Rice root properties for internal aeration and ... - Wiley Online Library

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Rice root properties for internal aeration and efficient nutrient acquisition in submerged soil Blackwell Publishing Ltd.

Guy J. D. Kirk1,2 1

Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EA, UK; 2National Soil Resources Institute, Cranfield University,

Silsoe MK45 4DT, UK

Summary Author for correspondence: Tel: +44 1525863294 Fax: +44 1525863253 Email: [email protected] Received: 31 January 2003 Accepted: 7 April 2003 doi: 10.1046/j.0028-646x.2003.00793.x

• The characteristics of Oryza sativa roots required for internal aeration may conflict with those for efficient nutrient acquisition, particularly the surface area available for absorbing nutrients and the extent of oxygenation of the rhizosphere. • A model was developed for calculating the steady-state diffusion of O2 through a primary root and its laterals and the simultaneous consumption of O2 in respiration and loss to the soil. Results for a realistic set of parameter values were compared with available experimental data, and a sensitivity analysis given. • It was seen that a system of coarse, aerenchmymatous, primary roots with gas-impermeable walls conducting O2 to short, fine, gas-permeable laterals (i.e. the basic architecture of current rice genotypes) provided the greatest absorbing surface per unit aerated root mass. • With this architecture and typical rates of root respiration, rates of O2 loss to the soil can be sufficient to, for example, nitrify sufficient NH4+ to NO3− to allow a plant to absorb half its N as NO3−, as well as to oxidize toxins such as Fe2+. Key words: aeration, anaerobic soil, diffusion, ferrous iron, Oryza sativa (rice), oxygen, rhizosphere oxidation. © New Phytologist (2003) 159: 185–194

Introduction The study and modelling of plant adaptations to anoxia in submerged soils has a long history (reviewed by Armstrong et al., 1991, 1996). But to date, the relation between root properties for internal aeration and those for efficient nutrient acquisition has not received attention. This is important because the characteristics of roots allowing internal aeration may conflict with those for nutrient acquisition, particularly the need for a large absorbing surface per unit root mass and possibly the need to influence conditions in the rhizosphere. This paper develops a simple model to explore these questions, with emphasis on rice. The relevant root characteristics are as follows. As a root grows through submerged, anoxic soil, the cortex in the region of the base partially disintegrates forming continuous gas channels between the base and the tip. This both permits gas transport from and to the aerial parts of the plant and lessens the amount of respiring tissue per unit root volume.

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Altered respiratory processes may further reduce the O2 requirement in particular tissues, and low permeability of the root wall to gases as a result of thickenings and suberization lessens the loss of O2 to the soil. The structure of the root is therefore apparently dominated by the need for internal gas transport. But on the face of it, this structure may conflict with the needs for efficient nutrient absorption. The development of gas-impermeable layers in the root wall seems likely to impair the ability of those parts of the root to absorb nutrients, and the disintegration of the cortex might impair transport from the apoplasm to the main solute transport vessels in the stele, though evidence for this is uncertain (Drew & Saker, 1986; Kronzucker et al., 1998). A further characteristic of rice roots in submerged soil is the system of short fine laterals (1–2 cm long and 0.1–0.2 mm in diameter) that develop as branches along the primary roots. These are much less aerenchymatous than the primary roots (porosities of 1–2% compared with ≤ 50%) and they do not develop secondary thickenings in their walls to the same

