Plant and Soil 218: 159–171, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands.
159
The importance of root gravitropism for inter-root competition and phosphorus acquisition efficiency: results from a geometric simulation model Zhenyang Ge1,2 , Gerardo Rubio2,3 and Jonathan P Lynch2,∗ 1 College
of Polytechnic, South China Agricultural University, Guangzhou 516042, P.R. China; 2 Department of Horticulture, The Pennsylvania State University, University Park, PA 16802, USA and 3 Faculty of Agronomy, University of Buenos Aires, 1417 Buenos Aires, Argentina Received 21 May 1999. Accepted in revised form 12 October 1999
Key words: competition, roots, common bean, mineral nutrition, models, phosphorus
Abstract We have observed that low soil phosphorus availability alters the gravitropic response of basal roots in common bean (Phaseolus vulgaris L.), resulting in a shallower root system. In this study we use a geometric model to test the hypotheses that a shallower root system is a positive adaptive response to low soil P availability by (1) concentrating root foraging in surface soil horizons, which generally have the highest P availability, and (2) reducing spatial competition for P among roots of the same plant. The growth of nine root systems contrasting in gravitropic response over 320 h was simulated in SimRoot, a dynamic three-dimensional geometric model of root growth and architecture. Phosphorus acquisition and inter-root competition were estimated with Depzone, a program that dynamically models nutrient diffusion to roots. Shallower root systems had greater P acquisition per unit carbon cost than deeper root systems, especially in older root systems. This was due to greater inter-root competition in deeper root systems, as measured by the volume of overlapping P depletion zones. Inter-root competition for P was a significant fraction of total soil P depletion, and increased with increasing values of the P diffusion coefficient (D e ), with root age, and with increasing root gravitropism. In heterogenous soil having greater P availability in surface horizons, shallower root systems had greater P acquisition than deeper root systems, because of less interroot competition as well as increased root foraging in the topsoil. Root P acquisition predicted by SimRoot was validated against values for bean P uptake in the field, with an r 2 between observed and predicted values of 0.75. Our results support the hypothesis that altered gravitropic sensitivity in P-stressed roots, resulting in a shallower root system, is a positive adaptive response to low P availability by reducing inter-root competition within the same plant and by concentrating root activity in soil domains with the greatest P availability. Introduction Root architecture, defined as the spatial configuration of a root system, is an important factor in the ability of a plant to acquire soil resources (Fitter, 1991; Lynch, 1995). By determining root deployment to distinct soil domains, root architecture should be particularly important for the acquisition of diffusion-limited nutrients, which can only move as much as 0.1 – 20 mm to the plant (Barber, 1995; Nye and Foster, 1961). ∗ FAX No: 814-863-6139. E-mail:
[email protected]
Root architecture also determines the extent of competition among roots of the same plant (‘inter-root competition’). Inter-root competition is an important component of the nutrient acquisition efficiency of root systems (Nielsen et al., 1994), which can be estimated as the volume of soil exploited per unit volume of root or per unit of carbon expended in root construction (Berntson, 1994; Fitter, 1987; Nielsen et al., 1994). The C costs of root construction and maintenance are appropriate to consider as an aspect of root efficiency since root C costs may comprise a substantial portion of the C economy of a plant, especially
160 under nutrient-limited conditions (Eissenstat, 1997; Nielsen et al., 1998). Root systems with low interroot competition are more efficient because they tend to minimize the overlapping of adjacent roots, which is an inefficient process as an overlapped volume is explored by several roots at the same time. Baldwin and Nye (1974) mathematically defined the radius of the depletion zone as the radial distance coincident with a decrease of 5% in the soil nutrient concentration. The length of this radius is a function of the diffusion coefficient of a specific nutrient in the soil and time. One of the principal components of root architecture is gravitropism, or the tendency of roots to grow with a certain orientation with respect to gravity (Evans, 1991). In annual dicot root systems, the basal roots form the skeleton or scaffold upon which much of the mature root system develops as a set of lateral roots (Stoffella et al., 1979). The growth trajectories of basal roots in response to gravity may affect the intensity of inter-root competition, because they control the spatial arrangement of the root system and the proximity of adjacent roots. Gravitropic sensitivity also controls the soil depth at which lateral roots form, and therefore the intensity of topsoil foraging by the root system. Shallower basal roots allow more intense topsoil foraging, which may be advantageous in P-limited environments since P availability in most soils is greatest in surface horizons (Keter and Ahn, 1986, Pothuluri et al., 1986). P gradually concentrates in the topsoil through the deposition of plant litter on the soil surface, and also by fertilization and manuring. Root trajectories with respect to gravity appear to be under genetic control (Oyanagi, 1991). In some genotypes of common bean, phosphorus deficiency decreased the gravitropic sensitivity of both basal and tap roots, which led to a shallower root system (Bonser et al., 1996). Bean genotypes with shallower basal roots had better performance in low P soils of the tropics (Bonser et al., 1996; Lynch and van Beem, 1993). Because of the difficulty in observing and analyzing the architecture of roots growing in soil, simulation modeling has been a useful approach in understanding some features of root architecture. After the early works by Hackett and Rose (1972) and Lungley (1973), several models that simulate root architecture have been developed (Lynch and Nielsen, 1996). Increased computing capabilities has enabled improved resolution and scale of these models. In the late 1980s the first 3D models were developed (Diggle, 1988; Pages et al., 1989). Three-dimensional models have
Table 1. General parameters used to simulate Carioca bean root system
Root axis growth rate (mm/h) Root radius growth coefficienta Gravitropism (mm per time step) Number of branch poles Branch angle (degree) Inter-branch distance (mm)
Tap root
Root type Basal root
Lateral root
0.49
0.85
0.16
0.04 1.00
0.04 0.80
0.04 0.25
4b
4
–
90
75
–
5.0
6.0
–
a In our simulation R =0.04 L−2 , where R is root radius; L is the rt rt
length from root tip. b This is the number of branch pole for lateral root on tap root; Basal
root also arise from tap roo. But the basal root number are limited as 14 for bean root system simulation.
been used to simulate some functional properties of root systems, such as water uptake (Clausnitzer and Hopmans, 1994; Doussan et al., 1998), water uptake and nutrient uptake (Somma et al., 1998), exploitation efficiency (Fitter et al., 1991) and carbon construction costs (Berntson, 1994; Nielsen et al., 1994). SimRoot is a dynamic geometric model of root systems based on empirical growth parameters (Lynch et al., 1997). It is able to simulate the relationship between the spatial distribution of the root system and properties such as resource acquisition or carbon expenditure (Lynch et al., 1997). In this paper we used this model to test the hypotheses that decreasing basal root gravitropism results in (i) decreased inter-root competition for P (IRCP ), and (ii) increased P acquisition efficiency (PAE), especially in stratified soils in which P availability is greatest in the topsoil.
Materials and methods Description of root model and input parameters structure SimRoot was used to simulate growth of common bean (Phaseolus vulgaris L.) roots, as previously described (Lynch et al., 1997). The basic root model employed was that of the bean genotype ‘Carioca’. Root growth parameters were taken from a study at the
161 CIAT Palmira Research Station in Colombia (Lynch and van Beem, 1993). The root growth parameters for the model (Table 1) included root architectural parameters. Physiological parameters of carbon cost (i.e., respiration C, C exudation, and biomass C) were also simulated in the model. Respiration, biomass deposition and exudation were measured on Phaseolus vulgaris seedlings under laboratory conditions (Nielsen et. al., 1994). Changes in root gravitropism To study the effects of root gravitropic curvature on IRCP and other parameters we generated nine root models (Fig. 1) ranging from shallow (root number 1, basal root gravitropic coefficient = 0.1 mm per time step) to deep (root number 9, basal root gravitropic coefficient = 5.9 mm per time step). The root growth parameters for root number 5 (basal root gravitropic coefficient = 0.8 mm per time step) were taken from field grown Phaseolus vulgaris cultivar Carioca (Lynch and van Beem, 1993). The gravitropic coefficient is a measure of the tendency of roots to grow downwards. It is a vertical vector, which varies according to the elongation during the time step and a constant parameter. In order to focus the study on the effects of basal root gravitropism, in this study we kept the root length, biomass and branching patterns of the nine root systems constant. At the end of our simulation time (320 h) the simulated root length and accumulated carbon cost were 28.3 m and 25.6 mmol C per root system. Variations in P diffusion coefficient and P distribution in the soil In order to investigate the influence of the phosphorus diffusion coefficient of the soil (De ) on IRCP we simulated soils with three De values: 1×10−7, 1×10−8 and 1×10−9 cm2 s−1 . The range of soil De for P employed in this study fully covered the range of values found in the field by Schenk and Barber (1979). The higher De is close to that found in an Aquic Argiudoll and the lower to a Typic Udipsamment (Schenk and Barber, 1979). For the estimation of the influence of P distribution in the soil on P uptake, we simulated two soils with different P distribution: soil A with homogenous P distribution, and soil B stratified with greater P availability at the surface. Both simulated soils had approximately the same total amount of P. We assigned both soils a value for De of P: 1×10−8 cm2 s−1 .
