Models often assume homogeneous distribution of nutrients, whereas soils are often biologically, chemically and physically heterogeneous over a range of length scales. Jackson & Caldwell (1993) found that all the variation in nutrient availability in a 120-m2 plot occurred within the rooting zone of a single plant, implying a spatial autocorrelation of the order of 1 m. This heterogeneity is often fractal over several length scales, implying that absolute heterogeneity decreases as the intervening distance decreases.
Heterogeneity at the root system scale
In general, nutrient concentrations vary markedly with depth. At the rhizosphere level, this means that roots experience different initial concentrations depending on the depth at which they form. This is easily dealt with by the look-up table approach of Darrah & Staunton (2000).
However, plants show strong plastic responses to exogenous conditions (Hodge 2004), and the relation between root density and depth is likely to be effected by the nutrient gradient down the profile (Alpert & Simms, 2002). To a large extent, this response to vertical heterogeneity is already included in existing models of root architecture that derive their rules by simulating the appearance of root systems that have presumably developed in soils with vertical gradients (Pagès et al., 2004). But there is a danger of circularity if models that have been constructed to mimic the appearance of a root system that is already modified by an external, unknown gradient, are then used to predict the response to nutrient gradients.
The roots of agricultural crops can also respond to local nutrient patches (Drew, 1975), whereas wild plants show a range of responses that are partially correlated with their intrinsic growth rate (Robinson & van Vuurren, 1998). These local responses are not generally built into the design of architectural models. The morphological responses of roots to nutrient gradients and patches may actually be maladaptive in agricultural monoculture (Maina et al., 2002), and competition between species might be required to achieve an adaptive advantage of plasticity (Robinson et al., 1999). We know that different species show very different morphological and physiological responses to nutrient heterogeneity (Hodge 2004), although the significance for nutrient capture is often uncertain.
Zhang & Forde (1998) identified components of the underlying sensory mechanism. The signal transduction pathway remains uncertain, however, with some evidence for the involvement of auxin in the responses to both N and P (Forde, 2002; Al-Ghazi et al., 2003), whereas Linkohr et al. (2002) found that auxin-deficient Arabidopsis mutants behave like wild-type plants. Encouragingly, Arabidopsis does show a proliferation response (Casimiro et al., 2003), and the sequencing of the genomes of rice and maize should allow rapid progress on this topic (Hochholdinger et al., 2004). The signalling pathways controlling root development in Arabidopsis are complex (Casson & Lindsey, 2003). However, both short-range (e.g. local NO3– availability) and long-range (e.g. N status of the plant) stimuli are important in modifying root architecture (Forde, 2002; Lopez-Bucio et al., 2003). The development and regulation of root system architecture is further complicated by the involvement of microorganisms (Persello-Cartieaux et al., 2003) and soil animals (Bonkowski, 2004), which can markedly change root morphology indirectly or directly via phytohormones.
Models of root architecture have not yet led to a full mechanistic understanding of how heterogeneity in nutrient distribution translates into heterogeneity of root distribution. However, they can help to quantify the theoretical costs and benefits of different degrees of plasticity (DeWitt et al., 1998). It is encouraging in this regard that predictions from some theoretical models have subsequently been borne out by experimental evidence. For example, Baldwin et al. (1975) predicted that lateral root development would be important for uptake of P but not of NO3–, and Fitter et al. (2002) used the axr4 mutant of Arabidopsis thaliana, which causes reduced number of lateral roots, to confirm this. Similarly, Gahoonia & Nielsen (2003) isolated a barley mutant that lacked root hairs and found that the wild type acquired twice as much P in root mat experiments, confirming the theoretical predictions about the importance of root hairs.
