale, building up on the conceptual framework developed by Dennis et al. (2010). The models of Allison (2005) and Schimel and Weintraub (2003) could also be considered as a first step to take into account the production of exoenzymes by rhizosphere microorganisms as related to rhizodeposition of carbon-rich substrates. However, models based on kinetic equations would still be difficult to calibrate and validate or adapt to existing formalisms (Jones et al. 2009; Toal et al, 2000). Indeed, those kinetic equations were not able to account for changes in microbial activities in response to variations of abiotic factors. In contrast, models based on thermodynamics equations have been successfully developed in order to simulate microbial activities such as fermentation, respiration, growth, exoenzymatic activities according to a large range of abiotic conditions (Jin and Bethke 2003, 2005). Nevertheless, these models have been only validated for aqueous media (hydrothermal fluid and seawater), which are quite far from the complexity of soils. Accounting for thermodynamics models of microbial activities in plant nutrition models shall be worth being attempted for simulating the changes in microbial activities in response to variations of abiotic properties at short time scales as occur in the rhizosphere. The dynamics of low molecular weight organic acids along soil horizon in Swedish forest soils, including respiration, sorption and leaching, have been successfully modelled by Van Hees et al. (2005). This model despite its empirical nature requiring calibration is a promising approach to upscaling the rhizosphere effects enhanced by C released from roots or rhizosphere microorganisms.

The rhizosphere microbial loop and trophic relationships including soil fauna

In addition to a direct role of rhizosphere microorganisms in the mobilization of poorly available nutrients to plants, the microbial loop as described for the fate of organic N shall also be considered in the case of P. This is based on the assumption that newly grown bacteria mobilize nutrients that are not easily accessible to plants, in particular N and P, which are then made available to plants by bacterial grazers (Clarholm 1985, 2005; Kuikman et al. 1991). Of these bacterial grazers, protozoa and nematodes play a major role via releasing nutrients sequestered in the bacterial biomass in the rhizosphere (Bonkowski et al. 2009; Villenave et al. 2004). These predators themselves are likely to benefit from increased plant growth since bigger plants may allocate more C belowground and support a greater root biomass and rhizodeposition, ultimateley resulting in increased prey (bacteria) density (Bonkowski 2004; Bonkowski and Brandt 2002; Phillips et al. 2003). The hypothetical mechanism for releasing N via predation is that bacteria have a lower C/N ratio (approximately 5:1) than their predators (e.g. bacteria-feeding nematodes with C/N ratio of approximately 10:1) and so the excess mineral N produced during grazing stimulates plant growth (Anderson and Domsch 1980). However, the effect of trophic relationships on P mineralization from either the P pool contained in bacteria or fungi has received much less attention than N, despite the importance of this P pool in the soil. The study of Djigal et al. (2004), showing that the presence of bacteria-feeding nematodes greatly increased P availability to maize plants indicates that this topic should be studied in greater details. Similar trophic relationships may also apply to fungal communities and the fauna feeding on fungi. Concerning N acquisition, Raynaud et al. (2006) showed that the whole microbial loop could be modelled to better describe the fate of N in the rhizosphere. Their model accounted for the stimulation of microorganisms by root-derived C, and also for predation of rhizosphere bacteria by the fauna (protozoa or nematodes). However, to our knowledge, no such modelling study aiming at taking into account the effect of the microbial loop on P acquisition by plants has been reported yet.

Plant-plant belowground interactions in the rhizosphere of plant communities

Most plant nutrition models have been developed for a single root segment or the whole root system of a single plant, with no account for intraspecific and interspecific interactions possibly occurring in the crop or forest stand. A major assumption in plant nutrition models cited above is that rhizosphere processes affect nutrient availability, and hence nutrient uptake, of the individual plant responsible for such rhizosphere processes (Geelhoed et al. 1999; Kirk 2002; Kirk and Saleque 1995; Leitner et al. 2010b; Mollier et al. 2008). Nevertheless, rhizosphere processes induced by one plant can lead to positive or negative effects on the nutrient uptake of other plants growing in its vicinity (Callaway 2002, 2007; Fridley 2001; Hinsinger et al. 2011). Similarly to root-root competition as mentioned above in neighbouring roots of a single root system, several studies demonstrated for nutrients with high diffusion coefficient that the nutrient depletion zone of one plant can overlap that of the neighbouring plants, leading to decreased nutrient uptake (Callaway 2007; Loreau 1998; Tilman 1997). A pioneer plant nutrition model, which accounted for rhizosphere interactions between competing plants of a crop stand is that of Dunbabin et al. (2002). These authors simulated that nitrate availability in the rhizosphere of narrow-leaf lupin (Lupinus angustifolius L.) was 2-fold lower when surrounded by neighbouring plants because of the overlapping of the rhizosphere zones. It was also shown that these competition interactions between plants and its consequence on nitrate nutrition were mainly controlled by the root growth rate and distribution, as these root parameters determined the degree of overlapping amongst the rhizosphere zones of the neighbouring plants.

