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The formation of root cortical aerenchyma (RCA) reduces root respiration and nutrient content by converting living tissue to air volume. It was hypothesized that RCA increases soil resource acquisition by reducing the metabolic and phosphorus cost of soil exploration.
To test the quantitative logic of the hypothesis, SimRoot, a functional–structural plant model with emphasis on root architecture and nutrient acquisition, was employed. Sensitivity analyses for the effects of RCA on the initial 40 d of growth of maize (Zea mays) and common bean (Phaseolus vulgaris) were conducted in soils with varying degrees of phosphorus availability. With reference to future climates, the benefit of having RCA in high CO2 environments was simulated.
The model shows that RCA may increase the growth of plants faced with suboptimal phosphorus availability up to 70 % for maize and 14 % for bean after 40 d of growth. Maximum increases were obtained at low phosphorus availability (3 µm). Remobilization of phosphorus from dying cells had a larger effect on plant growth than reduced root respiration. The benefit of both these functions was additive and increased over time. Larger benefits may be expected for mature plants. Sensitivity analysis for light-use efficiency showed that the benefit of having RCA is relatively stable, suggesting that elevated CO2 in future climates will not significantly effect the benefits of having RCA.
The results support the hypothesis that RCA is an adaptive trait for phosphorus acquisition by remobilizing phosphorus from the root cortex and reducing the metabolic costs of soil exploration. The benefit of having RCA in low-phosphorus soils is larger for maize than for bean, as maize is more sensitive to low phosphorus availability while it has a more ‘expensive’ root system. Genetic variation in RCA may be useful for breeding phosphorus-efficient crop cultivars, which is important for improving global food security.
Lysogenic root cortical aerenchyma (RCA) is cortical root tissue with large intercellular spaces formed by programmed cell death (Esau, 1977). RCA is usually considered to be an adaptation to hypoxia (Jackson and Armstrong, 1999). However, RCA can also be induced by suboptimal availability of nitrogen, phosphorus, sulfur and water (Konings and Verschuren, 1980; Drew et al., 1989; Bouranis et al., 2003, 2006; Fan et al., 2003; Zhu et al., 2010). We have proposed that RCA may be a positive adaptation to low nutrient availability by reducing the metabolic costs of soil exploration (Lynch and Brown, 1998, 2008). The purpose of this report is to quantitatively evaluate the potential benefit of having RCA for nutrient acquisition in a simulation model that considers root architecture, carbon allocation and nutrient acquisition.
Enhanced oxygen transport and reduced respiration are thought to be the two main functions of RCA formation under hypoxia (Jackson and Armstrong, 1999). Of these two, enhanced oxygen transport is the most researched function of RCA formation. Oxygen availability, however, does not limit root respiration in phosphorus-deficient plants or in any other of the mentioned RCA-inducing stresses and is therefore an unlikely function of RCA formation as an adaptive response to these stresses. The second function, a reduction in respiration, could be beneficial under conditions of suboptimal phosphorus availability (Lynch and Brown, 2008). Rhizo-economic theory (Lynch, 2006) predicts that phosphorus-deficient plants would be less deficient if they had more carbon available for investment in nutrient acquisition strategies. Phosphorus-deficient bean plants (Phaseolus vulgaris) devote up to 40 % of their daily photosynthesis on root respiration, with 57–89 % of the root respiration being devoted to maintenance of existing tissue, as opposed to respiration devoted to ion uptake and growth of new tissue (Nielsen et al., 1994, 1998). Fan et al. (2003) showed that maize and common bean roots with RCA have reduced root respiration rates. However, the significance of diverting carbon from root respiration to root growth for total plant growth is difficult to quantify because of interactions of increased nutrient acquisition with shoot growth and thereby carbon assimilation.
Fan et al. (2003) found that RCA formation reduces the phosphorus content of root tissue on a volume basis, since air spaces do not contain phosphorus. Although the amount of phosphorus released by RCA is small, this could have a significant effect over time as a small improvement in phosphorus status of the plant supports greater growth rates and hence greater soil exploration and phosphorus acquisition (Wissuwa, 2003).