Inter-root competition for P Depletion zone volume was calculated from the diffusion coefficient of a particular nutrient in the soil. The radius of the depletion volume is expressed as: p R dz = r + 2 D e t (1) where R is the radius of depletion zone around the root, measured from the root center; r is the radius of the root segment, De is the diffusion coefficient of the ion in the soil and t is the time period of root growth (Nye and Tinker, 1977; Fitter et al., 1991). This function indicates that as a root grows, its depletion volume will increase but at a decreasing rate (Fig. 2). In our model, the depletion zone volume of the whole root system is divided into a group of elements. Each element is represented by a cubic-form volume (voxel) within the depletion cylinder. Because each root segment has its own depletion cylinder and these cylinders can overlap with those of other root segments, the sum of the volumes of all the roots overestimates the depletion zone volume. Duplicate voxels (overlap volume) represent the inter-root competition. In this study we use relative inter-root competition for P (IRCP ) as a relative index, which is calculated as: IRCP =
Vo −Va 100% Va
(2)
where Vo is the depletion volume with overlap and Va is the actual depletion volume. Empirical validation of soil P supply capacity in the depletion volume used to simulate P uptake We used data from an experiment performed in a sand culture system (Nielsen, Eshel and Lynch, unpublished results) to calibrate our P uptake submodel. Common bean plants were grown in 20-l buckets with solid-phase-buffered pure silica sand providing a constant availability of low (1 µM), medium (10 µM) and high (30 µM) P concentration in the soil solution (Lynch et al., 1990). The plants were grown in a temperature controlled (22 – 30◦ C) greenhouse in University Park, Pennsylvania. Plants were harvested 14 days after planting and dry biomass and total P uptake were measured. For each obtained value of root biomass we calculated the corresponding depletion volume and then, by relating this volume with the P uptake, we obtained the P supply capacity for each P level. This capacity is expressed in terms of mg P cm−3 depletion volume day−1 . After this calibration,
162
Figure 1. Simulated common bean root systems differing in gravitropic growth of the basal roots, from shallow (root number 1) to deep (root number 9). Simulation time, 320 h. Empirical measurements of common bean Phaseolus vulgaris cv. Carioca (number 5) were used to parameterize the model. Reference axis, 0–40 cm.
Figure 2. Modeled depletion zone according to the equation rdz = r + 2(De t)1/2 . rdz , depletion zone radius; r, root radius; De , phosphorus diffusion coefficient (here De = 10−8 cm2 s−1 ); t, age of simulated root segment.
163 we validated the P uptake predictions under field conditions, by using a completely independent set of data. We used data from an experiment performed at CIAT (Palmira, Colombia). In this experiment, 23 common bean genotypes were cultivated on a low P Oxisol and at 14 days after planting dry biomass and P uptake were recorded (Sadeghian 1991). We compared these P values with the predictions of our model. Simulated P uptake was obtained by multiplying the depletion volumes by the P supply capacities obtained in the calibration phase. Phosphorus uptake and phosphorus acquisition efficiency P uptake (PU) was modeled by multiplying the actual depletion volume and the P concentration in the simulated soil (Cp ), i.e., PU = C p V a
(3)
It is assumed that all available P in the depletion zone is incorporated into the roots. In order to study the relationship between root gravitropism and root efficiency, we calculated the P acquisition efficiency (PAE). The term ‘nutrient efficiency’ has been used widely as a measure of the capacity of a plant to acquire and utilize nutrients for plant production. The definition of nutrient efficiency varies greatly. In general, approaches made at present can be divided into those emphasizing productivity and those emphasizing the internal nutrient requirement of the plant (Gourley et al., 1994). Phosphorus acquisition efficiency was calculated as total depletion zone volume for P accumulation divided by total root carbon cost. Working with the relationship between exploitation potential and exploitation efficiency, Fitter et al. (1991), Berntson (1994), and Nielsen et al. (1994) used similar approaches to estimate nutrient acquisition efficiency. We simulated the carbon cost of root growth and maintenance, which includes the carbon invested in root biomass, root exudation and respiration (Nielsen et al. 1994). By relating this ‘cost function’ with the ‘benefit function’ (depletion zone volume) we obtained the ‘efficiency function’ (PAE), Va (4) PAE = Cc where, Va is the depletion zone volume for P accumulation; Cc is the root carbon cost.