Plant-plant belowground interactions are not only negative as occurs in the case of competition for nutrients. Some of these are positive, as is the case of facilitation in which one plant species improves the growth or fitness of the neighbour plant species, e.g. via improved nutrition (Callaway 2007). This has been extensively studied for N nutrition in intercropping or agroforestry systems, which are mixing at least one non-legume species with a N2-fixing legume species. Hydraulic redistribution is another process likely to influence nutrient uptake of neighbouring plants, with deep-rooted plants transferring water up from depth into topsoil layers (Burgess 2011). Facilitation has been little studied so far for P, and recently reviewed by Hinsinger et al. (2011). Most of these studies reported the ability of one species to increase the availability of soil P via rhizosphere processes to its own benefit, and also to the benefit of the neighbouring species, as especially documented for cereal/legume intercropping systems (Cu et al. 2005; Hinsinger et al. 2011; Li et al. 2007; Li et al. 2008; Li et al. 2010). To explain such facilitation interactions, Li et al. (2008) suggested that the cereal would presumably benefit from the rhizosphere acidification mediated by the legume due to N2-fixation, as such acidification in alkaline/neutral soil may increase P availability through dissolution of P-minerals (Hinsinger 2001). The model developed by Devau et al. (2010, 2011b) and applied to durum wheat, showing that the root-induced increase in rhizosphere pH combined with Ca uptake could significantly increase P availability in non-calcareous soils somewhat challenges this hypothesis. It suggests that the cereal may also facilitate the acquisition of P by the intercropped legume, or that facilitation may occur both ways (Hinsinger et al. 2011). There is fewer evidence of facilitation occurring for other poorly mobile nutrients (Zhang et al. 2010). For instance, in bread wheat (Triticum aestivum L.) intercropped with chickpea (Cicer arietinum L.) Li et al. (2004) evidenced an improved acquisition of Ca, Mg, Mn and Zn when roots could intermingle, compared with a treatment where roots of the two species were separated by a physical barrier. In addition, Inal et al. (2007) and Zuo and Zhang (2008) have shown reduced chlorosis in peanut (Arachis hypogea L.) when intercropped with cereals in calcareous soils. These authors suggested that this was due to facilitation of both Fe and Zn acquisition in the legume (strategy I species) by the intercropped cereal (strategy II species), possibly due to increased availability of soil Fe and Zn as a consequence of phytosiderophores released by cereal roots.

Facilitation/competition in plant communities may drastically influence nutrient acquisition and efficiency, but very few plant nutrition models take such plant-plant belowground interactions into account (Huston and DeAngelis 1994; Loreau 1998; Raynaud et al. 2008; Tilman 1997). To the best of our knowledge, Raynaud et al. (2008) proposed the most achieved model in this respect. Their model tested the impact of citrate exudation on P bioavailability in the particular case when only one of the two intercropped species would be able to exude citrate. This work showed that citrate-exuding roots affected the P availability in their vicinity, to an extent which depended on citrate diffusion, and hence on soil water content. When diffusion was spatially restricted, which would be the case for citrate in most soils, this model showed that only those roots of the non-exuding species that were close enough to the roots of the exuding species could benefit from the improved availability of soil P in the rhizosphere (Raynaud et al. 2008). Given that many other P-solubilizing organic compounds occurring in the rhizosphere (carboxylates and phosphatases) are rather poorly mobile in the soil, P facilitation may therefore occur only if roots are closely intermingling which is in line with a number of pot and field experiments (Hinsinger et al. 2011; Li et al. 2007). The same spatial restriction would also occur for phytosiderophores and Fe (or Zn) facilitation when strategy I and II species are intercropped, challenging the evidence reported by Inal et al. (2007) and Zuo and Zhang (2008).

