Plant and Soil218: 159–171, 2000.© 2000Kluwer Academic Publishers. Printed in the Netherlands.

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The importance of root gravitropism for inter-root competition andphosphorus acquisition efficiency: results from a geometric simulationmodel

Zhenyang Ge1,2, Gerardo Rubio2,3 and Jonathan P Lynch2,∗1College of Polytechnic, South China Agricultural University, Guangzhou 516042, P.R. China;2Department ofHorticulture, The Pennsylvania State University, University Park, PA 16802, USA and3Faculty 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 commonbean (Phaseolus vulgarisL.), resulting in a shallower root system. In this study we use a geometric model to test thehypotheses that a shallower root system is a positive adaptive response to low soil P availability by (1) concentratingroot foraging in surface soil horizons, which generally have the highest P availability, and (2) reducing spatialcompetition for P among roots of the same plant. The growth of nine root systems contrasting in gravitropicresponse over 320 h was simulated inSimRoot, a dynamic three-dimensional geometric model of root growthand architecture. Phosphorus acquisition and inter-root competition were estimated withDepzone, a program thatdynamically models nutrient diffusion to roots. Shallower root systems had greater P acquisition per unit carboncost than deeper root systems, especially in older root systems. This was due to greater inter-root competition indeeper root systems, as measured by the volume of overlapping P depletion zones. Inter-root competition for P wasa significant fraction of total soil P depletion, and increased with increasing values of the P diffusion coefficient(De), with root age, and with increasing root gravitropism. In heterogenous soil having greater P availability insurface horizons, shallower root systems had greater P acquisition than deeper root systems, because of less inter-root competition as well as increased root foraging in the topsoil. Root P acquisition predicted by SimRoot wasvalidated against values for bean P uptake in the field, with anr2 between observed and predicted values of 0.75.Our results support the hypothesis that altered gravitropic sensitivity in P-stressed roots, resulting in a shallowerroot system, is a positive adaptive response to low P availability by reducing inter-root competition within the sameplant and by concentrating root activity in soil domains with the greatest P availability.

Introduction

Root architecture, defined as the spatial configurationof a root system, is an important factor in the ability ofa plant to acquire soil resources (Fitter, 1991; Lynch,1995). By determining root deployment to distinctsoil domains, root architecture should be particularlyimportant for the acquisition of diffusion-limited nu-trients, which can only move as much as 0.1 – 20 mmto the plant (Barber, 1995; Nye and Foster, 1961).

∗ FAX No: 814-863-6139. E-mail: JPL4@psu.edu

Root architecture also determines the extent of com-petition among roots of the same plant (‘inter-rootcompetition’). Inter-root competition is an importantcomponent of the nutrient acquisition efficiency ofroot systems (Nielsen et al., 1994), which can be es-timated as the volume of soil exploited per unit volumeof root or per unit of carbon expended in root con-struction (Berntson, 1994; Fitter, 1987; Nielsen et al.,1994). The C costs of root construction and mainten-ance are appropriate to consider as an aspect of rootefficiency since root C costs may comprise a substan-tial portion of the C economy of a plant, especially

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under nutrient-limited conditions (Eissenstat, 1997;Nielsen et al., 1998). Root systems with low inter-root competition are more efficient because they tendto minimize the overlapping of adjacent roots, whichis an inefficient process as an overlapped volume is ex-plored by several roots at the same time. Baldwin andNye (1974) mathematically defined the radius of thedepletion zone as the radial distance coincident witha decrease of 5% in the soil nutrient concentration.The length of this radius is a function of the diffusioncoefficient of a specific nutrient in the soil and time.

One of the principal components of root archi-tecture is gravitropism, or the tendency of roots togrow with a certain orientation with respect to grav-ity (Evans, 1991). In annual dicot root systems, thebasal roots form the skeleton or scaffold upon whichmuch of the mature root system develops as a set oflateral roots (Stoffella et al., 1979). The growth traject-ories of basal roots in response to gravity may affectthe intensity of inter-root competition, because theycontrol the spatial arrangement of the root system andthe proximity of adjacent roots. Gravitropic sensitiv-ity also controls the soil depth at which lateral rootsform, and therefore the intensity of topsoil foragingby the root system. Shallower basal roots allow moreintense topsoil foraging, which may be advantageousin P-limited environments since P availability in mostsoils is greatest in surface horizons (Keter and Ahn,1986, Pothuluri et al., 1986). P gradually concentratesin the topsoil through the deposition of plant litter onthe soil surface, and also by fertilization and manur-ing. Root trajectories with respect to gravity appearto be under genetic control (Oyanagi, 1991). In somegenotypes of common bean, phosphorus deficiencydecreased the gravitropic sensitivity of both basal andtap roots, which led to a shallower root system (Bon-ser et al., 1996). Bean genotypes with shallower basalroots had better performance in low P soils of thetropics (Bonser et al., 1996; Lynch and van Beem,1993).