Two possible beneficial functions of RCA formation under phosphorus deficiency are presented here: (1) reduced root respiration and (2) phosphorus remobilization. It is difficult to estimate the relative benefit of these effects for the whole plant because indirect benefits, arising from accelerated growth, may be more important than direct effects (Wissuwa, 2003). Furthermore, empirical assessment of the benefit of having RCA by physiological comparison of genotypes contrasting for RCA formation may be confounded by other root traits known to be beneficial for phosphorus uptake. Some of the confounding traits may be mechanistically correlated with RCA via induction by ethylene. Ethylene induces both RCA formation and several other responses to phosphorus deficiency, such as root hair formation (Zhang et al., 2003). Artificial induction and inhibition of RCA formation with ethylene and ethylene receptor blockers may be confounded for the same reason. Therefore SimRoot, a functional–structural plant model, was used to evaluate the potential importance of RCA as an adaptation to low phosphorus availability in a quantitative manner. SimRoot is a mechanistic model which allowed the quantitative relevance of the two proposed functions of RCA formation to be evaluated in phosphorus-deficient plants.
The model for maize (Zea mays) and common bean (Phaseolus vulgaris) was parameterized. Maize and common bean are both important agricultural crops. Maize is the number one cereal crop in the world. Maize and common bean form the staple food diet of many small-scale farmers, for whom phosphorus fertilizers are often not an option (Lynch, 2007). Botanically, maize and bean are in many respects contrasting species. Maize is a C4 Poaceae plant with a complex root system that encompasses many different root types with different diameters. Development of the root system is characterized by the periodic formation of new major axes. Maize has a high growth potential, and thereby a greater demand for phosphorus. In contrast, common bean is a C3 dicotyledon with a simpler root system. All the root classes are formed within the first 10 d after germination. Development of the root system centres round the extension of the major axes and the formation of lateral roots. Secondary growth in this species allows for thickening of the major axes. Common bean is a smaller plant with less demand for phosphorus. Despite the many differences, both maize and bean form RCA through programmed cell death unlike, for example, rice which forms RCA through cell separation (Evans, 2004).
This assessment of the potential benefits of RCA formation includes the effect of elevated CO2, since it is expected that atmospheric CO2 concentrations will continue to rise (Forster et al., 2007). A high CO2 environment may increase photosynthetic rates, especially in C3 plants like common bean, as photorespiration is reduced under elevated CO2 (Bowes, 1991). In C4 plants, like maize, a CO2 concentration mechanism already reduces the effect of photorespiration. Greater carbon assimilation may decrease the relative benefit of carbon-saving strategies like reduced respiration, while phosphorus remobilization from the cortex may become more significant. We suggest that the results could be used to support decisions made in breeding programmes for phosphorus-efficient maize and bean and that the results may be relevant in the future as the expected effects of climate changes on the benefits of having RCA were considered.
SimRoot, originally a root architectural model (Nielsen et al., 1994, 1997; Lynch et al., 1997; Ge et al., 2000; Ma et al., 2001; Rubio et al., 2001; Walk et al., 2004, 2006), was augmented into a whole plant model with emphasis on resource acquisition and utilization. For this study two resources were considered: phosphorus and carbon.
Simulation of root architecture by SimRoot has been described by Lynch et al. (1997). In SimRoot, the root system is represented by connected root nodes, spaced approx. 0·5–1 cm apart. Important root properties, e.g. phosphorus uptake, are calculated for each root node and integrated over the length of the root system. The shoot was not geometrically simulated, but rather it was represented by two pools – leaves and stems – and properties for these organs, such as photosynthesis or phosphorus demand, calculated not for individual leaves but for the leaf area as a whole.
A single plant was simulated, which, however, was not isolated but represented an individual in a monoculture field. Light interception was corrected for shading using a shading function developed for monoculture crops (see below) and root density and competition for phosphorus were kept realistic by virtually mirroring the root system at mid-distance between the simulated and the imaginary neighbouring plants.
Three modules – the carbon module, the phosphorus module and the RCA module – form the core of the simulations. The carbon module simulates carbon assimilation, utilization and carbon-driven growth. The phosphorus module simulates phosphorus uptake and demand and, when demand exceeds uptake, stress-induced effects on different physiological processes. The RCA module simulates the formation of lysigenous aerenchyma in the root cortex. Each module will be described in more detail below.