As reviewed by Hinsinger et al. (2011) plant-plant belowground facilitation processes are not only the consequence of plant functional diversity in terms of root-induced changes of rhizosphere biogeochemistry, as discussed so far. It may also occur through differences in microbial community structure or activity of the intercropped plant species (e.g. Fan et al. 2011; Wang et al. 2007), although the causal relationship with microbially-mediated changes of the fate of a nutrient has only been demonstrated for N so far (Fan et al. 2011). For P, an interesting work has been conducted on AMF though. Facelli et al. (2010) showed that the mixing of plant genotypes (whether or not able to form arbuscular mycorrhizae) strongly modifies the contribution of the arbuscular mycorrhizal pathway to P acquisition by tomato. In this study, the intercropping of a genotype which does not form symbiosis with AMF together with the wild-type genotype doubled the contribution of the arbuscular mycorrhizal pathway (70%), compared with that found with the wild type grown alone (35%). These data indicate therefore that plant and fungal competition could greatly influence which pathway, roots or arbuscular mycorrhizae, will be the main route for plant P uptake. The model outputs of Raynaud et al. (2008) demonstrate that plant-plant belowground interactions possibly implied in nutrient acquisition in plant communities strongly depend on plant, soil and nutrient properties. It only accounted for rhizosphere microorganisms via their impact on the decay rate of citrate. Therefore, a novel modelling approach of rhizosphere biogeochemistry, also accounting for the various roles of rhizosphere microorganisms, would thus be clearly needed to correctly assess facilitation/competition interactions, which can potentially affect plant nutrition in functionally diverse plant communities.

Conclusions—Roots are the new routes for an ecological intensification of agroecosystems ?

Our knowledge of the biological, biochemical and biogeochemical processes governing nutrient acquisition has considerably increased over the last decades (Hinsinger et al. 2009), and is currently much more advanced than for biophysical processes. How to make use of the accumulated knowledge on rhizosphere biophysics and biogeochemistry to face the issue of ecological intensification of agroecosystems, and especially that of improving N and P efficiencies and micronutrient fortification in plants is still a major challenge (Hinsinger et al. 2011; Zhang et al. 2010).

The perspectives for further intensification of agroecosystems based on a better use of genetic resources are limited, given that the yield potential cealing is close to be reached by now (Wissuwa et al. 2009). Plant breeding has essentially been conducted in non limiting environments, thereby leading to the selection of highly productive genotypes under high fertilizer input conditions, while leaving aside rustic genotypes which may be better adapted to low input conditions (Dawson et al. 2008). This has ultimately led to a considerable impoverishment of the genetic diversity in commercial varieties of most crop species (Khush 2001; Rengel and Marschner 2005). We thus need to fully revise the breeding schemes to account for new criteria such as nutrient use efficiency in low input agroecosystems (Ismail et al. 2007; Lynch 2007; Rengel and Marschner 2005; Tilman 1999; Wissuwa et al. 2009). As pointed out by Lynch (2007), the “roots of the second Green Revolution” rely on better accounting for root traits and soil-root-microbe interactions that occur in the rhizosphere (Wissuwa 2003, 2005; Wissuwa et al. 2009). However, even if including such new traits, we may still have it all wrong pursuing the quest of the champion genotype of each of our favorite crops. Nevertheless, as shown by the work of Wissuwa (2005), modelling occurs to be a rather unique tool to define ideotypes or root traits worth being used in future breeding strategies.

Progress is to be expected in terms of increased yield stability, hence phenotypic plasticity, and sustainability, via increased use efficiency of soil resources (Tilman et al. 2002). For this purpose, the development of an ecological engineering of agroecosystems is a promising alternative, which shall take its inspiration from the understanding of natural ecosystems. A major difference between intensive agroecosystems and natural ecosystems is biodiversity, especially so at the level of plant community. While most natural ecosystems are made of complex assemblages of plant species, agroecosystems are characterised by extremely simple plant communities, most often a single species and a single variety in a field. A better nutrient use efficiency shall be expected from more diverse systems, either pluri-specific such as intercropping or agroforestry systems, where niche complementarity and facilitation occur (Hinsinger et al. 2011; Jose et al. 2006; Li et al. 2007; Tilman et al. 2002). Designing the best performing pluri-specific agroecosystems may be rather tedious for experimental approaches, given the number of combinations to be tested. At this point of view, modelling nutrient efficiency of such plant communities might be a much more powerful approach.

