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V. The Influence of Configuration on Uptake

V. The Influence of Configuration on Uptake

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2. The Irlfluence of Root Hairs

As noted in Section IV, when c,, 4 co, most of the uptake is likely to

occur via the root hairs. Before evaluating the role of the hairs in uptake,

we need to know the time for which they continue to absorb nutrients.

Unfortunately such information is meager. Hairs may persist for long

periods in many species, but they do not necessarily continue to absorb

ions, as the walls of persistent hairs may thicken or even become lignified (McDougall, 1921). Root hairs generally collapse after a few days or

weeks, but in the Gramineae, and in the cereals in particular, the hairs

tend to persist, thin-walled hairs being found on all parts of the root

system. A recent report that the root hairs of barley, Hordeum vulgare

L., live for only 2 days (McElgunn and Harrison, 1969) should be discounted, as the roots were illuminated brightly and stained at hourly

intervals with neutral red, and this treatment kills cells in the barley root

(Patterson, 1941). In dicotyledons having roots that show extensive

secondary thickening -and these include the common pasture legumes

(Soper, 1959)-the root hair cells are lost together with the rest of the

epiderm as thickening proceeds, but in other dicotyledons the hairs may

persist for weeks or even months (Whitaker, 1923).

a . Qualitative Efects. The most important function of root hairs may

well be the maintenance of liquid continuity between water in the cell

wall and pore water in the soil. Main roots and laterals are far too wide to

occupy the narrow voids into which water menisci retreat as the soil

dries. Even those voids that can just be entered by hairs (radius = 5 p )

drain at a suction of only 0.3 bar. However, the hairs are more effective

than this value would indicate, as their walls secrete mucilage, and the

mucilage infiltrates into finer pores. The author has observed that more

mucilage is secreted when the soil is dry than when it is moist. Although

the existence of 3 “junction resistance” has not yet been established for

hairless roots grown in situ, a resistance of this kind has to be invoked to

explain the low ion uptake observed when roots are disturbed and pressed

back onto the soil (Clarke and Barley, 1968; see particularly their Fig. 7).

In addition to any effect that root hairs may have on junction resistance,

the significance of local alteration of the soil around the hairs needs to be

considered. Local changes in sorption characteristics resulting, for example, from pH shifts, or complexing with diffusible exudates or rhizosphere products, can set up diffusion gradients either toward or away from

the root. Wilkinson et al. (1 968) show how such effects can lead to local

jepletion of calcium independently of uptake.

b. Geometrical Efects. The geometrical effects of root hairs on nutri-



ent transfer lend themselves to mathematical description. The choice of

boundary conditions in published investigations has been highly arbitrary.

Bouldin ( I96 I ) treats the problem as though the hairs acted independently.

But the hairs are so closely spaced that, even in highly buffered soils,

the zones of depletion around individual hairs begin to overlap after about

a day. Further difficulties arise when the hairs are commensurate in

width with the soil granules, as bulk values of the transfer coefficients are

then unlikely to apply in the vicinity of the hairs.

One line of approach adopted first by Passioura ( 1 963) is to replace the

real root with a suitably defined equivalent cylinder of radius a , and to

consider transference within the composite cylindrical region bounded internally by the epidermal ring of radius r), and defined by r) -= r s a s r < @J.

In certain circumstances we can predict the influence of hairs on uptake with reasonable confidence. In particular, if the region occupied by

the hairs is exhausted in a time that is negligible compared with the period

of uptake under consideration, we can adopt the condition


where c' is the volumetric concentration of extractable forms of the element considered, and a = r) 1, where 1 is the length of the root hairs: and

define the uptake per unit length of hairless root as


and that of a root with hairs as

The above condition will hold for a lightly buffered ion, when the root has

a high propensity for uptake, and the flux through the soil is small. Nye

( 1 966) considers the nonconvective case Y = 0, for which an explicit

solution is available [Carslaw and Jaeger, 1959, p. 336, Eq. @)I. As one

illustration of his results we find that when r) = 0.02 cm, a = 0.1 cm,

k, = 1 X lop8cm2sec-l, andj= 1, the uptake over 1 week is doubled by the

hairs. A steady-state solution is readily obtained for Y > 0 [Gardner,

1965, p. 567, Eq. (49)], from which it can be seen that the influence of

the hairs diminishes as v increases.