The carbon module defines carbon sources and sinks and a set of allocation rules. Seed reserves and photosynthetic CO2 assimilation are the two carbon sources. Carbon availability from seed reserves is based on (a) the initial seed dry weight and (b) an ‘on demand’ release function. A constant conversion factor, 0·42 (Latshaw and Miller, 1924), between dry weight and carbon is used in the whole model as carbon to dry weight ratios are relatively stable (Loomis and Lafitte, 1987). Photosynthesis is simulated as in the LINTUL (Light INTerception and UtiLization simulator) model (Spitters and Schapendonk 1990; Bouman et al., 1996; Farré et al., 2000; van Ittersum et al., 2003; http://www.cwe.wur.nl/UK/Downloads/LINTUL). Growth of leaf area is based on carbon allocation to leaves and the specific leaf area. Leaf area is converted to leaf area index (LAI in cm2 cm−2) using a user-specified area per plant which is the inverse of the planting density. The intercepted light (μmol cm−2 d−1) is calculated using the following formula in which K is a crop-specific extinction coefficient (unit-less) and PAR is the photosynthetically active radiation (μmol cm−2 d−1) (Bonhomme et al., 1982; Varlet-Grancher et al., 1982):
Intercepted light is converted to photosynthesis using a light-use efficiency factor (g μmol−1). The PAR was kept constant in the presented simulations at 4000 µmol cm−2 d−1 which corresponds to the PAR on an average summer day in Pennsylvania.
Sink strength in SimRoot is based on the carbon needed for potential growth, respiration and exudates. Potential growth is based on measured growth rates for all root classes, and measured relative growth rates of leaves and stems (Table 1 and Supplementary data, available online). Thicker roots have higher longitudinal potential growth rates and therefore larger sink strength (Pagès, 2000). Carbon needed for secondary growth is calculated by the volumetric increase needed for potential secondary growth. Potential secondary growth depends on the age, distance along the root and the root class of each root segment. Respiration is calculated as a function of organ biomass and age. Separate respiration coefficients were used for each organ (Supplementary data). No explicit distinction was made between growth respiration, respiration caused by exudates and maintenance respiration. Nielsen et al. (1998) show that maintenance respiration forms the largest portion of respiratory costs, while respiration associated with exudates forms < 3·5 % of the daily carbon budgets of common bean. Maize produces even fewer exudates (Sauer et al., 2006). Growth respiration is implied in the respiration function, as the root apical meristems have a much higher respiration coefficient in the model (Supplementary data). The higher respiration of meristems is not affected by RCA, as RCA only forms in older root segments. The third sink, carbon cost of exudates, is calculated based on root class and root age using empirical data (Supplementary data). The carbon costs of nitrogen fixation were not included, even though common bean is capable of symbiotic nitrogen fixation. The simulations, however, imply a high nitrogen environment (nitrogen deficiency was not considered) in which nitrogen fixation is reduced. In addition, common bean is a poor nitrogen fixer, even in soils with reduced nitrogen availability, fixing at the most 50 kg N ha−1 (Bliss, 1993).
Carbon partitioning rules were based on a hierarchical binary partitioning method where sink strength, priority and limits determine the partitioning between two sinks. First carbon is partitioned between growth and non-growth sinks. The non-growth sinks are exudates and respiration, which are both considered obligate costs. Secondly, carbon is partitioned between shoot and root, with the shoot receiving priority over the root system. However, limits are set on the relative allocation to the shoot. Carbon allocated to the shoot is partitioned between stems and leaves proportional to sink strength. Carbon allocated to the root is partitioned between primary and secondary growth. Secondary growth is given as much carbon as is needed to maintain the allometry between secondary growth and leaf area (de la Riva, 2010). Thus, the present model simulated root etiolation (Lynch and Brown, 2008) which is a reduction in secondary growth of beans grown in soils with low phosphorus availability. The remaining carbon for root growth is allocated to primary growth of the root system. Carbon for primary growth is divided over the major axes and fine roots. The major axes, within limits, are given priority over fine roots (Mollier and Pellerin, 1999). For maize the number of nodal and brace roots is scaled allometrically according to the leaf area at emergence of the roots (Mollier and Pellerin, 1999). Within each group of root classes, carbon is allocated to the root tips proportional to their relative sink strength. The model includes temporal carbon storage (Dingkuhn et al., 2005), which increases when the carbon available for growth exceeds the carbon that is required for potential growth. This storage will act as a carbon source when the potential carbon requirements cannot be met, and as long as the storage contains carbon.
The carbon module includes both positive and negative feedbacks over time, as root and shoot growth lead to changes in sink strength and resource capture. Therefore a predictor-corrected integration method, Runge-Kutta 4, was used for computational efficiency and numerical accuracy. A carbon balance check was included to verify the consistency of the model by comparing the cumulative carbon expenditure with the cumulative carbon assimilation. For the carbon balance organ dry weights were recalculated from their geometric dimensions.