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extent (Matsuo & Hoshikawa, 1993). They account for a small part of the root mass but the bulk of the external surface, and they are plumbed directly into the main water and solute transport vessels in the stele of the primary root. It therefore seems likely that the laterals are responsible for the bulk of the nutrient absorption by the root system and compensate for any impairment of nutrient absorption by the primary roots as a result of adaptations for internal aeration. The question arises: what combination of fine laterals and aerenchymatous primary roots provides the greatest absorbing surface per unit of root material? Not having impermeable wall layers and having a large surface area to volume ratio, the laterals will tend to leak O2 more rapidly than the adjacent primary root. A related question is therefore how the O2 budget of the root system is affected by the combination of primary roots and laterals. Armstrong et al. (1990, 1996) modelled O2 release from adventitious and lateral roots of the rhizomatous wetland species Phragmites australis, and found that for the appropriate combination of root types, properties and dimensions, and a large but realistic soil O2 demand, the ratio of O2 consumption in root respiration to that in loss to the soil was 13:1 for adventitious roots but 0.15:1, i.e. reversed, for laterals. Evidence for preferential loss of O2 from laterals in rice includes measurements of Fe oxide coatings on roots placed in deoxygenated agar containing Fe(II) (Trolldenier, 1988); changes in redox potential as roots grew across rows of Pt electrodes in anaerobic soil (Flessa & Fischer, 1992); and the abundance of methane oxidizing bacteria, which are obligate aerobes, along rice lateral roots in anaerobic soil (Gilbert et al., 1998). Although O2 leakage compromises the root’s internal aeration, some leakage is desirable for a number of purposes. These include oxidation of toxic products of anaerobic

metabolism in submerged soil such as ferrous iron (van Mensvoort et al., 1985); nitrification of ammonium to nitrate, there being benefits in mixed NH4+ –NO3− nutrition (Kronzucker et al., 1999, 2000); and mobilization of sparingly soluble nutrients such as phosphorus (Saleque & Kirk, 1995) and zinc (Kirk & Bajita, 1995) as a result of acidification due to iron oxidation and cation-anion intake imbalance. In some situations rates of nitrogen acquisition by rice in submerged soil are limited by the size and characteristics of the root system (Kirk & Solivas, 1997), so the pay-off between requirements for internal aeration and those for efficient nutrient capture is important. A further point is the extent to which the greenhouse gas methane, which is produced in large quantities in submerged rice soils, may be oxidized in the rhizosphere before it can escape from the soil via the root gas channels. Model calculations indicate that roots allowing greater gas transmission may suppress, rather than enhance, methane emission as a result of greater oxidation in the rhizosphere (Arah & Kirk, 2000). In this paper a simple model is developed to explore these questions, and the model is used to calculate maximum tolerable rates of O2 release from the root system and compare these with measured rates in different experimental systems. Theory Table 1 gives the nomenclature used. Structure of the root system Figure 1 shows the main features of the root system of rice growing in submerged soil. The root system and the biogeochemistry of the soil change rapidly during the initial

Table 1 Nomenclature Symbol

Meaning

Units

AR a DG FO 2 fG k LV LVL N [O2]G Rroot Rsoil Q r x WR θG ρ

Surface area of root capable of absorption Radius of root, subscripted L for laterals and P for primary Diffusion coefficient of oxygen in air Flux of oxygen across root surface Impedance factor for diffusion in cortical gas space Coefficient for distribution of laterals along primary root Length density of roots, subscripted P for primary roots Length density of lateral roots Number of primary roots per hill of plants Concentration of oxygen in the cortical gas space Rate of oxygen consumption in root respiration Rate of oxygen loss to soil Rate of oxygen consumption in root respiration Axial distance from base of root; subscripted as in Fig. 2 Radius of cylinder containing laterals Mass of root Root porosity Density of root tissue

cm2 primary root−1 cm cm2 s−1 mol cm−2 (root) s−1 cm cm cm−3 (soil) cm cm−3 (lateral root cylinder) mol cm−3 (gas space) mol cm−3 (root) s−1 mol cm−3 (root) s−1 mol g−1 (root) s−1 cm cm g primary root−1 cm3 cm−3 (root) g cm−3 (tissue)

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Fig. 1 Main features of a typical rice root system in submerged soil.