Because of the difficulty in observing and analyz-ing the architecture of roots growing in soil, simula-tion modeling has been a useful approach in under-standing some features of root architecture. After theearly works by Hackett and Rose (1972) and Lungley(1973), several models that simulate root architecturehave been developed (Lynch and Nielsen, 1996). In-creased computing capabilities has enabled improvedresolution and scale of these models. In the late 1980sthe first 3D models were developed (Diggle, 1988;Pages et al., 1989). Three-dimensional models have

Table 1. General parameters used to simulate Carioca bean rootsystem

Root type

Tap root Basal root Lateral root

Root axis growth

rate (mm/h) 0.49 0.85 0.16

Root radius growth

coefficienta 0.04 0.04 0.04

Gravitropism 1.00 0.80 0.25

(mm per time step)

Number of branch

poles 4b 4 –

Branch angle

(degree) 90 75 –

Inter-branch

distance (mm) 5.0 6.0 –

a In our simulationRrt=0.04L−2, whereRrt is root radius;L is thelength from root tip.bThis is the number of branch pole for lateral root on tap root; Basalroot also arise from tap roo. But the basal root number are limitedas 14 for bean root system simulation.

been used to simulate some functional properties ofroot systems, such as water uptake (Clausnitzer andHopmans, 1994; Doussan et al., 1998), water uptakeand nutrient uptake (Somma et al., 1998), exploitationefficiency (Fitter et al., 1991) and carbon constructioncosts (Berntson, 1994; Nielsen et al., 1994).

SimRootis a dynamic geometric model of root sys-tems based on empirical growth parameters (Lynchet al., 1997). It is able to simulate the relationshipbetween the spatial distribution of the root system andproperties such as resource acquisition or carbon ex-penditure (Lynch et al., 1997). In this paper we usedthis model to test the hypotheses that decreasing basalroot gravitropism results in (i) decreased inter-rootcompetition for P (IRCP), and (ii) increased P acquis-ition efficiency (PAE), especially in stratified soils inwhich P availability is greatest in the topsoil.

Materials and methods

Description of root model and input parametersstructure

SimRootwas used to simulate growth of commonbean (Phaseolus vulgarisL.) roots, as previously de-scribed (Lynch et al., 1997). The basic root modelemployed was that of the bean genotype ‘Carioca’.Root growth parameters were taken from a study at the

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CIAT Palmira Research Station in Colombia (Lynchand van Beem, 1993). The root growth parametersfor the model (Table 1) included root architecturalparameters. Physiological parameters of carbon cost(i.e., respiration C, C exudation, and biomass C) werealso simulated in the model. Respiration, biomassdeposition and exudation were measured onPhase-olus vulgarisseedlings under laboratory conditions(Nielsen et. al., 1994).

Changes in root gravitropism

To study the effects of root gravitropic curvature onIRCP and other parameters we generated nine rootmodels (Fig. 1) ranging from shallow (root number1, basal root gravitropic coefficient = 0.1 mm pertime step) to deep (root number 9, basal root gravit-ropic coefficient = 5.9 mm per time step). The rootgrowth parameters for root number 5 (basal root grav-itropic coefficient = 0.8 mm per time step) were takenfrom field grownPhaseolus vulgariscultivar Carioca(Lynch and van Beem, 1993). The gravitropic coef-ficient is a measure of the tendency of roots to growdownwards. It is a vertical vector, which varies ac-cording to the elongation during the time step and aconstant parameter. In order to focus the study on theeffects of basal root gravitropism, in this study wekept the root length, biomass and branching patternsof the nine root systems constant. At the end of oursimulation time (320 h) the simulated root length andaccumulated carbon cost were 28.3 m and 25.6 mmolC per root system.