For P, there are many potential options for increasing acquisition efficiency in crop species (Hinsinger 2001; Ismail et al. 2007; Lambers et al. 2006; Raghothama 1999; Raghothama and Karthikeyan 2005; Vance et al. 2003). Lambers et al. (2006) stressed that we should have a closer look at how wild species cope with low availability of P in poor soils to design new strategies. These could be based on root traits that relate to rhizosphere biophysics, such as root architecture, root hairs or root extensions by mycorrhizal hyphae (Gahoonia and Nielsen 2004a,b; Gahoonia et al. 2001; Ge et al. 2000; Hodge 2009; Lynch 2007; Lynch and Brown 2001; Rubio et al. 2003 ; Wissuwa 2003, 2005). Alternative strategies could rely on root traits that relate to rhizosphere biogeochemistry, via the physiology of plant roots, namely the exudation of protons, carboxylates or phosphatases (Hinsinger 2001; Neumann and Römheld 1999; Raghothama and Karthikeyan 2005; Richardson et al. 2000, 2001; Tang et al. 2004; Vance et al. 2003; Wissuwa 2003, 2005; Yan et al. 2004). Other potential strategies could exploit traits related to the physiology of associated microorganisms, either symbiotic such as mycorrhizal fungi (Hetrick et al. 1993, 1996; Zhu et al. 2001), or free-living rhizosphere microorganisms such as P-solubilizing bacteria and fungi (Marschner et al. 2006). There are many ‘tricks’ and possible routes, but contrary to much of the past research, following more than a single one maybe the best way not to get lost!

In that respect developing more sophisticated models accounting for rhizosphere complexity is urgently needed as they represent unique tools to understand the complex interplay between numerous biological, biophysical and bio(geo)chemical processes mediated by plant, soil microbial and faunal communities in agroecosystems. Plants are ecosystem engineers sensu Jones et al. (1994) as they deeply alter the availability of nutrients for themselves and other living biota (Lambers et al. 2009), and rhizosphere is an ecologically complex system of which modelling remains a challenge for our scientific community. Rhizosphere is indeed a really complex portion of the agroecosystem, being composed of many objects that interact, and ultimately feedback onto plant growth and nutrition. These interactions change according to the abiotic environment and biological context, which evolve with time, physiological status of the plant and the structure of microbial communities. Interactions with soil fauna and other plants shall be taken into account as well, although intensive agroecosystems are often made of rather simplified communities, made of e.g. a single plant species/genotype being grown over a whole field plot). The aggregation of our present knowledge in a comprehensive, mechanistic model could be a temptation, but elaborating such a sophisticated model might be misleading, as it would require much too many parameters to be determined to represent the dynamics of such complex systems. Alternative approaches could be explored, such as multi-agent modelling, which may consist in considering each root segment as an individual, which grows, takes up resources and excretes substances according to the status of the whole plant system as well to local conditions in space and time for plant, soil and microbial communities. This would make it possible to integrate local heterogeneities (in space and time) of plant and soil structures and functions, including interactions with soil fauna and microbial communities. Models, and the diversity of modelling approaches, are unique tools for exploring such complexity. Simulations of large ranges of scenarios for in silico experiments are especially valuable in that respect. These approaches shall thus help us to make better use of plant roots and rhizosphere dynamics to design the best routes towards an ecological intensification of agroecosystems, in order to improve nutrient efficiency in low input agriculture.


The senior author deeply thanks Prof Alan D. Robson for having further convinced him to pursue his research in the field of plant nutrition, during his postdoctoral stay at University of Western Australia, Soil Science and Plant Nutrition in 1993–1994. This review was written on the basis of the ‘Plant and Soil Lecture’ presented by the senior author at the International Plant Nutrition Colloquium (IPNC) held in Sacramento, USA in August 2009. The financial support provided by IPNC organizers (Dr Patrick Brown) to present this lecture is gratefully acknowledged, as well as the financial support provided by ANR (Agence Nationale de la Recherche) SYSTERRA programme ANR-08-STRA-11 (PerfCom) to attend the IPNC.

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