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II. Geometrical Description of the Root System

II. Geometrical Description of the Root System

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162



K. P. BARLEY



composite samples can be prepared from sample cores in the conventional

manner. There is no need to remove foreign material from the separate

unless root weight or composition is also required. Total root length and

the length of hair-bearing root may be recorded separately using a twochannel counter, the latter quantity being of particular interest when

lengths are correlated with nutrient uptake.

The local distribution of roots can be described by locating root intercepts on polished sections of the soil, the sections being made at randomly chosen loci in the direction of the principal planes of symmetry of

the root system. In an early study, Fitzpatrick and Rose ( 1 936) counted

the ends of roots protruding from the faces of soil cores. More recently

the method has been refined by the use of polished sections and low

power microscopy (Barley and Sedgley, 1961; Melhuish, 1968). The

nature of the distribution -random, under-, or overdispersed -can be

ascertained by measuring distances to the nearest and successive neighbors, the distribution of neighbors of all orders being related to the xz

distribution (Thompson, 1956).

When polished sections are prepared for examination of the root distribution, root length can be estimated from counts of the number of roots

intercepted. The theory of random lines in three-dimensional space shows

that, when numerous straight lines intersect unit cube, the mean length of

the secants is 2/3 (Kendall and Moran, 1963, p. 76). If we represent roots

by straight segments meeting at bends, then, provided the individual segments within a given volume of soil can be considered to be located and

oriented at random, so that the intercepts which they make with each

principal plane are distributed at random, it follows easily from the above

result that

Lv = 2m

(2)

where Lv(cm-2), the rooting density, is the length of root per unit volume

of the soil, and m (cm-2), is the arithmetic mean of the number of root axes

intercepted per unit area of plane for the three principal planes. In practice

(2) provides a useful estimate of Lv for well established'root

systems in uniform soils (Melhuish and Lang, 1968). Where the root disstribution is markedly anisotropic, as in the early seedling stage when the

main roots and first-order laterals are growing geotropically, or in coarsely

structured soils, Lv can be found from the anisotropy and the sum

mI mII mrrIfor the three principal planes (Lang and Melhuish, 1970).

As noted in Section I a key item of information needed in uptake studies

is the apparent path-length for the transfer of nutrients to a set of roots.

Usually we wish to know the volume fraction of the region containing a



m.



+ +



THE CONFIGURATION OF THE ROOT SYSTEM A N D NUTRIENT UPTAKE



163



nutrient that lies within any given distance of the root network in that

region. The probability distribution dPld6 of the distance 6 from random

points of origin to the nearest point of contact with slender, straight rods

distributed randomly in three-dimensional space has been derived by

Ogston ( 1958), Eq. ( 1 2). Provided that the root segments are randomly

located, we can employ Ogston’s solution, and, by integration,



where E6
part of the root of radius 77, and 6 is the number of segments per unit

length of root that meet in acute bends. In deriving dP/d6 Ogston assumed

that all orientations of rods were equally likely, however, Eq. (3) remains

valid where the angular distribution is anisotropic -for one example see

Giddings et al. ( I 968). The fraction of the soil within the zone penetrated

by the root hairs may be obtained by setting A = I , where 1 is the length

of the hairs. We note that the volume occupied by the axial part of the

roots ( T L I $ ) and the weighted mean values of v2 and q3 are small; roots

rarely occupy more than 2 per cent of the volume of the soil.

Root lengths separated from the soil or root intercepts located on sections may be identified with an individual plant, or with a given component

in a mixture, by labeling the tops of the chosen plant or component with a

readily translocated radioisotope one or two days before sampling. After

separation or sectioning, the labeled roots are found by autoradiography

(Nielson, 1964). This approach may also help to distinguish living from

dead roots. Ueno et al. ( I 967) took the presence of I4C in a root, after

labeling the tops of a plant, as evidence of the viability of the root.

Related methods have been developed to provide an indirect measure

of the volumetric distribution of living roots within the soil (Racz et al.

1964; Russell and Ellis, 1968). The tops of the plants are labeled with a

readily translocated radioactive tracer, and after a lapse of one or two

days soil samples are assayed directly without the roots being separated.