Variations in P diffusion coefficient and P distributionin the soil

In order to investigate the influence of the phosphorusdiffusion coefficient of the soil (De) on IRCP we sim-ulated soils with threeDe values: 1×10−7, 1×10−8

and 1×10−9 cm2 s−1 . The range of soilDe for P em-ployed in this study fully covered the range of valuesfound in the field by Schenk and Barber (1979). ThehigherDe is close to that found in an Aquic Argiudolland the lower to a Typic Udipsamment (Schenk andBarber, 1979). For the estimation of the influence ofP distribution in the soil on P uptake, we simulatedtwo soils with different P distribution: soil A withhomogenous P distribution, and soil B stratified withgreater P availability at the surface. Both simulatedsoils had approximately the same total amount of P.We assigned both soils a value forDe of P: 1×10−8

cm2 s−1.

Inter-root competition for P

Depletion zone volume was calculated from the diffu-sion coefficient of a particular nutrient in the soil. Theradius of the depletion volume is expressed as:

Rdz = r + 2√Det (1)

whereR is the radius of depletion zone around theroot, measured from the root center;r is the radiusof the root segment,De is the diffusion coefficientof the ion in the soil andt is the time period of rootgrowth (Nye and Tinker, 1977; Fitter et al., 1991).This function indicates that as a root grows, its de-pletion volume will increase but at a decreasing rate(Fig. 2). In our model, the depletion zone volume ofthe whole root system is divided into a group of ele-ments. Each element is represented by a cubic-formvolume (voxel) within the depletion cylinder. Becauseeach root segment has its own depletion cylinder andthese cylinders can overlap with those of other rootsegments, the sum of the volumes of all the roots over-estimates the depletion zone volume. Duplicate voxels(overlap volume) represent the inter-root competition.In this study we use relative inter-root competition forP (IRCP) as a relative index, which is calculated as:

IRCP = V o− V a

V a100% (2)

whereVo is the depletion volume with overlap andVais the actual depletion volume.

Empirical validation of soil P supply capacity in thedepletion volume used to simulate P uptake

We used data from an experiment performed in asand culture system (Nielsen, Eshel and Lynch, un-published results) to calibrate our P uptake submodel.Common bean plants were grown in 20-l buckets withsolid-phase-buffered pure silica sand providing a con-stant availability of low (1µM), medium (10µM)and high (30µM) P concentration in the soil solu-tion (Lynch et al., 1990). The plants were grown ina temperature controlled (22 – 30◦ C) greenhouse inUniversity Park, Pennsylvania. Plants were harvested14 days after planting and dry biomass and total Puptake were measured. For each obtained value ofroot biomass we calculated the corresponding deple-tion volume and then, by relating this volume with theP uptake, we obtained the P supply capacity for eachP level. This capacity is expressed in terms of mg Pcm−3depletion volume day−1. After this calibration,

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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 beanPhaseolus vulgariscv. Carioca (number 5) were used toparameterize the model. Reference axis, 0–40 cm.

Figure 2. Modeled depletion zone according to the equationrdz = r + 2(De t)1/2. rdz, depletion zone radius;r, root radius;De, phosphorusdiffusion coefficient (hereDe = 10−8 cm2 s−1); t, age of simulated root segment.

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we validated the P uptake predictions under field con-ditions, by using a completely independent set of data.We used data from an experiment performed at CIAT(Palmira, Colombia). In this experiment, 23 commonbean genotypes were cultivated on a low P Oxisol andat 14 days after planting dry biomass and P uptakewere recorded (Sadeghian 1991). We compared theseP values with the predictions of our model. SimulatedP uptake was obtained by multiplying the depletionvolumes by the P supply capacities obtained in thecalibration phase.