Nutrient uptake was simulated by each root node using the Barber–Cushman model (Barber and Cushman, 1981) including root hairs as described by Itoh and Barber (1983). The kinetic parameters (Imax = 0·0555 µmol.cm−2 d−1, Km = 5·45 µm and Cmin = 0·2 µm) were kept constant as well as the soil transport parameters (De = 1·99e-4 cm d−1 and b = 400). Phosphorus availability with depth was not varied to exclude allometric effects on the depth of the root system. Thus uptake was a function of root class, root development, root hair development and intra-root competition (see below) only. Effects of exudates and mycorrhiza on nutrient uptake were not included in this study, as quantitative and mechanistic understanding of both processes is still lacking. Inter-root competition for nutrients cannot be dealt with using a three-dimensional explicit method as the Barber–Cushman model is only a one-dimensional, radial model. Therefore the average mid-distance between roots in the vicinity of each root segment was used as the outer boundary for the Barber–Cushman model, across which the nutrient flux is assumed zero. The mid-distance between root segments is adjusted each time a new root grows into the vicinity of other roots. The initial nutrient concentration to which new roots are exposed is corrected for nutrient depletion by other roots. The uptake rate of all root nodes is integrated over the length of the root system and over time to calculate the total nutrient uptake by the plant. The plant is given an initial amount of nutrients from the seed reserves.
Optimal and minimal nutrient to dry weight ratios are used to compute target nutrient content in the different plant parts. A stress factor is then calculated based on the actual uptake in comparison to minimum and optimal nutrient content of the whole plant. This stress factor is used to adjust potential leaf area expansion rate and photosynthetic efficiency of the leaves. Phosphorus-deficient plants have smaller leaves and slower leaf appearance (Lynch et al., 1991; Rodríguez et al 1998a, b; Fletcher et al., 2008). The stress factor is used to reduce the potential leaf area expansion rate, thus reducing the sink strength of the shoot and increasing relative allocation of carbon to the root system. Although phosphorus is needed for photosynthesis (Heldt et al., 1978), the quantitative effect of phosphorus deficiency on photosynthesis is less clear in the literature, in part because these effects may depend strongly on the experimental conditions, such as buffered versus non-buffered phosphorus availability (Elliott et al., 1983), duration of the experiment, plant species involved and the severity of the stress (Mollier and Pellerin, 1999). It was assumed for the present simulations that the photosynthetic efficiency of the leaf area is reduced up to 50 % for both maize (Jacob and Lawlor, 1991) and bean (Lynch et al., 1991). Therefore a sensitivity analysis for this reduction in light-use efficiency was included as these numbers vary in the literature. In the model, respiration rates are not affected by the plant's internal phosphorus status, since both increases (Lynch and Ho, 2005) and decreases (Gniazdowska et al., 1998; Fan et al., 2003; Zhu et al., 2005) in respiration under phosphorus deficiency have been reported in the literature. There are no feedbacks of nutrient status of the plant on uptake kinetics in the model.
RCA formation is computed for each root node, based on developmental age as measured by Lenochová et al. (2009) where RCA formation started when the root tissue was 2 d old and increased linearly. Thus RCA does not form in the cell expansion zone behind the root tip, but is formed soon after cell expansion is completed. RCA formation presumably stops after reaching a genetically controlled maximum. Fan et al. (2003) measured a maximum of 39·3 and 26·8 % RCA formation of root cross-sectional area for maize and bean respectively, grown in a low (1 µm)-phosphorus solution. In the simulation, these maxima were reached when a root segment was 20 d old. It was assumed that all root classes are equal in the formation of RCA. This distribution of RCA over the root system is clearly a simplification from reality; however, strong quantitative data on other factors that influence RCA formation are currently lacking in the literature. Plasticity responses of RCA formation to phosphorus deficiency were not simulated. This means that the simulated maxima for RCA formation, which were based on measurements of phosphorus-deficient plants, may be too high for non-deficient plants. However, instead of simulating plasticity responses, which would make comparison of treatments difficult, a sensitivity analysis for RCA formation is presented. Furthermore, despite these high maxima, the respiratory benefit of having RCA in non-stressed plants, as is shown by the results, is small.