stages of plant growth and as soil reduction proceeds. But the picture given in the figure is reasonable from about the mid-tillering stage until flowering. The roots in the anoxic soil beneath the floodwater – soil interface, receiving their oxygen solely from the aerial parts of the plant, are considered. The distribution of primary roots beneath a hill of plants is approximately hemi-spherical with the individual roots randomly distributed with respect to the vertical and horizontal directions. Thus if there are N primary roots per hill, the length of primary roots per unit soil volume, LVP, at any distance r from the centre of the hill is: L VP(r ) =

dN /dr N = . dV /dr 2πr 2

Eqn 1

About each primary root there is a cylinder of laterals, increasing in density with distance from the root base as shown in Fig. 2. The laterals may develop up to sixth-order branches. A simple equation to describe this is: L VL (r ) = L VLmax

r2 (k + r )2

Eqn 2

where LVL is the length density of laterals in the cylinder of soil occupied by them, k is a coefficient, equivalent to the distance at which LVL(r) = 0.25LVLmax, and r0 < r ≤ rlat. If the cylinder has outer radius x and inner radius aP (i.e. the radius of the primary root), and x and aP are constant along the root length, then the total length density of primary and lateral roots at distance r from the centre of the hill is: L V (r ) =

N 2πr 2

 r2  2 2 1 + π x − a P L VLmax (k + r )2  .  

(

)

Eqn 3


Fig. 2 Idealized primary root and its cylinder of laterals. The parallel lines indicate the increasing length density of laterals along the primary root. The branching of the laterals is not represented.

Eqn 3 gives reasonable fits to measured profiles of LV with depth under field conditions using the parameter values given below (data not shown). Structure of an individual primary root and its laterals The internal structure of a primary root approximates three concentric cylinders corresponding to the central stele, the cortex and the wall layers. The porosity of the cortex, permeability of the root wall and the coverage of the root with laterals vary along the root length, with a much smaller porosity, more-permeable wall and no laterals in the region of the tip. Where the laterals emerge from the primary root, there are generally cracks in the epidermis a few µm wide and apparently directly connected to the primary root aerenchyma (Butterbach-Bahl et al., 2000). It seems likely these will be important in gas transfer, though there are no direct measurements showing this. Beneficial bacteria can evidently enter the root through such cracks, but pathogenic bacteria are somehow excluded (James et al., 2002). In practice leakage of O2 from the cracks and axial gradients of O2 within laterals will lead to gradients of O2 release along laterals. However, for the intended purpose of the model – which is to explore the

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Porosity

Length density of laterals

r2 < r < rmax r1 < r ≤ r2

0 0

rlat < r ≤ r1

θG2 θG1 – α(r − r1) θ − θG2 where α = G1 r2 − r1 θG1

r0 < r ≤ rlat

θG1

L VLmax

0

r2 (k + r )2

effects of root properties required for internal aeration vs those for nutrient absorption – an elaborate treatment of these effects is not necessary; it is sufficient that the loss of O2 increases with the density of laterals. A constant leakage along the length of laterals is therefore assumed. Figure 2 defines, for the purposes of the model, the distances at which the porosity of the primary root and coverage with laterals change, leading to four zones with properties summarized in Table 2. The porosity of the laterals is assumed to be the same as that of the primary root tip. The corresponding equations for the root mass and total surface area capable of absorbing nutrients in each zone are given in the Appendix. It is assumed that, because of the changes in wall permeability along the root, nutrients are only absorbed by the primary root in the zones beyond the laterals (rlat < r < rmax) and by the laterals. This is also the surface across which O2 leaks. Transport and respiration in the roots Transport of gases through the cortical gas spaces is solely by diffusion. A mass flow of air could occur if the O2 consumed in respiration was not replaced by an equal volume of gaseous CO2, the CO2 being much more soluble. However, Beckett et al. (1988) have shown that convection by this means will always be subordinate to diffusion in nonthroughflow systems and will only ever have a minor effect. Hence diffusion is the principal means of gas transport. Radial homogeneity in tissue respiration rates is assumed. In practice, there may be radial differences in respiratory demand and gas permeability resulting in radial oxygen gradients, and some plants can tolerate a degree of anoxia in the stele, substantially decreasing the oxygen requirement per unit root volume. Armstrong & Beckett (1987) show how this can be modelled. However, it has not been allowed for here, as to do so would unduly complicate the model. More important for the present purposes are the axial differences in respiration rates. As well as differences due to changes in tissue mass per unit root volume as the aerenchyma develops, there are differences due to changes in root function along the root. Hence the growing tip and the parts of the root actively absorbing nutrients have greater respiratory demands.