Phosphorus uptake and phosphorus acquisitionefficiency

P uptake (PU) was modeled by multiplying the ac-tual depletion volume and the P concentration in thesimulated soil (Cp), i.e.,

PU= CpV a (3)

It is assumed that all available P in the depletionzone is incorporated into the roots. In order to studythe relationship between root gravitropism and rootefficiency, we calculated the P acquisition efficiency(PAE). The term ‘nutrient efficiency’ has been usedwidely as a measure of the capacity of a plant to ac-quire and utilize nutrients for plant production. Thedefinition of nutrient efficiency varies greatly. In gen-eral, approaches made at present can be divided intothose emphasizing productivity and those emphasizingthe internal nutrient requirement of the plant (Gour-ley et al., 1994). Phosphorus acquisition efficiencywas calculated as total depletion zone volume for Paccumulation divided by total root carbon cost. Work-ing with the relationship between exploitation poten-tial and exploitation efficiency, Fitter et al. (1991),Berntson (1994), and Nielsen et al. (1994) used similarapproaches to estimate nutrient acquisition efficiency.We simulated the carbon cost of root growth and main-tenance, which includes the carbon invested in rootbiomass, root exudation and respiration (Nielsen et al.1994). By relating this ‘cost function’ with the ‘bene-fit function’ (depletion zone volume) we obtained the‘efficiency function’ (PAE),

PAE= V a

Cc(4)

where,Va is the depletion zone volume for P accumu-lation;Cc is the root carbon cost.

Statistics

ANOVA was performed with results corresponding tosimulation withDe=1×10−8cm2s−1 in roots number1, 5, and 9. Each simulation model was replicated fourtimes by changing the seed of the random number gen-erator used to drive stochastic processes in the growthof each root system, resulting in roots with the sameoverall gravitropic coefficient but slightly different ar-chitecture (Fig. 3) This variation represents the naturalvariation of roots of the same genotype and also theinfluence of soil heterogeneity on root geometry. Thecorrelation of observed and predicted P uptake wasanalyzed with Pearson’s linear correlation.

Results

P acquisition efficiency

Phosphorus acquisition efficiency increased over timein the whole range of root systems studied (Fig. 4).After 160 h of simulated growth, the model predicteda PAE of 5.7 cm3 mmol C−1 and at 320 h this valueincreased 42.4% (to 8.2 cm3 mmol C−1, average of thethree types of root systems). Since we estimated PAEas the carbon cost per unit of soil volume depleted ofP, PAE is affected by the overlap between depletionzones of adjacent roots. When a root segment overlapsthe depletion volume of an older segment, the carboncosts invested in that segment do not add any newdepletion volume, so an inverse relationship betweenoverlap of depletion zones and acquisition efficiencycould exist. But we observed that the overlap of deple-tion zones also increases over root age (Fig. 5) fasterthan PAE. This means that overlap of depletion zonesis not the only architectural factor influencing PAE.

Analysis of variance showed that root architecturesignificantly affected PAE and depletion zone overlap.The deeper root systems were less efficient than theshallow and medium root systems, especially at 240and 320 h. This is due to their greater overlap volumes(Fig. 5). No difference between the shallower rootand Carioca root was detected in these parameters. At320 h, around 40 cm3of depletion zone overlap wasgenerated in the shallow root system. Carioca showedalmost the same values, but in the deeper root systemoverlap raised to 66 cm3 of the total depletion volume.

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Figure 3. Replicates of simulated root systems (simulation time 320 h). Each root system was based on the same growth parameters but adifferent seed for the random number generator. Reference axis, 0–30 cm.

Inter-root competition for P

The primary effect of increasing root age, P diffu-sion coefficient and gravitropism was to increase theIRCP, 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 indeep roots and in soils with higherDe. Increased IRCPin younger roots was related to the growth of rootsin soil volumes previously depleted by older roots.This increase in explored soil came from both the en-largement of each root unit and the continued lateralbranching of basal and tap roots. Our simulations in-dicated that the soil volume adjacent to the root crownwas thoroughly depleted and that the initial portion ofeach lateral root encountered intense competition withtheir parent roots.

IncreasingDe from 10−9 to 10−7 led to an ex-pansion of the size of the depletion volume and,consequently, to greater overlap between neighboringroots and to a higher IRCP. The IRCP for the youngerroots (120 h of simulation) was around 6.5%±SE0.5, average of the nine root systems atDe = 10−9,8.8%±SE 0.4 atDe = 10−8 and 19.7%±SE 0.8 atDe =10−7. These values increased substantially in theolder roots (simulation time = 320 h): atDe = 10−9

the IRCP ranged from 10.1 to 17.0%, and atDe =10−7 the intensity of competition varied between 48.9and 120.1%. Values higher than 100% mean that, onaverage, each portion of root is competing with at leastone neighbor root.