In the cases that we have been considering, apart from the initial uptake, the flow of ions occurred solely from the bulk of the soil to the region

occupied by the hairs. At the other extreme we consider conditions in

which depletion occurs only within a thin shell of soil in close proximity to

the epidermal cells, and in which repletion is so slow as to be unimportant.

This may hold, for example, for the uptake of manganese from those

soils, in which uptake is thought to depend upon the “constant reduction” of insoluble MnOr (Passioura and Leeper, 1963). As hair growth

commonly increases the surface area of the outer epidermal walls from 2

to 10 times, the hairs are potentially influential in the uptake of such

nutrients. Their actual effect depends, however, on the extent to which

they grow through voids rather than on or in the soil matrix, so that

where a is now the radius describing the effective surface area of the root,

and S = g(t) is the rate at which the element is transferred to the root per

unit area of the surface so defined.

c . Experimental Studies. The presence of absorbed P and Sr in

root hairs has been shown directly with the X-ray microanalyzer

(Lauchli, 1967). Similar resolution does not appear to have yet been

achieved in studies of the depletion of soil around roots. Conventional

autoradiography can show the macroscopic pattern of depletion around

roots, and, following the observations of Walker and Barber (1961) on

the depletion of Rb, a variety of such patterns has been observed. As

noted above, great care needs to be taken in inferring conclusions about

uptake from observations of local depletion around roots. When there is

independent evidence of uptake commensurate with the depletion and

ion convection is small, the interpretation of depletion patterns is relatively straightforward.

Observations particularly pertinent to the root hair problem have been

made by Lewis and Quirk (1967),who worked with an acid soil known for

its high phosphate sorption. They showed that, after 5 days uptake, the

zone in which P was depleted around wheat roots had a clearly delineated

boundary that coincided with the tips of the root hairs. Moreover the

width of the zone changed little in the subsequent 26 days, and was little

altered by a 3-fold increase in the added phosphate: these observations

suggest that the width of the zone was governed chiefly by the length of

the hairs.

The chief difficulty in measuring the effects of the hairs on uptake is to

obtain a suitable control. Clearly what is required for comparison is a


18 1

hairless root in an equivalent physiological state; comparisons with hairless roots obtained by altering the conditions of the culture are of little

value as the roots may differ anatomically and physiologically in many

ways besides the presence or absence of hairs. Champion and Barley

( 1969) have shown that it is possible to grow roots along clay slopes with

and without penetration of the clay by hairs by controlling the mechanical

state of the clay. This approach may prove profitable in uptake studies.

In horizons where peds are highly developed, roots tend to be clustered

in the macrovoids. The peds are often coated with cutans; as certain

cutans are known to impede ion diffusion (Soileau et al., 1964), the question of whether or not root hairs are able to penetrate the surface of peds

has some significance for nutrition. Champion and Barley show that root

hairs are capable of penetrating moderately resistant, remolded clays,

and that they do not grow only in existing voids.

In describing the effects of root hairs on the uptake of exchangeable

ions, we may expect that in general k,, K , , will have one set of values in

the region 7 s r s a and a second set of values in the region r > a. Perhaps the most profitable approach to adopt, since we cannot measure the

values in the inner region directly, is to measure the bulk values of the

transfer coefficients together with the surface conductance a at r = 7 and

the uptake, Q. The required value of k, = K , may be found using a nonreactive ion, and the case k, # K , may then be examined using a reactive ion

having the same charge.



1 . Abundance

Under this heading we consider the problem of the minimum length of

root needed to meet plant demand for absorbed nutrients. For spaced

plants the relevant measure of abundance is length per plant; for closed

communities it is often more convenient to refer to LA,the length of root

under unit area of ground surface.

We deal first with the case in which there is no external resistance to

nutrient transfer. This is exemplified by uptake from well stirred solution, when the rate of uptake depends only on the conductance a and the

solution concentration C. In general, a increases with whole plant demand, and decreases as the plant approaches salt-saturation. The demand

per unit length of root can be varied either by amputating part of the plant,

or, with less physiological disturbance, by dividing the roots between a

complete solution and one lacking a specified nutrient. Following the

latter approach, Gile and Carrero (1917) found that the rate of uptake of



N , P, K, or Fe per unit weight of root by young maize plants rose to a

maximum as the proportion of roots being supplied was reduced. A maximum of this kind pertains to a specified value of C, and should be distinguished clearly from the maximum I/ found when supply is nonlimiting

(see Section IV). The 50-year-old experiment of Gile and Carrero needs

to be repeated using shorter uptake periods and a wider range of concentrations; but in the absence of more recent data we use their results to

obtain a crude estimate of the minimum length of roots required to meet

a given demand. If we assume that their maize roots had a specific length

of 5 x lo3 cm g-I (author's data for maize), the maximum rate of uptake

of nitrate measured by Gile and Carrero is equivalent to 4 peq cm-' sec-I.