Statistics ANOVA was performed with results corresponding to simulation with De =1×10−8cm2 s−1 in roots number 1, 5, and 9. Each simulation model was replicated four times by changing the seed of the random number generator used to drive stochastic processes in the growth of each root system, resulting in roots with the same overall gravitropic coefficient but slightly different architecture (Fig. 3) This variation represents the natural variation of roots of the same genotype and also the influence of soil heterogeneity on root geometry. The correlation of observed and predicted P uptake was analyzed with Pearson’s linear correlation.
Results P acquisition efficiency Phosphorus acquisition efficiency increased over time in the whole range of root systems studied (Fig. 4). After 160 h of simulated growth, the model predicted a PAE of 5.7 cm3 mmol C−1 and at 320 h this value increased 42.4% (to 8.2 cm3 mmol C−1 , average of the three types of root systems). Since we estimated PAE as the carbon cost per unit of soil volume depleted of P, PAE is affected by the overlap between depletion zones of adjacent roots. When a root segment overlaps the depletion volume of an older segment, the carbon costs invested in that segment do not add any new depletion volume, so an inverse relationship between overlap of depletion zones and acquisition efficiency could exist. But we observed that the overlap of depletion zones also increases over root age (Fig. 5) faster than PAE. This means that overlap of depletion zones is not the only architectural factor influencing PAE. Analysis of variance showed that root architecture significantly affected PAE and depletion zone overlap. The deeper root systems were less efficient than the shallow and medium root systems, especially at 240 and 320 h. This is due to their greater overlap volumes (Fig. 5). No difference between the shallower root and Carioca root was detected in these parameters. At 320 h, around 40 cm3 of depletion zone overlap was generated in the shallow root system. Carioca showed almost the same values, but in the deeper root system overlap raised to 66 cm3 of the total depletion volume.
164
Figure 3. Replicates of simulated root systems (simulation time 320 h). Each root system was based on the same growth parameters but a different seed for the random number generator. Reference axis, 0–30 cm.
Inter-root competition for P The primary effect of increasing root age, P diffusion coefficient and gravitropism was to increase the IRCP , and there were strong (and generally positive) interactions among these factors (Fig. 6). Older roots (320 h) had higher IRCP than younger roots (120 h) and the difference between these ages was greater in deep roots and in soils with higher De . Increased IRCP in younger roots was related to the growth of roots in soil volumes previously depleted by older roots. This increase in explored soil came from both the enlargement of each root unit and the continued lateral branching of basal and tap roots. Our simulations indicated that the soil volume adjacent to the root crown was thoroughly depleted and that the initial portion of each lateral root encountered intense competition with their parent roots.