Loss of oxygen to the soil Oxygen is also consumed in loss to the rhizosphere. It is assumed that the primary root wall is completely impermeable to oxygen in the zone covered with laterals (i.e. r0 < r < rlat). In fact the wall is not completely impermeable in this zone, but as discussed in the previous section, it is sufficient to combine the resulting flux with that from the laterals. The sink for oxygen in the surrounding soil will vary in a complicated way with soil conditions and time. Oxygen is consumed in the soil in both microbial reactions, mainly fuelled by root-derived carbon, and nonmicrobial reactions, mainly with ferrous iron. The rates of O2 consumption in microbial and nonmicrobial reactions are often similar in different submerged soils under steady-state conditions (Howeler & Bouldin, 1971; Reddy et al., 1980; Kirk & Solivas, 1994). However, in the rhizosphere, microbial O2 consumption will tend to increase with time as root-derived carbon accumulates, whereas nonmicrobial consumption will tend to decrease as ferrous iron and other reductants are depleted. Hence the overall rate may be roughly constant. Differences across the root system will also tend to cancel each other (Kirk & Du, 1997). The declining O2 concentration in the root with distance from the base coincides with a declining root length density. So although the internal concentration of O2 will be greater towards the root base, the flux out of the root will not increase correspondingly because the external concentration will be greater as a result of the greater density of neighbouring roots leaking O2. Given these considerations, the additional complexity involved in allowing for differences in flux across the root system is unjustified and a constant flux from the laterals and the primary root in the zone beyond the laterals is assumed. Also a steady state is assumed to exist in which the flux of oxygen across the root base equals the net consumption in root respiration and loss to the soil. Hence the concentration profile through the root is constant over time, the concentration varying from atmospheric at the root base to near zero at the apex. This is realistic because the rate of root elongation is small compared with the rate of gas transport. The model calculates the maximum primary root length that can be kept aerated for a given set of root characteristics and external sink conditions. Equations for transport, respiration and loss The following equation describes the steady-state diffusion of oxygen through the root and its simultaneous consumption in respiration and loss to the soil: d dr

d [O2 ]G    DGθG f G dr  − R root − R soil = 0  

Eqn 4

where Rroot is the rate of consumption in tissue respiration and Rsoil the rate of loss to the soil, both on a per unit root volume


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basis. Rroot at a particular distance along the root is the sum of the respiration in the primary root and in any laterals emerging from it. Hence, if the rate of respiration per unit root mass is Q, R root = ρ(1 − θG )Q +

ρ(1 − θG2 )Q πaL2 π(x 2 − a P2 )L VL

. Eqn 5

πa P2

Likewise Rsoil at a particular distance is the sum of the rates of loss from the primary root and from the laterals. Hence, if FO is the flux across unit root surface: 2

R soil =

2πaPFO

2

πa P2

+

2πaL FO π(x 2 − a P2 )L VL 2

πa P2

.

Eqn 6

It is assumed that Q is independent of [O2]G until it reaches a very low value, below which it is zero (Armstrong et al., 1991). Boundary conditions At the root base [O2]G = [O2]G0 r = r0 and at the root apex [O2]G = [O2]Gmin r = rmax where [O2]Gmin is the minimum O2 concentration required for root respiration (≈ 30 nmol cm−3 (gas space)). Solution of the equations Eqns 4 to 6 were solved, subject to the boundary conditions, using standard numerical methods (Smith, 1985). Copies of the program for the numerical solution, written in Fortran, are available from the author. Distance steps of 0.01 mm were used; 10-fold smaller distance steps gave the same results, indicating that the solution is stable.