Shallow roots (i.e., root models 1 – 5 in Fig. 6)showed almost the same values for IRCP in the rangeof simulation time and diffusion coefficient studied.This group presented the smallest values of IRCP, sug-

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Figure 4. Phosphorus acquisition efficiency (total depletion volumeper unit of carbon invested in roots, including construction cost,respiration and exudation) as affected by root gravitropism and rootage. Three root systems were used: shallow (root number 1 in Fig.1), Carioca (root number 5) and deep (root number 9). Data shownas the mean± standard error of the mean (n = 4).

Figure 5. Overlapped volume of depletion zone of three root sys-tems as affected by root age. Three root systems were used: shallow(root number 1 of Fig. 1), Carioca (root number 5) and deep (rootnumber 9). Data shown as mean± standard error of the mean (n =4).

gesting that the shallower roots are more efficient thanthe deeper ones. For example, after 320 h growth andatDe = 10−8 the shallower root system had an IRCP of18.2%± SE 0.2 and Carioca 18.8%± SE 0.2. Thesevalues increased to 34.2%± SE 1.2 in the deeperroot system. Among deep roots (root models 6 – 9),there was a close relationship between gravitropismand IRCP, with deeper root systems having greaterinter-root competition.

The effects of gravitropism, root age andDe ontotal depletion volume had an opposite tendency thanon IRCP because: (i) all our simulated root systemshad the same total length, and (ii) in SimRoot the de-pletion volume before inter-root competition is a directfunction of root length. A graphical representation ofthe total depletion volume of Carioca is shown in Fig.

7. For roots at 320 h the total depletion volume in asoil with De = 10−9 was 97, 95 and 88 cm3 in theshallow, Carioca and deep root systems, respectively.At De=10−8 the values were 219, 218 and 191 cm3andatDe = 10−7 were 830, 805 and 557 cm3.

Effect of gravitropism on P uptake in soils withheterogeneous P distribution

Analysis of variance showed that root architecture sig-nificantly affected P uptake in homogenous and instratified soils (Fig. 8). With homogenous P distribu-tion, the shallower root system was able to capture15% more P than the deeper one. In our simulationsall the root systems had the same total root length andtherefore the same potential for depleting the soil. Thismeans that the observed effect of gravitropism in ho-mogenous soil can be ascribed to the lower IRCP (i.e.,lower depletion zone overlap) of the shallower rootsystems. In a stratified soil with greater P availabilityat the surface, the shallow root system absorbed 10 and34% more P than Carioca and the deep root system,respectively. In the heterogenous soil, the advantage ofthe shallow root system was related to both its lowerIRCP and to the greater concentration of root foragingin the soil layer with greatest P availability.

Verification

From the experiment we used for calibrating our sim-ulations of P uptake, growth parameters and P uptakevalues were available for beans growing under threesoil P levels (i.e., low, medium and high). We usedthese data to estimate the P supplying capacity forthe three different P levels. By using this coefficient,we observed that 2-week P uptake by bean plantsgrowing in the field followed the same pattern aspredicted P uptake (Fig. 9). There was statisticallygood agreement between observed and predicted P up-take (r2=0.75). We used these P supplying capacitycoefficients to simulated stratified soils.

Discussion

Two processes account for increased soil exploitationduring vegetative growth; first, root elongation, andsecondly, the enlargement of the radius of the deple-tion 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 increaseswithDe and also with the square-root function of time

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Figure 6. Inter-root competition for phosphorus (IRCP) of nine simulated root systems as affected by soil diffusion coefficient (De) and rootage. The root systems vary from shallow (root number 1) to deep (root number 9). See Fig. 1 for graphical representation of the different rootsystems.