Increasing De from 10−9 to 10−7 led to an expansion of the size of the depletion volume and, consequently, to greater overlap between neighboring roots and to a higher IRCP . The IRCP for the younger roots (120 h of simulation) was around 6.5% ±SE 0.5, average of the nine root systems at De = 10−9 , 8.8%±SE 0.4 at De = 10−8 and 19.7%±SE 0.8 at De =10−7 . These values increased substantially in the older roots (simulation time = 320 h): at De = 10−9 the IRCP ranged from 10.1 to 17.0%, and at De = 10−7 the intensity of competition varied between 48.9 and 120.1%. Values higher than 100% mean that, on average, each portion of root is competing with at least one neighbor root. Shallow roots (i.e., root models 1 – 5 in Fig. 6) showed almost the same values for IRCP in the range of simulation time and diffusion coefficient studied. This group presented the smallest values of IRCP , sug-
165 7. For roots at 320 h the total depletion volume in a soil with De = 10−9 was 97, 95 and 88 cm3 in the shallow, Carioca and deep root systems, respectively. At De =10−8 the values were 219, 218 and 191 cm3 and at De = 10−7 were 830, 805 and 557 cm3 . Effect of gravitropism on P uptake in soils with heterogeneous P distribution
Figure 4. Phosphorus acquisition efficiency (total depletion volume per unit of carbon invested in roots, including construction cost, respiration and exudation) as affected by root gravitropism and root age. Three root systems were used: shallow (root number 1 in Fig. 1), Carioca (root number 5) and deep (root number 9). Data shown as the mean ± standard error of the mean (n = 4).
Analysis of variance showed that root architecture significantly affected P uptake in homogenous and in stratified soils (Fig. 8). With homogenous P distribution, the shallower root system was able to capture 15% more P than the deeper one. In our simulations all the root systems had the same total root length and therefore the same potential for depleting the soil. This means that the observed effect of gravitropism in homogenous soil can be ascribed to the lower IRCP (i.e., lower depletion zone overlap) of the shallower root systems. In a stratified soil with greater P availability at the surface, the shallow root system absorbed 10 and 34% more P than Carioca and the deep root system, respectively. In the heterogenous soil, the advantage of the shallow root system was related to both its lower IRCP and to the greater concentration of root foraging in the soil layer with greatest P availability. Verification
Figure 5. Overlapped volume of depletion zone of three root systems as affected by root age. Three root systems were used: shallow (root number 1 of Fig. 1), Carioca (root number 5) and deep (root number 9). Data shown as mean ± standard error of the mean (n = 4).
gesting that the shallower roots are more efficient than the deeper ones. For example, after 320 h growth and at De = 10−8 the shallower root system had an IRCP of 18.2% ± SE 0.2 and Carioca 18.8% ± SE 0.2. These values increased to 34.2% ± SE 1.2 in the deeper root system. Among deep roots (root models 6 – 9), there was a close relationship between gravitropism and IRCP , with deeper root systems having greater inter-root competition. The effects of gravitropism, root age and De on total depletion volume had an opposite tendency than on IRCP because: (i) all our simulated root systems had the same total length, and (ii) in SimRoot the depletion volume before inter-root competition is a direct function of root length. A graphical representation of the total depletion volume of Carioca is shown in Fig.
From the experiment we used for calibrating our simulations of P uptake, growth parameters and P uptake values were available for beans growing under three soil P levels (i.e., low, medium and high). We used these data to estimate the P supplying capacity for the three different P levels. By using this coefficient, we observed that 2-week P uptake by bean plants growing in the field followed the same pattern as predicted P uptake (Fig. 9). There was statistically good agreement between observed and predicted P uptake (r 2 =0.75). We used these P supplying capacity coefficients to simulated stratified soils.
Discussion Two processes account for increased soil exploitation during vegetative growth; first, root elongation, and secondly, the enlargement of the radius of the depletion zone around existing roots. The Nye and Tinker (1977) approach, which was used in the present work, proposes that the radius of the depletion zone increases with De and also with the square-root function of time
166
Figure 6. Inter-root competition for phosphorus (IRCP ) of nine simulated root systems as affected by soil diffusion coefficient (De ) and root age. The root systems vary from shallow (root number 1) to deep (root number 9). See Fig. 1 for graphical representation of the different root systems.
(Fig. 2). In our simulations, a strong dependence of total depletion volume on De was verified in all root systems. A novel perspective provided by our simulations is that root architecture and thereby depletion zone overlap modulates the magnitude and distribution of the exploited soil volume. One source of overlap volume is generated by the intersection between new root laterals and their parent roots after every new branching event. This portion of overlap is an unavoidable consequence of lateral branching. Only after the new root segment grows longer than the depletion
volume generated by its parent, will it enter potentially unexplored soil. Another factor influencing root overlap is the branching pattern and root curvature. These root traits determine the spatial arrangement of roots in space, which includes the distance and overlap among root segments. Nielsen et al. (1994) analyzed the effect of branching patterns on the intensity of competition and demonstrated that simulated bean roots presented lower IRCP than a herringbone or dichotomous root systems. Fitter et al. (1991) observed that decreases in inter-branch distances could lead to decreases in ex-
167
Figure 7. Graphical representation of the root system of Carioca bean plants (A) and the depletion volume for that root system at De = 10−7 cm2 s−1 (B), De = 10−8 cm2 s−1 (C), and De = 10−9 cm2 s−1 (D). Simulation time, 320 h. Reference axis, 0–30 cm.