RCA formation is used to simulate a reduction in root respiration and to reduce the optimal and minimal phosphorus content of the root. Empirical data were used for the reduction in respiration and phosphorus content of the root segments as reported by Fan et al. (2003). They reported a linear decline in both respiration and phosphorus content of a root segment with increasing RCA formation: 30 % RCA formation resulted in 70 % reduction in root respiration and 30 % reduction in root phosphorus content.
All simulations were run for 40 d of growth after germination. These were full factorial designs, which included two plant species, maize (Zea mays L.) and common bean (Phaseolus vulgaris L.), four RCA configurations and 26 levels of initial phosphorus availability varying from 1 to 18 µm in the soil nutrient solution. The four RCA configurations were: no RCA formation; maximum RCA formation, where maximum was 39·3 % and 26·8 % for maize and bean, respectively (see RCA module); and two treatments where RCA either only effected root respiration or only resulted in phosphorus remobilization. In total, 2 × 4 × 26 runs were carried out.
The with and without RCA simulations represent extremes among a wide variation of RCA formation that has been observed. Therefore, a sensitivity analysis was included in which varying amounts from 0 to the mentioned maxima were simulated to understand how much varying degrees of RCA formation may benefit phosphorus-deficient plants. This sensitivity analysis was conducted for fewer phosphorus-availability levels, which, however, still represented the full range of phosphorus availability.
In an effort to understand possible effects of elevated CO2 on the benefit of having RCA for phosphorus-deficient plants, a sensitivity analysis for the light-use efficiency factor was conducted, varying it from 3·5–5·0 × 10−7 g μmol−1. The light-use efficiency for ambient CO2 conditions, used for all other simulations, was 3·8 × 10−7 g μmol−1.
Parameterization of the model was based on empirical data of several experiments and the literature (Table 1). No parameters were obtained by calibration. Root classes were assumed to be identical when root class-specific measurements were lacking.
To verify the model, simulated data for root length, root dry weight and shoot dry weight were compared with data from 30 different publications in the literature. These publications were independent from the papers used to parameterize the model. The data obtained from these papers came from a variety of experimental conditions, mostly pot studies, and different genotypes. As a result, the data represent a large variation. To minimize the variation, measurements were used on control plants only. Collecting a similar dataset for low phosphorus proved difficult, as the intensity of phosphorus stress is often not well controlled or specified in the literature.
The model results were verified against an independent data set from the literature (Fig. 1). Model results agree well with the literature data, although the root dry weight of both bean and maize is relatively high in the model results. The simulated bean plants were smaller than the simulated maize plants (Figs 2 and and3,3, compare y-axes), but had, under all conditions, relative to their shoot biomass, longer root length with more fine roots (data not shown). In maize, root development centred around the growth of new major root axes, especially nodal and crown roots, while, in bean, root development centred around secondary growth and the extension of the initial axes and lateral roots. Both plants allocated more carbon to the shoot than the root, although this difference became small in phosphorus-deficient plants (Fig. 4). The slower-growing bean plants spent relatively more energy on respiration than maize. Respiration became an increasing cost over time as relative growth rates decreased and total plant biomass increased. Phosphorus deficiency increased the root : shoot ratio and reduced the plant growth rate. Consequently, phosphorus-deficient plants had relatively greater respiratory costs (Fig. 4).
Plants responded to phosphorus deficiency with a typical sigmoid growth curve (Fig. 3). Relative growth reduction in response to low phosphorus was less for bean than for maize, suggesting that bean is better at coping with phosphorus deficiency than maize (Fig. 3 and and4).4). Plants were not deficient in high phosphorus soils, but in soils with reduced phosphorus availability deficiency occurred after 12–13 d (Fig. 5). At later stages, an improvement in the phosphorus status of the bean plants occurred, as altered root/shoot carbon allocation resulted in additional root growth and consequently phosphorus acquisition while carbon fixation was reduced (Fig. 5). Maize plants only recovered from phosphorus deficiency in soils with medium phosphorus availability (6 µm phosphorus).