(Fig. 2). In our simulations, a strong dependence oftotal depletion volume onDe was verified in all rootsystems. A novel perspective provided by our simu-lations is that root architecture and thereby depletionzone overlap modulates the magnitude and distributionof the exploited soil volume. One source of overlapvolume is generated by the intersection between newroot laterals and their parent roots after every newbranching event. This portion of overlap is an un-avoidable consequence of lateral branching. Only afterthe new root segment grows longer than the depletion

volume generated by its parent, will it enter potentiallyunexplored soil. Another factor influencing root over-lap is the branching pattern and root curvature. Theseroot traits determine the spatial arrangement of roots inspace, which includes the distance and overlap amongroot segments. Nielsen et al. (1994) analyzed the effectof branching patterns on the intensity of competitionand demonstrated that simulated bean roots presentedlower IRCP than a herringbone or dichotomous rootsystems. Fitter et al. (1991) observed that decreases ininter-branch distances could lead to decreases in ex-

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Figure 7. Graphical representation of the root system of Carioca bean plants (A) and the depletion volume for that root system atDe = 10−7

cm2 s−1 (B),De = 10−8 cm2s−1(C), andDe = 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 Pwith depth and the other has a heterogeneous distribution. Concentration of phosphorus in the soil solution in each soil type in the soil profile isshown. 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 23common bean genotypes were cultivated on a low P Oxisol (Sadeghian, 1991). 1:1 line is shown. Correlation coefficient (r2)=0.75.

ploitation efficiency. In the present work, to analyzethe effects of root curvature separately and to not con-found the effects of branching and root curvature, weheld the branching parameters of the simulated rootsystems constant.

As predicted by our first hypothesis, shallower rootsystems have lower IRCP. The dependence of IRCP onroot growth trajectories can be understood consideringthe three-dimensional arrangement of the root system.Because basal roots of common bean extend radiallyfrom the conjunction of the hypocotyl and taproot,they tend to disperse over time in root systems withlow gravitropic sensitivity, whose basal roots developclose to the soil surface. In deep root systems (e.g.,models 6 – 9), the stronger downward tendency ofthe roots led them to remain closer together and, in-deed, close to the tap root and its lateral roots. Thisresulted in a sharp increase in IRCP as root systemsbecame deeper (Fig. 6). In deep root systems, the av-erage distance among root components decreased andcompetition took place among basal roots, tap root andlateral roots from both basal and tap roots. We alsoobserved a strong dependence of IRCP values onDe,which indicates that competition among roots is notjust an inherent characteristic of root geometry, butalso has a close dependence on the surrounding me-dium, as represented by the differentDe values. Our

simulations suggest that the benefits of root systemshallowness for P acquisition are more important insoils with higherDe. HigherDe values represent awider radius of depletion volumes and a higher prob-ability that neighboring root segments overlap eachother. AtDe = 10−7 we found IRCP values higherthan 100%, meaning that the average unit of depletionvolume around the root cylinder is exploited by morethan two roots at the same time.

As expressed by the relationship between C ex-penditure in the root system and depletion volume,PAE is supposed to be inversely related with IRCP. Butwe observed that, despite the fact that IRCP showed aconsistent tendency to increase over time, older rootswere more efficient in P acquisition (Fig. 4). This over-compensation can be attributed to the increase of theradius of the depletion zone over time. Fig. 2 showsthat even in older root systems (i.e., 320 h) rootswere still actively increasing the radius of the deple-tion zone. Nevertheless, we predict that this increasein PAE turns into a decrease over time later on due toaccumulated carbon costs and the increasing influenceof IRCP.

Our data also support our second hypothesis thatdecreasing basal root gravitropism results in increasedP acquisition efficiency (PAE), especially in stratifiedsoils in which P availability is greatest in the topsoil.

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Many factors contribute to the concentration of soilP in upper horizons: (i) P in shoot residues returnsto the soil at the surface; (ii) fertilizer P applicationsare generally at or near the soil surface; (iii) soil Pavailability is typically greatest at the surface becauseof more favorable chemical, physical, and microbio-logical conditions; and (iv) the relative immobility ofP in soil retards P leaching. Considering these factors,shallow roots should be the most efficient in captur-ing soil P. According to our simulations, shallow rootsystems captured 34% more P than deep root systemsin a stratified soil with P concentrated in the topsoil.Shallow root systems were also able to capture more Pin a homogeneous soil; in this case the difference was10%. This means that shallower root distribution couldbe beneficial for P acquisition not only because of thespatial coincidence of roots and resources, but also be-cause of their lower inherent IRCP. These findings areconsistent with the work of Bonser et al. (1996), whoshowed that among a set of bean genotypes, those withshallower basal roots performed better in low P soils inthe tropics. On the other hand, because dry conditionsnear the soil surface are common in field conditions,mortality of fine roots in shallow root systems couldbe higher than in deeper ones (Espeleta and Eissenstat,1998). This factor could depress the efficiency of shal-lower root systems. Another disadvantage of shallowroot systems could be the lower ability for acquiringresources located lower in the profile, such as water.Thus in field settings, the utility of root shallownessmay depend on several interacting factors in additionto P availability and distribution.