obic soil, and Kirk & Bajita (1995) obtained 1–2 pmol cm−2 (root) s−1 with the same experimental system but a soil with a smaller ferrous iron content. These calculations underestimate the total O2 flux because they do not allow for O2 consumed by rhizosphere microbes. Kirk & Du (1997) obtained values of 1– 4 pmol cm−2 (root) s−1 for rice plants grown in sand perfused with deoxygenated nutrient solution, and Bedford et al. (1991) obtained slightly smaller fluxes in a similar system but without sand. These measurements also underestimate fluxes for soil-grown plants because the external sink for O2 is smaller. But measurements in which an infinite external sink for O2 is provided (Sorrell & Armstrong, 1994) overestimate fluxes for soil-grown plants. In practice the external sink will depend on O2 consumption in both microbial and nonmicrobial processes, depending on such factors as the soil organic matter content, the reducible iron content, and the rate of water percolation through the soil. The standard flux is a realistic mean for different rice soils. The concentration of O2 in the gas space at the root base, [O2]G0, is that in air at s.t.p., 8.75 mol cm−3 (gas space).

Results and Discussion The model calculates the maximum length of primary root that can be kept wholly aerobic for given root dimensions, transport properties, respiration rates, coverage with laterals and leakiness to oxygen. The effects of the fraction of the primary root length covered with laterals (rlat /rmax) on the maximum primary root length (rmax) and on the total root surface area available for nutrient absorption per unit root mass (AR/WR) are presented. I also assess how much absorbing root surface the plant gets for its investment in sending O2 to the roots (i.e. the net O2 consumption in root respiration and loss to rmax

Standard values of parameters and coefficients The dimensions of the root system are taken from Matsuo & Hoshikawa (1993) and personal observations: aP = 0.5 mm, aL = 0.075 mm, x = 1.5 cm, LVLmax = 15 cm cm−3, k = 12.5 cm and ρ = 1 g cm−3. For the dimensions of a primary root: r0 = 2, rmax − r1 = 3 and rmax – r2 = 1 cm; astele = 0.25 and acortex = 0.47 mm, i.e. if 70% of the cortex is occupied by gas space, θG1 = 0.44 and θG2 = 0.095 cm3 cm−3 (root). The maximum θG in rice cultivars averaged over the primary root is about 0.5. For the gas transport properties of the root: DG = 2.07 × 10−1 cm−2 s−1 at s.t.p. and fG = 1 (Armstrong, 1979). For the rate of root respiration: Q = 6.5 × 10−6 mmol g−1 (root) s−1 at the root tip (and in the laterals) and 40% of this at r0 ≤ r < r2, falling linearly from the tip to r 2 (from Luxmoore et al., 1970; Armstrong et al., 1991). For the flux of O2 across root surfaces: FO2 = 5 pmol cm−2 (root) s−1. For soil-grown rice plants Begg et al. (1994) obtained fluxes of 1–12 pmol cm−2 (root) s−1, calculated from rates of Fe2+ oxidation near planar layers of rice roots in anaer-


the soil,

(Rroot + R soil ) ⋅ dr = QWR + FO AR). How these 2

r0

relations are affected by root transport properties, respiration rates and gas leakiness, are tested and comparisons with experimental data, where available, are made. Results for the standard parameter values Figure 3 shows that for the standard parameter values (i.e. porosity of cortex = 0.7; the effects of differences in porosity are discussed below): the maximum primary root length is 27.3 cm declining to 17.7 cm as the coverage with laterals increases from < 5–80% of the root length; although the maximum root length decreases as the coverage with laterals increases, the absorbing root surface per unit root mass increases more than 2-fold as the coverage with laterals increases from < 5–80%; and the net oxygen consumption in root respiration and loss to the soil decreases as the coverage with laterals increases above about 50%, in spite of the larger surface releasing oxygen.

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Fig. 4 Effect of cortical porosity and fraction of root covered with laterals on relations between (a) O2 consumed in root respiration and loss to the soil and (b) O2 consumed in respiration in the lateral roots and the primary root. The points for a given porosity correspond to different rlat/rmax values as in Fig. 3. Numbers on curves are porosities; other parameters have standard values.