Plants with RCA were less stressed (Fig. 5) and grew faster under suboptimal phosphorus availability (Fig. 3). This benefit of having RCA increased with time (Fig. 6). After 40 d, phosphorus-deficient plants with RCA were up to 14 % (bean) and up to 70 % (maize) larger than plants without RCA (Fig. 7). RCA had a small positive effect on the growth of non-deficient plants (18 µm phosphorus treatment), caused by a reduction in root respiration. The two proposed functions of RCA benefited plant growth to different degrees (Fig. 7). The most important function of RCA was remobilization of phosphorus from cortical tissue, which increased growth of phosphorus-deficient maize plants (P availability <12 µm in soil solution) up to 35 % and for bean plants up to 12 %. Reduced respiration due to RCA formation had smaller effects on plant growth (Fig. 7). This function of RCA increased maize root growth up to 60 % and, as a result of increased phosphorus uptake, maize shoot growth up to 30 % (data not shown). Reduced respiration increased the growth of phosphorus-deficient bean by <4 %. The root system of phosphorus-deficient plants with RCA had lower relative respiration rates but not lower total respiration than root systems of phosphorus-deficient plants without RCA, as phosphorus-deficient plants with RCA had larger root systems (Fig. 4). Presumably, the remobilization and respiration functions of RCA occur simultaneously, and the model suggests that the benefits of the two functions are additive, and maybe synergistic in maize grown in soils with low phosphorus availability. Sensitivity analysis showed a linear correlation of RCA formation and plant growth (Fig. 8).
An increase in light-use efficiency resulted in an increase in total biomass production of plants grown at 4 µm phosphorus (Fig. 9), but it had little effect on plants grown at 18 µm phosphorus, as growth of high-phosphorus plants is mostly sink limited (data not shown). At low phosphorus availability (4 µm phosphorus), the benefits of having RCA decreased slightly with increasing light-use efficiency for bean, but initially increased for maize (Fig. 9).
SimRoot, a functional–structural model, was used to mechanistically simulate the benefit of having RCA in maize and bean plants under suboptimal phosphorus availability. In the simulations, RCA always had a positive effect on the growth of phosphorus-deficient plants, increasing biomass production up to 14 % for bean and up to 70 % for maize (Fig. 7). The results support the hypothesis that RCA is an adaptive trait in soils with suboptimal phosphorus availability, and possibly with other edaphic stresses. Quantitative support has been provided for the hypothesis that RCA could benefit plant growth through reduced respiration and remobilization of phosphorus.
The simulated benefit of having RCA was less than the benefit of having RCA in maize grown under drought, as was measured in a study with genotypes contrasting for RCA formation (Zhu et al., 2010). Only 40 d of plant growth, during which the benefit of having RCA increased over time, was simulated (Fig. 6). We anticipate larger benefits of RCA formation for mature plants. Extensive extrapolation of the results, however, is not realistic since many simulations show a partial or full recovery from stress as increased root growth and decreased shoot growth restore the phosphorus to carbon homoeostasis in the plant (Fig. 5). This was especially true for plants grown in soils with moderately low phosphorus availability. A similar recovery was often observed in field experiments. The importance of delayed phenology for coping with phosphorus deficiency has been emphasized by Nord and Lynch (2008, 2009).
The model predicts a decline in the benefit of having RCA at very low phosphorus availability. Phosphorus uptake rates by the roots decline at low phosphorus availability, while the investment costs of constructing and maintaining root tissue, in terms of phosphorus and carbon, do not. Thus, at very low phosphorus availability, root growth has an unfavourable cost : benefit ratio. In the model, the benefit of having RCA strongly depends on the cost : benefit ratio of the roots. In a theoretical environment devoid of phosphorus, the cost : benefit ratio goes to infinity and there is no benefit of having RCA, or any other root trait to enhance phosphorus acquisition. In reality, plants have strategies in addition to root growth for increasing nutrient uptake, e.g. root hair formation, production of exudates and mycorrhizal colonization. Some of these strategies may have better cost : benefit ratios in low-phosphorus soils. For example, plants growing in extremely low phosphorus environments often rely on exudates in small clusters of roots (Shane and Lambers, 2005). Root hairs have low construction cost but increase phosphorus uptake significantly, and thereby influence the cost benefit ratio of the root system favourably (Bates and Lynch, 2000, 2001). Fine roots have a better cost : benefit ratio as well (Zhu and Lynch, 2004). Carbon-limited root systems, however, have shorter laterals and less opportunity to grow roots of higher branching order because of the reduced number and length of lower branching orders (Mollier and Pellerin, 1999) and thereby have a higher cost : benefit ratio. Root growth requires investment of both carbon and phosphorus. The time for a given root segment to take up the phosphorus needed for its own construction can be considered the pay-off time. The pay-off time is short in high-phosphorus soils, but longer in low-phosphorus soils. The respiratory benefit of having RCA is partly lower than expected because, for the duration of the pay-off time, the extra carbon for root growth causes the phosphorus status of the plant to deteriorate, thus reducing shoot growth temporarily. Reduced root respiration has a negative effect on shoot growth of plants grown at very low phosphorus availability (data not shown).