Use of an energetic gamma emitter such as 86Rbenables the assay of large

soil samples. Although the isotope tends to concentrate in the root apices,

and a little may be lost to the soil, comparisons of relative root weights in

different zones determined indirectly with “Rb and directly by washing

the roots free from soil show that good agreement can be obtained (Ellis

and Barnes, 1968).

I t is apparent from the above remarks that efficient methods are now

available for the measurement of rooting density and distribution on a

fine scale. The lingering neglect of root system geometry in agronomic



164



K. P. BARLEY



work reflects attitudes set at a time when only coarse and arduous

methods were available.



B. PRINCIPAL

GEOMETRICAL

FEATURES

The primary root originates from the radicle in the embryo, and in

dicotyledons the primary root and its laterals constitute the entire root

system. In monocotyledons, the primary root, and any other seminal roots

belonging initially to the embryo, are generally supplemented with

adventitious roots that arise from the basal nodes of the stem. In

tillering species of Gramineae the adventitious root system becomes

prominent after the onset of tillering. In perennial grasses the primary

root system may be lost completely after the first growing season.

Young seedlings have a simple root system consisting of one or more

unbranched roots, but as growth proceeds primordia develop in the pericycle of the main roots and give rise to first-order laterals. The firstorder laterals in turn produce second-order laterals, and laterals of third,

fourth, or even fifth order may be produced. Numerous fine root hairs

arise as protuberances on epidermal cells toward the proximal end of the

zone of elongation on main roots and laterals, and grow out into the soil.

The constituent parts of the root system are shown schematically in Fig.

1, together with data describing typical dimensions and abundance in

top soils under well established cereal crops.



t.

Order of root

Diameter (cm)



Main

5x16'



1st order lateral



2 x 10-2



2nd order lateral



1 x 10-2



3rd order lateral



5x



d

Root hair

1



No. per cm of root

of next higher order



-



2



1



5x 16'



iX1o3



Length (cm) per

C.C. of soil



1



5



2



5x 16'



I x~03



FIG. 1. The constituent parts of the plant root system. The geometical data pertain to

roots of cereals in topsoils.



THE CONFlGURATlON OF THE ROOT SYSTEM A N D NUTRIENT UPTAKE



165



The main roots and laterals have a meristematic region just behind the

root cap in which new cells are produced continually by division. The

new cells enlarge chiefly in the axial direction, pushing the growing tip

and cap forward into the soil. In uniform soils having properties favorable to growth, the main primary or adventitious roots elongate at

speeds ranging from 0.5 to 3 cm day-’ or more to attain lengths of 1-2 m.

Laterals elongate less rapidly than the subtending main roots, their speed

and ultimate length generally decreasing with increasing order of branching (May et al., 1965). The frequency of branching of laterals varies commonly from 0.5 to 5 per centimeter of subtending root, the frequency

being low on laterals of high order (Dittmer, 1938).

The root hairs generally attain a length of 0.5 to 1.5 mm within 1 day.

Under exceptionally favorable conditions each epidermal cell may produce a hair (Cormack, I944), but in many species, even under good conditions, hairs are produced only by alternate cells in each epidermal file.

In less favorable conditions the proportion of cells giving rise to hairs

may fall to 1 in 10 or less. The diameter of root hairs ranges from 5 to 20

p in different species (Dittmer, 1949). They are generally spaced at intervals of the order of 100 p, the number per square millimeter of root ranging from 50 to 500.

The main primary root of dicotyledons is generally orthogeotropic,

tending to grow vertically downward in response to gravity. The main

seminal and nodal roots of grasses also follow a preferred path with respect to gravity, but the angle to the vertical -“liminal” angle-differs

widely among species and cultivars, ranging from 10” to 80”. First-order

laterals grow at an obtuse angle to the subtending main root and usually

at a high liminal angle for at least several centimeters; then they may turn

to follow a more downward path. The bigger roots of widely spaced plants

generally radiate around the base of the plant (see, for example, Fig. 60b

of Kutschera, 1960), a preferred direction of growth tending to be maintained despite local deflection of the tip due to the heterogeneity of the

soil (Wilson, 1967). But the roots do not always radiate around the plant;

for example, in cultivars of wheat, Triticum aestivum L., the horizontal

component of the path taken by the seminal roots tends to be oriented in

the direction of the geomagnetic field (Pittman, 1964). Higher-order

laterals follow a more or less random path in finely structured soils,

ramifying among the granules for a few centimeters, and so filling in the

pattern blocked out by the main roots and first-order laterals.