Fig. 3 Effect of cortical porosity of primary root and fraction of root covered with laterals on: (a) maximum primary root length; (b) absorbing root surface per unit root mass; and (c) absorbing root surface per primary root as a function of net O2 consumption (as it varies with rlat/rmax). Numbers on curves are porosities; other parameters have standard values.

Root respiration is the main sink for O2, accounting for more than 30 times the O2 loss to the soil at the minimum coverage with laterals, though less than five times the loss to the soil at the maximum coverage with laterals (Fig. 4a). Respiration in the lateral roots exceeds than in the primary root by 4-fold at the maximum coverage with laterals (Fig. 4b). These values compare with ratios of respiration to loss of 13:1 in adventitious roots of Phragmites australis and 0.15:1 in laterals estimated by Armstrong et al. (1990) with a somewhat larger FO2 than here. The results broadly tally with experimental findings for rice. The maximum length of primary roots required to sustain a plant depends on soil conditions and planting density. Typically the depth to the plough pan in a puddled ricefield is less than 20 cm, and a typical spacing between plant hills is 25 cm × 25 cm, though this varies with rice variety, soil fertility and other factors. The maximum primary root length required to explore this volume of soil would be 26.7 cm, which is within the range calculated with the model. Note


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that some roots with a greater coverage of laterals could be shorter than this, exploring the soil at shallower depths. The rates of loss of O2 to the soil are also credible. If the radius of the zone of soil that O2 from a root reacts with is b, then the rate, M, of O2 consumption in this zone is: M = i.e.

2πaFO

2

π (b 2 − a 2 )

, b = a2 +

2aFO

2

M

.

Howeler & Bouldin (1971) found rates of O2 consumption by reduced soil cores exposed to atmospheric O2 of 100–1000 pmol cm−3 s−1, roughly equally distributed between microbial and nonmicrobial reactions. The soils had a range of organic C and reducible Fe contents. Substituting these values of M in the above equation together with the standard values of aL (= 0.075 mm) and FO (= 5 pmol cm−3 s−1) gives b = 0.28– 2 0.11 mm. For comparison, the mean mid-point between laterals is 1/ πL V , i.e. 0.73 mm for the maximum density of laterals. To give an idea of the significance of the flux of O2 to the soil, the amount of iron that could be oxidized outside the root can be calculated as follows. The amount of O2 released 2πaFO t 2 per unit root mass in time t is . Therefore, ρ (1 − θG )πa 2 because 1 mol of O2 oxidizes 4 mol of Fe2+ (O2 + 4Fe2+ + 10H2O → 4Fe(OH)3 + 8H+), the standard flux is sufficient to oxidize 0.53 mmol (Fe) g−1 (primary root dry mass) in 7 days, or 60 mg Fe(OH)3 g−1 (root dry mass) which is in the range typically found for plants growing in the field. Alternatively, to compare O2 fluxes on a per unit soil surface basis, the rates of loss per primary root (Fig. 4a) are multiplied by the number of primary roots per hill of plants and the number of hills per unit area, e.g. for N = 500 roots per hill and a hill spacing of 25 cm × 25 cm, the factor is 0.8 roots cm−2. Thus for FO AR = 0.2 nmol s−1, the rate of 2 release is 160 pmol cm−2 (soil surface) s−1. For comparison Howeler & Bouldin (1971) measured fluxes of O2 into unplanted cores of reduced soils exposed to atmospheric O2 at their surfaces of 10–100 pmol cm−2 (soil surface) s−1. Typically maximum rates of N uptake by rice crops are ≤ 5 kg h−1 day−1 (Peng & Cassman, 1998), or 40 pmol cm−2 (soil surface) s−1. Therefore if half the O2 released from the roots was used to nitrify NH4+ in the rhizosphere (NH4+ + 2O2 → NO3− + 2H+ + H2O), and half the NO3− produced was recovered by the roots, an O2 release of 160 pmol cm−2 (soil surface) s−1 would be sufficient to nitrify half the N absorbed by the roots. The results also indicate limits on rates of methane oxidation in the rice rhizosphere. Estimates of methane oxidation in the rice rhizosphere range from 5 to > 50% of the CH4 transported (Epp & Chanton, 1993; van der Gon & Neue, 1996; Arah & Kirk, 2000; Krüger et al., 2002). Studies of the growth rates of CH4-oxidizing methanotrophic bacteria