The rate of uptake of N03-N by cereal crops in the tillering phase is

generally about 1 kg ha-' day-' (8 peq cmT2sec-'), so that, if there were no

external resistance, this supply could be maintained when LA > 2 cm-l.

This value is exceeded after 1 or 2 weeks growth of cereal crops, and by

the late tillering stage LA usually exceeds 200 cm-*.

Greater lengths of root will be needed to meet the plant nutrient requirement in the soil than in stirred solution, because the soil offers a resistance

to ion transfer, and because roots compete in depleting the soil. Moreover for most nutrients c is buffered at low vdlues. (We note, without

considering further here, that when convection brings ions to the root

faster than they can be absorbed, the resistance of the soil to back

diffusion serves to raise c at the root surface above the initial concentration.)

Subject to the physiological maxima described above, the maximum

rate of uptake from the soil that can be achieved by a root system can be

predicted by treating the roots as a perfect sink (condition of Eq. 16).

When the roots are spaced widely so that they act independently, their

steady rate of uptake subject to condition (16) is given by Gardner

[ 1965, p. 567, Eq. (49)].* To take one example: if c, = 1 me 1-', 7 = 0.02

cm, v,, = 1 X lo-' cm sec-I, k , = 1 X 10-6cm2sec-', O=O.l,andj= 1, then

Q = 0.17 peq cm-' sec-', and an uptake of N 03-N at the rate of 1 kg ha-'

day-' could be maintained when LA9 47 cm-'. In general, however, the

roots may not act independently, and in the next section we consider

what happens when they compete during uptake.

2. Densiry

The resistance offered by the soil to the transfer of ions depends not

only on soil transfer coefficients k,, K, etc., but also on the rooting density

Lv.Where the roots have a reasonably uniform propensity for uptake, we

*Incorrectly; the exponent in Gardner's Eq. (49) should be w/2?rDO.



may profitably define a radius of influence b (cm) as

The value of b in topsoils under dense crops or pastures is usually less

than 2 mm even when the root hairs are neglected: and, as mobile ions

can move rapidly through distances of a centimeter a day in moist soils,

roots are certain to compete strongly in the top soil.

a. Theoretical. Although the problem of transference to sets of competing roots may at first appear intractable, it can be solved if, following

Philip ( I957), we consider radial transfer in the hollow cylinder 1) s r s b for the present we ignore any effect of root hairs- subject to the condition

aclOr= 0,

r = b,

t >0

For v = 0 explicit solutions of Eq. (8) are available subject to condition

(21) above and to certain specified conditions operating at the root surface, r = 17 (Carslaw and Jaeger, 1959, pp. 334-339). For v > 0, Eq. (8)

may be solved numerically (Passioura and Frere, 1967).

To provide a concrete illustration of the effects of rooting density on

ion uptake the solution of Eq. (8) subject to condition (21) and the condition of constant conductance a defined by Eq. (12) has been evaluated

for u = 0, for specified values of k,, 8 , and 7 and t = 4 days. Remembering

that the value of LITin top soils under dense crops or pastures varies from

2 to 50 cm-2, it is apparent from Figs. 3a and 3b that when a> 1 X lops

cm sec-’ and j = 1, more than sufficient roots are likely to be present to

deplete the topsoil thoroughly and rapidly. When a < lopscm sec-I and

j 3 100 uptake is linearly related to L,. over all of the above range. This

suggests that plants with a low rooting density are likely to be susceptible

to deficiency of the less mobile nutrients and there is some evidence to

support this view (Cornforth, 1968). Transpiration (v > 0) tends to increase the rate of uptake at any given value of Lv,but this hardly affects

the generality of our conclusion for ions that are strongly buffered by

adsorption, as the solution concentration, and hence the convective

flux, of such ions is always small. Root hairs also tend to increase the rate

of uptake at given values of LIT.When effects of hairs are mainly geometrical they may be expected to displace the curves shown in Fig. 3 so as

to increase the rate of depletion. But the effects of hairs on competition

between neighboring roots are far less certain when local qualitative

changes in the soil occur. A given uptake may be satisfied, for example,

by the depletion of a relatively narrow shell of soil when the sorption









DENSITY (cm-2)