Jackson & Caldwell (1996) used the minimal model to investigate the importance of heterogeneous distribution at several spatial scales. At the plant scale, three- and fivefold increases in the initial nutrient concentration increased predicted uptake by 3.2–4.3-fold and 4.9–6.6-fold, respectively, for P. The range resulted from the simulation time used (2 or 10 days) and whether morphological and physiological plasticity was allowed for. The response was to be expected given the known sensitivity of the minimal model to the initial nutrient concentration (Barber, 1995). More revealing was their model of the response to spatial heterogeneity, in which they simulated areal heterogeneity by dividing the soil into 25 volumes and running independent minimal models in each. They modelled plasticity by changing the Michaelis–Menten parameters (defining the physiological response) and the root growth rate (defining the morphological response) in two steps associated with medium and high concentrations of nutrient relative to the control. For P, allowing plasticity increased the uptake by 28% in 10 days, with approximately equal contributions from morphological and physiological plasticity. Note that plasticity in this case imposed an additional cost in new roots (and presumably increased numbers of transporters) without any compensatory decrease elsewhere in the system. Plastic responses to NO3– were larger but were almost entirely due to physiological up-regulation. Finally, Jackson and Caldwell investigated an extreme case of heterogeneity by imposing a hypothetical patch structure on the 25-cell array: the same amount of nutrient was either distributed uniformly or heterogeneously. Plasticity was advantageous in these circumstances, with less P being extracted in all heterogeneous simulations compared with homologous conditions without plasticity. With plasticity included, results favoured growth in homogeneous or heterogeneous conditions depending on the nutrient.
More recently, the effect of root architecture on nutrient acquisition has been investigated with architectural models. Ge et al. (2000) used SimRoot to investigate the effect of competition by altering the branching angle of basal roots (roots emitted from the stem), which was equivalent to changing the strength of response of the roots to the gravitational field. The effect was to generate root systems with different depth-density distributions. Examination of the figures reveals that competition was significant only for simulated root systems with very strong gravitational responses so that basal roots were growing parallel to one another in a very narrow cylinder or for solutes that diffused rapidly. In a second study, Ge et al. modified SimRoot to allow multiple root systems sharing the same soil domain to be simulated (Rubio et al., 2001) and concluded that competition between roots from different plants was always more intense than competition between roots of the same plant with the same architecture and that shallow and deep rooting architectures in neighbouring plants led to better resource partitioning. However, the limit to the accuracy of the estimation of inter-root competition has to be borne in mind.
Although more complicated, RootMap is conceptually reminiscent of the multiple-minimal model approach of Jackson & Caldwell (1996). Dunbabin et al. (2003) used RootMap to simulate different architectures by changing the structural laws underlying the construction of the root system. Each simulation was assigned the same amount of carbon so that the volume of each root system was comparable at each time, allowing the efficiency of nutrient capture to be assessed in terms of construction costs. The simulations were for NO3– uptake on sandy soils with the potential for large leaching losses if roots failed to intercept the NO3–. The coarse herringbone form that had been considered optimal for uptake of NO3– as a result of its long diffusional distance (Robinson et al., 1999) wasn't in this case, and an intermediate, more dichotomous form was favoured as this allowed the roots to intercept NO3– more effectively. The model included plasticity by linking the signal representing plant demand to a signal representing the capacity of a root segment to supply NO3– via a positive feedback: thus when demand for NO3– was large, more of the root growth was allocated to segments in local patches of NO3– (Dunbabin et al., 2004).
Heterogeneity at the rhizosphere scale: resolution and downscaling issues
The responses of some plants to nutrient heterogeneity, toxicity or deficiency are inducible, involving, for example, organic acid production (Jones et al., 2003), exudate production (Dakora & Phillips, 2002) or pH change (Hinsinger et al., 2003). This means that many different rhizospheres could develop, depending on the local context, with root responses perhaps ranging from minimal behaviour in nutrient-rich patches through enhanced exudation at intermediate patches and major pH modifications in poor patches. Mycorrhizal status is also correlated with nutrient deficiency. Other responses might give different root behaviour over time; for example, nutrient deficiency experienced as the plant matures might translate into extra exudation flow into the rhizospheres of young tips.
An extreme response to this downscaling feedback would be to model the rhizosphere at the root scale and to simulate the soil around all segments of root simultaneously. Conceptually, this would be straightforward: sophisticated finite-element packages already exist that could simulate the simultaneous rhizospheres around the static root system of a maize plant. However, it is probably not feasible computationally. A more promising solution would be to define a finite range of behaviours and use both spatial and temporal averaging to allow for simultaneous up- and downscaling.