indicate that heterotrophs will out-compete methanotrophs for O2 except at very small O2 concentrations, less than a few µM (van Bodegom et al., 2001b). The activity of methanotrophs may also be limited by N availability in unfertilized rice soils (Bodelier et al., 2000). Rates of CH4 emission through the plant are typically ≤ a few tens of pmol cm−2 (soil surface) s−1 (Arah & Kirk, 2000; van Bodegom et al., 2001a). This range is therefore consistent with the above estimates of O2 flow through the roots. Effect of root transport properties Figure 3 shows that for a given θG, the greater the coverage with laterals the smaller is the primary root length that can be kept aerated but the larger the total absorbing root surface per unit root mass. As the coverage with laterals increases, the proportion of the primary root length capable of absorbing nutrients – and releasing oxygen – decreases, but the effect of this on the total absorbing surface is much smaller than the effect of the greater surface area of laterals (Fig. 3b). For a given coverage with laterals, with increasing θG the maximum length of primary root increases and the root surface per unit root mass also increases, though to a lesser extent. A longer more porous primary root means a greater proportion of the root mass will be present as laterals and the surface per unit root mass is correspondingly larger. Figure 3c shows that as the root porosity increases a given rate of O2 consumption by the roots produces a larger absorbing surface area, less O2 being consumed in respiration in the primary root. Effect of respiration rates Figure 5 shows the effect of the maximum root respiration rate, Q 0. As pointed out earlier, in reality there is some radial variation in Q across the roots, which the model does not allow for. The standard value of Q 0 used here is realistic for the region of the growing root tip and for laterals actively absorbing nutrients, but the decrease in Q with distance from the root tip may be greater than allowed for in the model. A decrease in Q 0 allows a greater maximum root length for a given rlat/rmax (Fig. 5a). But there is no effect on the absorbing surface per unit root mass (AR/WR); the changes in AR/WR with rlat/rmax for different values of Q 0 fall roughly on the same line (Fig. 5b). With increases in θG, as in Fig. 3, as rmax increases more of the root mass can be apportioned to laterals. But in the absence of changes in θG the relation between AR/ WR and rlat/rmax is fixed. Effect of flux of oxygen out of the roots Figure 6 shows the effect of the flux of O2 across the roots, FO . The range of FO values considered is realistic for roots grow2 2 ing in submerged soils (see earlier). Figure 6(a) shows how rmax for a given rlat/rmax decreases as FO increases in this range, and Fig. 6b 2

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Fig. 5 Effect of maximum root respiration rate (Q0) and fraction of root covered with laterals on: (a) maximum primary root length; (b) absorbing root surface per unit mass; and (c) absorbing root surface per primary root as a function of net O2 consumption (as it varies with rlat/rmax). Numbers on curves are value of Q0; other parameters have standard values.

Fig. 6 Effect of flux of O2 across root surfaces ( FO 2 ) and fraction of root covered with laterals on: (a) maximum primary root length; (b) absorbing root surface per unit mass; and (c) absorbing root surface per primary root as a function of net O2 consumption (as it varies with rlat/rmax). Numbers on curves are values of FO 2 ; other parameters have standard values.