DENSITY (cm-*)


FIG.3 . The influence of rooting density L I .on the depletion of the labile pool. ( T o p ) for

cm sec-' and different buffering capacitiesj, (borrorn) for j = 10 and roots of

a =' 1 X

cm2 sec-'; t = 4 days;

different surface conductance a. v = 0 ; 7 = 5 x lo-' cm; k, = I x

6, = 0.2.

capacity is decreased by hair exudates. We can now see the importance

of the root hair problem outlined in Section V; its solution is needed

before we can describe the effects of rooting density on uptake with

greater realism.

b. Experimental. Although it is difficult to control the rooting density

precisely, a range of densities can be obtained with a variety of methods.

The main difficulty is to avoid confounding the density with changes in

whole plant demand or with the total supply.



If density is varied by amputating some of the roots, there may well be

an unknown compensatory increase in the conductance a of the remaining roots in response to the greater plant demand per unit length

of root. Insofar as variation in a is likely to accompany actual variation

in LIr,this is acceptable to the experimenter. Of more concern is the likelihood of compensatory growth, particularly in long-term experiments.

Provided not too many roots have been amputated, the relative growth

rate of the remainder increases so that there is little change in the absolute

rate of increase of root dry weight per plant (Humphries, 1958). When

amputation has been more severe the rate of increase in weight may decline, but, whether this happens or not, the remaining roots branch more

frequently and lateral elongation is enhanced. Because of the compensatory production of laterals rooting density in the amputated treatment rapidly overhauls that in the control and may even surpass it

(Brouwer, 1966).

An alternative approach adopted by several investigators is to vary the

plant density itself, or, in pot culture, the volume of soil per pot. Careful

interpretation is needed as the rooting density is now confounded with

the total supply per plant. Moreover, the rooting density near the base of

the plant remains relatively high on all treatments, even though the spaceaverage value differs between treatments. Following this approach,

Cornforth ( 1968) obtained results, which, despite the difficulties of interpretation mentioned, are indicative of the effects predicted theoretically

in the preceding section. Cornforth’s method was to vary the depth of a

nitrogen- and phosphorus-deficient soil in pots. His results for oats,


Root Concentration and Nutrient Uptake from Soil Columns of Different Depth

(Cornforth, 1968)

Soil depth (cm)



Root dry weight (g/l)

4,.(meq/l soil)

4,.(meq/l soil)


Root dry weight (g/I)

qS (medl soil)

q p (meq/l soil)











( P = 0.05)




0. I4

2. I








3 .O

0.2 I






0.1 I






Avena sativa, L., and kale, Brassica oleracea L., given in Table 111, show

that the uptake of nitrogen per unit volume of soil ( q Nwas

) independent of

rooting density for both plants, and this suggests that the deficient soil

was depleted thoroughly at all densities. In contrast the uptake of

phosphorus per unit volume of soil (qr) decreased as the rooting density

decreased, the relative reduction in qf. being less than the relative reduction in density, probably because of the associated increase in the total


A better method of controlling density, free from the above effects of

demand, supply, or compensatory growth, would be to divide the roots in

differing proportions between given volumes of labeled and unlabeled

soil having a common nutrient status. The author has been unable to find

published data, which include a record of rooting density, obtained by

such means.


I. Local Distribution

In Section V, B we treated the radius of influence as though it could be

specified by a single value. In fact b represents a mean of a set of values,

and we now consider effects that the nature of the local distribution may

have on uptake at any given rooting density.

Though quantitative data are lacking, local aggregation (clumping) of

roots is likely to be common, particularly if soil peds are strong, when the

roots tend to follow the larger voids (Edwards er al., 1964). Underdispersion might be expected due to local depletion of the less mobile nutrients

in the zones around the earlier formed roots. However, the pattern resulting from competition is not simple and depends on the scale of observation. Competition may even give rise to fine scale aggregation, owing to

younger roots growing preferentially in the gaps left vacant between the

regions depleted by the older roots [compare with the whole plant distributions described by Pielou (1960)l. As noted in Section 11, A, the intercepts made by roots of any particular component in a mixture can be

identified with autoradiography after labeling the tops of the component

with a readily translocated radioisotope. In a two-component mixture,

departures from random association can be detected by finding the freunquency of nearest neighbor pairs in the possible classes (labeled

labeled -:

--) and applying a x2 test (Pielou, 196 1). In this

way Litav and Harper ( 1 967) examined the local mixing of the roots of

two component mixtures of cereals and of a mixture of oats and peas.