Figure 8. Phosphorus uptake per plant of three contrasting root systems in two different soils. One soil has a homogeneous distribution of P with depth and the other has a heterogeneous distribution. Concentration of phosphorus in the soil solution in each soil type in the soil profile is shown. The three root systems are shallow (root number 1 in Fig. 1), Carioca (root number 5) and deep (root number 9). Data shown as mean ± standard error of the mean (n = 4).
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Figure 9. Measured and simulated P uptake by common beans over 14 days of growth. Measured values from a field experiment, where 23 common bean genotypes were cultivated on a low P Oxisol (Sadeghian, 1991). 1:1 line is shown. Correlation coefficient (r 2 )=0.75.
ploitation efficiency. In the present work, to analyze the effects of root curvature separately and to not confound the effects of branching and root curvature, we held the branching parameters of the simulated root systems constant. As predicted by our first hypothesis, shallower root systems have lower IRCP . The dependence of IRCP on root growth trajectories can be understood considering the three-dimensional arrangement of the root system. Because basal roots of common bean extend radially from the conjunction of the hypocotyl and taproot, they tend to disperse over time in root systems with low gravitropic sensitivity, whose basal roots develop close to the soil surface. In deep root systems (e.g., models 6 – 9), the stronger downward tendency of the roots led them to remain closer together and, indeed, close to the tap root and its lateral roots. This resulted in a sharp increase in IRCP as root systems became deeper (Fig. 6). In deep root systems, the average distance among root components decreased and competition took place among basal roots, tap root and lateral roots from both basal and tap roots. We also observed a strong dependence of IRCP values on De , which indicates that competition among roots is not just an inherent characteristic of root geometry, but also has a close dependence on the surrounding medium, as represented by the different De values. Our
simulations suggest that the benefits of root system shallowness for P acquisition are more important in soils with higher De . Higher De values represent a wider radius of depletion volumes and a higher probability that neighboring root segments overlap each other. At De = 10−7 we found IRCP values higher than 100%, meaning that the average unit of depletion volume around the root cylinder is exploited by more than two roots at the same time. As expressed by the relationship between C expenditure in the root system and depletion volume, PAE is supposed to be inversely related with IRCP . But we observed that, despite the fact that IRCP showed a consistent tendency to increase over time, older roots were more efficient in P acquisition (Fig. 4). This overcompensation can be attributed to the increase of the radius of the depletion zone over time. Fig. 2 shows that even in older root systems (i.e., 320 h) roots were still actively increasing the radius of the depletion zone. Nevertheless, we predict that this increase in PAE turns into a decrease over time later on due to accumulated carbon costs and the increasing influence of IRCP . Our data also support our second hypothesis that decreasing basal root gravitropism results in increased P acquisition efficiency (PAE), especially in stratified soils in which P availability is greatest in the topsoil.