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shows that there is no effect of FO on the relation between 2 AR/WR and rlat/rmax, as for the effect of Q 0 shwn in Fig. 5b. Figure 6c shows that at a high coverage of laterals, the O2 consumed in maintaining a given absorbing surface is larger at larger FO because loss of O2 from the roots (= FO AR) makes 2 2 a much larger contribution to the total O2 consumption (=QWR + FO AR ). But at a low coverage with laterals, the 2 reverse applies. At a low coverage of laterals, a low FO means 2 a long primary root and low AR and therefore a high QWR.

Conclusions • The model provides a coherent representation of the rice root system in submerged soil and simulates measured maximum root lengths and rates of oxygen release to the soil satisfactorily. • A system of coarse, aerenchmymatous primary roots with gas-impermeable walls conducting O2 down to short, fine, gas-permeable laterals provides the best compromise between the need for internal aeration and the need for the largest possible absorbing surface per unit root mass. This is the basic architecture of wetland rice root systems. • With this arrangement the roots can tolerate losses of O2 to the soil at rates sufficient to greatly alter the chemistry of the rhizosphere. For example, calculations here indicate sufficient NH4+ may be nitrified to NO3− in the rhizosphere to allow half the plant’s N to be absorbed as NO3−, in spite of denitrification losses, with consequent benefits to plant growth. • Attempts to modify the characteristics of the rice root system through plant breeding methods, must allow for the complicated interplay between adaptations for internal aeration and those for efficient nutrient acquisition, shown here.

Acknowledgements I am grateful to Bill Armstrong for his generous help with this paper.

References Arah JRM, Kirk GJD. 2000. Modelling rice plant-mediated methane emission. Nutrient Cycling in Agro-Ecosystems 58: 221–230. Armstrong W. 1979. Aeration in higher plants. In: Woolhouse HW, ed. Advances in botanical research, vol. 7. London, UK: Academic Press, 192–197. Armstrong W, Armstrong J, Beckett PM. 1990. Measurement and modelling of oxygen release from roots of Phragmites australis. In: Cooper PF, ed. The Use of constructed wetlands in water pollution control. Oxford, UK: Pergammon Press, 41–51. Armstrong J, Armstrong W, Beckett PM, Halder JE, Lythe S, Holt R, Sinclair A. 1996. Pathways of aeration and the mechanisms and beneficial effects of humidity- and Venturi-induced convections in Phragmites australis (Cav.) Trin. ex Steud. Aquatic Botany 54: 177–198. Armstrong W, Beckett PM. 1987. Internal aeration and the development of stelar anoxia in submerged roots. New Phytologist 105: 221–245.


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Appendix Mass of root and total surface of root capable of absorbing nutrients in each of the zones defined in Table 2 Zone

r2 < r < rmax

Mass

Absorbing surface area

rmax

rmax

ρ (1 − θG2 ) πaP2 ⋅ dr =

2πaP ⋅ dr =

r2

r2

ρ (1 − θG2 ) πaP2( rmax − r2 ) r2

r1 < r ≤ r2

ρ {1 − θG1 + α(r − r1)} πaP2 ⋅ dr =

rlat < r ≤ r1

2πaP ⋅ dr =

r1

ρ π aP2 {1 − θG1 − αr1)( r2 − r1) +

1 α ( r 22 − r 12)} 2

r1

ρ (1 −

− rlat )

rlat

2π aP ( r1 − rlat )

r1

ρ (1 − θG1)πaP2 ⋅ dr +

2πaLπ (x2 − aP2 ) =

r0

rlat

rlat

ρ (1 −

2π aP ( r2 − r1)

r1

rlat

rlat

r0 < r ≤ rlat

r1

2πaP ⋅ dr =

ρ (1 − θG1)πaP2 ⋅ dr = θG1) π aP2( r1

2π aP ( rmax − r2 )

r2

θG2 )πaL2π( x2

r0

−

aP2 )LVLmax

r2 ⋅ dr = ( k + r )2

2π aLπ ( x2 − aP2 )

ρ (1 − θG1)π aP2( rlat − r0 ) +

  1 1   ρ (1 − θG2 )π aL2π( x2 − aP2 )LVLmax rlat − r0 − k 2  −  k + r0    k + rlat  