RCA formation varies among and within species (Fan et al., 2003; Zhu et al., 2010). Maize forms nearly twice as much RCA as bean (Fan et al 2003), which partly explains the four times larger growth benefit of having RCA in maize plants. However, maize plants, with the same amount of RCA formation as bean plants, still benefit nearly twice as much from RCA as bean plants do (Fig. 8, compare maize at 50 % with bean at 100 %). Bean plants have a finer root system (Halsted and Lynch, 1996) with more root hairs and are thereby less sensitive to phosphorus availability in the soil (Figs 3 and and4).4). These results agree with data from both greenhouse (A. M. Fita-Fernandez and J. A. Postma, unpubl. res.) and field experiments (Zhang and J. A. Postma, unpubl. res.). At a phosphorus concentration of 3 µm, the shoot growth of maize is reduced to 16 % of potential, while for bean plants the shoot growth is at 30 % of growth potential. The relative, but not the absolute, benefit of having RCA for bean is thereby reduced. Furthermore, at these phosphorus availabilities, bean, with its finer root system and less reduced shoot size, spends relatively less carbon on root respiration, namely 15 % of daily photosynthesis, versus 35 % for maize. Therefore a reduction in root respiration due to RCA formation in bean has less effect on the total carbon budget of the plant. Similarly, phosphorus remobilization from the roots has less effect on the phosphorus status of the plant because bean has a lower root : shoot ratio than maize (0·91 versus 1·5). Comparing maize and bean at similar shoot growth reductions is difficult, since the cost : benefit ratio for root growth strongly depends on phosphorus availability.
Dilution of phosphorus can also occur when shoot and root growth are not functionally balanced. In this case, the increasing phosphorus deficiency of the plant will reduce shoot growth rates, effectively making more carbon available for root growth. This quantitative response, however, is not necessarily optimal and small oscillations are present in the model results (see for example the not smooth curves in Fig. 7). These oscillations are not related to the numerical time step of the model, but rather to over-adjustment of the shoot/root ratio. Currently, we do not know what an optimal response would be or if it would include these oscillations. We also do not expect plants to be able to respond in an optimal way other than what was necessary for survival in their respective evolutionary environments, which included many more stresses than low phosphorus availability. Rather the nutrient-deficiency response was simulated after observing nutrient-deficient plants and these oscillations were noted in the simulation results. The lack of an optimal response for resource allocation may have affected the simulated benefit of having RCA. RCA might have been more beneficial if the plant's initial benefit did not result in increased deficiency during later growth stages. This becomes apparent in very low-phosphorus soils where RCA increased total plant biomass while reducing shoot biomass of both maize and bean (data not shown).
Apparent contradictions exist in the literature on the carbon limitations of root growth in soils with low phosphorus availability (Mollier and Pellerin, 1999). Some experiments show that root growth under low phosphorus availability is limited by the maximum growth rate of the root system (sink limited), not source limited (Wissuwa et al., 2005), while others have suggested that root growth is source limited (Mollier and Pellerin, 1999). The present results show both source- and sink-limited growth periods exist and that the dominance of either depends on the severity of the stress and the plant species involved. For example, maize plants with 50 % growth reduction, comparable to the severest deficiency in Wissuwa's experiments, have at the end of the simulation accumulated carbon reserves, while their root growth is limited by their maximum root growth capacity. Indeed, moderate phosphorus stress did not affect root biomass in either the model or in Wissuwa's results. On the other hand, Mollier and Pellerin (1999) reported source-limited growth in experiments with maize at more severe stress, which agrees with the model results. Even at these deficiencies, however, the model predicts that growth is temporarily restricted by sink limitations. These temporary sink limitations may reoccur in later stages, since temporary source limitations would reduce the future sink strength of the root system by reducing the root length along which new root tips can be generated. Thus, RCA may increase the sink strength to the extent that a sink-limited period may not occur. Besides effects on sink strength, phosphorus availability has strong effects on carbon assimilation and the proportional amount of carbon that is sent to the root system. At low phosphorus availability, carbon assimilation is strongly reduced by the reduced leaf area in both maize (Mollier and Pellerin, 1999) and bean (Lynch et al., 1991). Smaller reductions in carbon assimilation may originate from negative effects of leaf phosphorus status on photosynthesis. This drop in photosynthesis is thought to be largely caused by a reduction in carbon fixation rates (Jacob and Lawlor, 1992; Barrett and Gifford, 1995), not by stomatal closure, which is an observed response to low phosphorus availability (Clarkson et al., 2000). Different reductions in photosynthesis have been reported for different species (Jacob and Lawlor, 1991; Halsted and Lynch, 1996). Stronger reductions in carbon assimilation rates may cause the plant to be source limited for longer periods of time.