169 Many factors contribute to the concentration of soil P in upper horizons: (i) P in shoot residues returns to the soil at the surface; (ii) fertilizer P applications are generally at or near the soil surface; (iii) soil P availability is typically greatest at the surface because of more favorable chemical, physical, and microbiological conditions; and (iv) the relative immobility of P in soil retards P leaching. Considering these factors, shallow roots should be the most efficient in capturing soil P. According to our simulations, shallow root systems captured 34% more P than deep root systems in a stratified soil with P concentrated in the topsoil. Shallow root systems were also able to capture more P in a homogeneous soil; in this case the difference was 10%. This means that shallower root distribution could be beneficial for P acquisition not only because of the spatial coincidence of roots and resources, but also because of their lower inherent IRCP . These findings are consistent with the work of Bonser et al. (1996), who showed that among a set of bean genotypes, those with shallower basal roots performed better in low P soils in the tropics. On the other hand, because dry conditions near the soil surface are common in field conditions, mortality of fine roots in shallow root systems could be higher than in deeper ones (Espeleta and Eissenstat, 1998). This factor could depress the efficiency of shallower root systems. Another disadvantage of shallow root systems could be the lower ability for acquiring resources located lower in the profile, such as water. Thus in field settings, the utility of root shallowness may depend on several interacting factors in addition to P availability and distribution. Although the focus of this work was on P, it is possible to extend the results of our simulations to other nutrients. De values found in the literature for ammonium, potassium, and molybdenum are close to those found for P (Barber, 1995). De for boron is usually higher (around 10−6 cm s−1 ). Hence, its IRCP values would be greater, and the difference among the shallow and deep root systems would be greater compared to that found for P. In the case of iron (De around 10−10 cm s−1 ), the overlap volume, IRCP and the influence of root gravitropism on these parameters would be smaller. The advantage of shallow root systems for P acquisition could not be extended to mass-flow nutrients, like nitrate, sulfate, calcium or magnesium. In the case of nitrate, at root densities often found in soil, the entire root zone is almost depleted of nitrate unless replenished by nitrification or fertilization (Jungk and Claassen, 1996). Because nitrate supply to plants usually includes soil volumes
not included in the rooted layer, the incidence of root architecture on the acquisition of this nutrient should be smaller than for diffusion-limited nutrients. Phosphorus acquisition capacity is enhanced in most higher plants by mycorrhizal symbiosis. External hyphae can absorb and translocate P to the plant from soil outside the root depletion volume. Unfortunately, we are not aware of unambiguous data in the published literature that would permit us to quantitatively estimate the influence of external hyphae on root depletion zones. However, in common bean, root architecture is related to P acquisition efficiency independently of mycorrhizal effects (Bonser et al., 1996; Lynch and Beebe, 1995). We propose that this may occur because of the concentration of hyphal P uptake near host roots. In other words, that a shallower root system may also have shallower hyphal foraging. This issue deserves further research. Most theoretical models of resource acquisition normally assume roots are evenly distributed in soil (Claassen and Barber, 1976; Nye and Tinker, 1977; Smethurst and Comerford, 1993). In such models, root input is made in terms of root length per unit depth or volume, and three-dimensional distribution of roots or overlap among them are not considered explicitly. Here we show that root systems of the same total length but differing in architecture have an ample variation in overlap volumes and IRCP , resulting in variation in P acquisition, indicating that root length is valid only as a first approximation for describing root capacity for nutrient acquisition. The implications of incorporating a nonuniform root distribution in such models have not been explored yet, although several three-dimensional models of root geometry have been developed to date (for references, see Introduction). Results from the present work and others (e.g., Somma et al., 1998) suggest that the accuracy of these models could be notably enhanced by the introduction of a non-uniform root spatial distribution. The overall picture emerging from our simulations is that root architecture plays a major role in determining root deployment, soil exploration, and consequently, the efficiency of nutrient uptake. A variable proportion of the root system is not active in nutrient uptake due to overlap among soil volumes explored by root segments of the same plant. It was shown that IRCP increases as roots become older and as a consequence of increased root gravitropic sensitivity and soil diffusion coefficient. The combined effect of these three factors resulted in a range of variation in the IRCP values as large as 20-fold. There was
170 little variation of IRCP in shallow roots but a sharp increase in IRCP when root geometry becomes deeper (root systems 6 – 9). The soil diffusion coefficient greatly modifies the intensity of competition among roots, accentuating the effects of root gravitropism. Differences in root architecture also resulted in differences in nutrient uptake as a result of the coincidence between root and soil nutrient location but also of the different IRCP of the nine studied root systems. In this report we consider the overlap among roots of a single plant. Root overlap also occurs among neighboring plants, which can compete among themselves. In a subsequent paper we will address this question by analyzing IRCP and P uptake of simulated roots of different root architecture growing in competition.
Acknowledgements The authors thank Kai Nielsen for allowing us to use his unpublished data, Xiaolong Yan for valuable discussions and Bob Snyder for technical help. Z Ge thanks South China Agricultural University for a cooperative research leave. The research was financially supported by United States Department of Agriculture/National Research Initiative grant 97-35100-4456 to J P Lynch.
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