The null hypothesis of random mixing was tenable except when nitrogen

++, +-, -+,




was applied to the leaves of one component. This led to undermixing.

Undermixing also occurs when substances exuded from the roots of one

plant inhibit those of its neighbors; this is known to occur in guayule

(Parthenium argenratum A.) (Bonner, 1946). Overmixing might be expected if the roots of one plant make the local environment more favorable for those of another. This may occur, for example, when a nodulated

legume and a grass are grown together, although, as noted above, Litav

and Harper found no evidence of this in a mixture of peas and oats.

In the absence of any published account, a highly simplified theoretical

outline of the influence of the local distribution of roots on ion uptake is

given below. We treat the problem as two-dimensional and consider

radial transfer to a root of radius r).

For any given set of roots a region of influence may be associated with

any particular root by describing the area containing all points of space

nearer to that root than to any other. When the centers of the roots are

distributed randomly so that they constitute a Poisson field of points, the

regions so defined are “Voronoi” polygons with a mean number of six

sides (Miles, 1970). The area variance of the Voronoi polygons is given

by Gilbert (1962) as 0.280 m-2, where m is the number of points (root

axes) in unit area. For each polygon so defined we substitute a circle of

equal area having radius Bi.For a random distribution of roots the variance of Bi is obtained immediately from the area variance given above.

Higher order moments were not known to the author, but direct measurement of the areas associated with a sample of 300 points showed that the

distribution of Bi fitted a gamma distribution. In addition, a slightly skewed

distribution of Bi was obtained, without altering the mean and with only

a negligible change in variance, by applying the transformation

where Bi = skewed value, Bi = gamma value, 4 = constant, s2 = variance

of the gamma distribution, a n d 3 = mean of the gamma distribution.

As in the density problem we consider the region r) 6 r c Bi and solve

Eq. (8) subject to boundary conditions (12) and (21) for a suitable range

of values of Bi. The uptake Qi for each value of Bi is then multiplied by

the appropriate frequency, and finally the total uptake is found by


The nature of the distribution might be expected to exert its greatest

influence at intermediate values of the density m and buffering capacity j.

A range of parameter values corresponding to 0.2 6 m C 2, 1 S j 6 1000



was examined in terms of the model outlined above. The rate of depletion

did not differ by more than 5% between the most efficient (regular) and

the least efficient (4 = 1.5) distribution.

It would be interesting to examine uptake by more highly aggregated

sets of roots, but the model is unsatisfactory when the centers of equivalent circles deviate widely from those of the corresponding polygons.

Moreover, real roots have hairs, and, when the roots are aggregated,

overlap between the regions penetrated by the hairs of neighboring roots

becomes important at relatively low densities. For the random distribution the probability of overlap has been derived by Roach, 1968, Eq. (4.1)

and is given by



1 - exp [-47rm(r)

+ fj2]


If r ) + f = 1 mm the hairs of one fifth of the total number of roots overlap

when m = 2.0 cm-2.

Several investigators have varied the local distribution of roots by

growing plants in pots filled with resistant peds of coarse or fine size.

Results are difficult to interpret as local distribution has invariably been

confounded with rooting density, owing to differences in growth in the

two grades of peds. As expected, the uptake of the most mobile ions

(NOs-, C1-) is little altered by ped size, the soil being depleted rapidly

whatever the ped size (Wiersum, 1962).

2. General (Macroscopic) Distribution

Gross genotypical differences in the distribution of roots are often of

considerable ecological or agronomic significance. One example is pcovided by the history of pasture development on the “Ninety Mile Desert”

of south eastern South Australia. In this region, which owes its name not

to low rainfall but to dearth of nutrients in the sandy soils, depauperate

scrubland has been converted to productive pasture by applying superphosphate together with trace amounts of copper and zinc salts and introducing exotic species. The pastures were at first based on subterranean

clover, Trifolium subterraneum L. The residual value of the applied

phosphate is high, but, when the superphosphate is withheld after several

annual applications, the clover soon exhibits sulfur deficiency. If lucerne,

Medicago sativa L., is grown instead, sulfur deficiency does not arise

(J. K. Powrie, unpublished data). Most of the applied sulfate is leached

from the topsoil during the winter, and it accumulates at 4 m in the deeper

sands. This is well below the clover roots, few of which penetrate below

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V. The Influence of Configuration on Uptake

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