Although the focus of this work was on P, it ispossible to extend the results of our simulations toother nutrients.De values found in the literature forammonium, potassium, and molybdenum are close tothose found for P (Barber, 1995).De for boron is usu-ally higher (around 10−6 cm s−1). Hence, its IRCPvalues would be greater, and the difference amongthe shallow and deep root systems would be greatercompared to that found for P. In the case of iron (Dearound 10−10 cm s−1), the overlap volume, IRCP andthe influence of root gravitropism on these paramet-ers would be smaller. The advantage of shallow rootsystems for P acquisition could not be extended tomass-flow nutrients, like nitrate, sulfate, calcium ormagnesium. In the case of nitrate, at root densitiesoften found in soil, the entire root zone is almostdepleted of nitrate unless replenished by nitrificationor fertilization (Jungk and Claassen, 1996). Becausenitrate supply to plants usually includes soil volumes

not included in the rooted layer, the incidence of rootarchitecture on the acquisition of this nutrient shouldbe smaller than for diffusion-limited nutrients.

Phosphorus acquisition capacity is enhanced inmost higher plants by mycorrhizal symbiosis. Externalhyphae can absorb and translocate P to the plant fromsoil outside the root depletion volume. Unfortunately,we are not aware of unambiguous data in the publishedliterature that would permit us to quantitatively estim-ate the influence of external hyphae on root depletionzones. However, in common bean, root architectureis related to P acquisition efficiency independently ofmycorrhizal effects (Bonser et al., 1996; Lynch andBeebe, 1995). We propose that this may occur be-cause of the concentration of hyphal P uptake nearhost roots. In other words, that a shallower root systemmay also have shallower hyphal foraging. This issuedeserves further research.

Most theoretical models of resource acquisitionnormally 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 unitdepth or volume, and three-dimensional distributionof roots or overlap among them are not consideredexplicitly. Here we show that root systems of the sametotal length but differing in architecture have an amplevariation in overlap volumes and IRCP, resulting invariation in P acquisition, indicating that root length isvalid only as a first approximation for describing rootcapacity for nutrient acquisition. The implications ofincorporating a nonuniform root distribution in suchmodels have not been explored yet, although severalthree-dimensional models of root geometry have beendeveloped to date (for references, see Introduction).Results from the present work and others (e.g., Sommaet al., 1998) suggest that the accuracy of these modelscould be notably enhanced by the introduction of anon-uniform root spatial distribution.

The overall picture emerging from our simula-tions is that root architecture plays a major role indetermining root deployment, soil exploration, andconsequently, the efficiency of nutrient uptake. A vari-able proportion of the root system is not active innutrient uptake due to overlap among soil volumesexplored by root segments of the same plant. It wasshown that IRCP increases as roots become older andas a consequence of increased root gravitropic sens-itivity and soil diffusion coefficient. The combinedeffect of these three factors resulted in a range of vari-ation in the IRCP values as large as 20-fold. There was

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little variation of IRCP in shallow roots but a sharpincrease in IRCP when root geometry becomes deeper(root systems 6 – 9). The soil diffusion coefficientgreatly modifies the intensity of competition amongroots, accentuating the effects of root gravitropism.Differences in root architecture also resulted in differ-ences in nutrient uptake as a result of the coincidencebetween root and soil nutrient location but also of thedifferent IRCP of the nine studied root systems. Inthis report we consider the overlap among roots of asingle plant. Root overlap also occurs among neigh-boring plants, which can compete among themselves.In a subsequent paper we will address this questionby analyzing IRCP and P uptake of simulated roots ofdifferent root architecture growing in competition.

Acknowledgements

The authors thank Kai Nielsen for allowing us to usehis unpublished data, Xiaolong Yan for valuable dis-cussions and Bob Snyder for technical help. Z Gethanks South China Agricultural University for a co-operative research leave. The research was financiallysupported by United States Department of Agricul-ture/National Research Initiative grant 97-35100-4456to J P Lynch.

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Section editor: A A Meharg