Despite source limitations of root growth, phosphorus-deficient plants may not benefit from elevated CO2 levels. Phosphorus-deficient plants have lower maximum carbon fixation capacity and reach this maximum earlier (Jacob and Lawlor, 1991). Maximum carbon fixation rates are reached at lower CO2 pressure in C4 plants than in C3 plants in phosphorus-deficient plants. Maize (C4) may reach this maximum even under current (2010, 388 ppm; http://www.esrl.noaa.gov) ambient conditions (Jacob and Lawlor, 1991). In contrast, C3 plants like common bean, have higher maximum assimilation rates which are only reached at higher CO2 concentrations, even when they are grown in soils with suboptimal phosphorus availability (Jacob and Lawlor, 1991). Elevated CO2 may therefore increase the light-use efficiency of beans grown under suboptimal phosphorus availability, but is unlikely to increase the light-use efficiency in maize. SimRoot predicts that higher light-use efficiency would increase plant growth at low phosphorus availability (Fig. 9). In maize, an initial increase in the benefit of having RCA with higher light-use efficiency followed by a decrease is seen, while in bean the benefit of having RCA declines with higher light-use efficiency (Fig. 9). This decrease is partly caused by the decreasing benefit of reduced respiration, which confirmed our hypothesis. Thus at high CO2 levels, reallocation of phosphorus becomes even more important. The predicted decline in the benefit of having RCA for bean at elevated CO2 was smaller (3 %) in soils with lower phosphorus availability (<3 µm; data not shown). It can be concluded that RCA will still be beneficial in future high CO2 environments for maize plants and may be beneficial for bean plants grown in soils with low phosphorus availability.
In the present simulations, RCA always increased plant growth, even in non-deficient plants. Significant genetic variation in the formation of RCA exists (Fan et al., 2003; Zhu et al., 2010), including genotypes that form no RCA at all and genotypes that form RCA under optimal growth conditions. Such genetic variation suggests that there are trade-offs for RCA. Trade-offs for RCA formation are largely unknown, although several have been suggested in the literature. RCA may reduce radial water conductivity (Fan et al., 2007) or radial nutrient transport (Henry, 2009). It may reduce the mechanical strength of the roots (Striker et al., 2007), a trait especially important for maize. We suggest that RCA may affect mycorrhizal colonization or response to pathogens (Fan et al., 2003). Other functions of the cortex, like energy storage and detoxification, may be affected as well. Our model does not include these trade-offs and it is currently difficult to predict to what extent they might affect model results. The frequent occurrence of RCA in maize (Lenochová et al., 2009) may suggest that the benefit of having RCA outweighs potential trade-offs in most environments, and indeed the benefit is large in both the present study and that of Zhu et al. (2010). Beans form less RCA and the smaller benefit of having RCA in beans may be an evolutionary explanation for less production of RCA in beans than in maize.
Quantitative support is provided for the hypothesis that RCA formation is an adaptive trait in soils with suboptimal phosphorus availability. The functions of RCA under phosphorus deficiency are (a) reduced root respiration, allowing carbon to be used for greater soil exploration, and (b) remobilization of phosphorus, which is more important than reduced respiration in stimulating growth.
Low phosphorus availability is a major constraint to agricultural production, often reducing yields to <10 % of yield potential (Lynch, 2007). It is at these severe deficiencies where RCA has the most benefit. Significant genotypic variation in RCA formation exists in maize and bean. We suggest that such variation may be useful for breeding phosphorus-efficient crops. Since RCA forms in many species in response to several nutrient deficiencies, we hypothesize that RCA may be a positive trait for nutrient acquisition in general and could be part of a breeding strategy for more nitrogen-efficient crops as well. Even though RCA may have general utility for soil exploration, potential trade-offs merit research.
This research was supported by United States Department of Agriculture (NRI 2007-35100-18365), the Dry Grain Pulses Collaborative Research Program of the US AID-Development Grant Program (EDH-A-00-07-00005-00] and the National Science Foundation (DBI-0820624).