In homogeneous, penetrable soils, root system patterns generally

approximate well defined forms, such as hemispheres, shallow or deep

cylinders, cones, inverted cones. But the patterns are often distorted,



166



K. P. BARLEY



the effects of mechanical heterogeneity on a macroscale being particularly

marked (Greacen et al., 1968). Heterogeneity in the supply of materials,

produced for example by fertilizer placement or by uptake by competing

plants, also has a strong influence on the distribution, particularly on the

local abundance of laterals and root hairs.

The extensive investigations of Weaver (1 920, 1926) and Weaver and

Bruner (1927) in North America, and Kutschera (1960) in Europe provide a wealth of qualitative data on interspecific differences in the form of

the root system. Wide differences may also be found within a species.

Jean (quoted by Weaver, 1926) showed that in Pisum sativurn (L) root

depth, like stem height, is simply inherited. Kiesselbach and Weihing

(1938) found that the root systems of corn hybrids tended to be more

extensive than those of their selfed parents. Currently there is considerable agronomic interest in the question of whether dwarf or semidwarf

varieties of cereals root as deeply as do standard varieties (Stickler and

Pauli, 1961).

As we are usually interested in relating data on root abundance and

distribution to uptake patterns, it is unfortunate to find that almost all

the quantitative data published have been expressed gravimetrically.

“Root weight” data are notoriously unreliable because of contamination

with mineral soil and foreign organic matter; moreover, most of the weight

is contributed by main root axes, whereas laterals generally account for

most of the length of root and probably for most of the uptake (see Section

IV). In many biennial and perennial dicotyledons, particularly, root

weight means little in relation to uptake, as most of the weight consists of

“fleshy” parenchymatous roots that act as organs of storage.

The value of root length per unit volume of soil Lvunderwell established

crops or pastures decreases with depth, the order of magnitude (cm-*)

ranging from 10 in topsoils through 1 at 0.5 m to 0.1 at 1 m depth. Lower

values are obtained when roots have been washed from large blocks of

soil with jets of water as finer laterals are usually lost in such procedures.

Deep-rooted plants frequently sustain Lv values approaching 1 cm-* to

depths of 1 m. Little is known about the variation of Lv with distance

measured horizontally from the base of widely spaced plants, though

Evans (1 938) data provides some indication. Under dense plant cover the

lateral spread of the individual root system is often small (see Fig. 3 of

Nielson, 1964), and, except near the base of the plants, there may be little

systematic horizontal variation in Lv.Values of Lv obtained with reliable

methods are shown in Table 1. Less information is available on the root

length per unit area of ground surface LA,as few investigators pursue

roots throughout their depth. Values range from 50 to 500 cm-’ for field



THE CONFIGURATION OF THE ROOT SYSTEM A N D NUTRIENTUPTAKE



167



TABLE 1

Values of Lv (Root Length per Unit Volume of Soil) for Plants in the Field

~



Species

Herbs: Gramineae

Poa pratensis

Cereals (oats, rye, wheat)



Herbs: Non-Gramineae

Siylosanthes gracilis



Depth

(cm)



L I’

(cm-’)



0-15



50

5-25

4

2



0-15

25-50

75-100



0-10



40-50

90- 100

Medicago sativa

Glycine max

Woody plants

Tea (Camellia sinensis)



Pinus radiata



0-10

0-15



0-2.5

45-47.5

68.5-70.0

0-8

25-45

91-106



30

3



Source of data



Dittmer (1938)

Dittmer (1938); C. Walter

(Unpublished data)



Torssell et al. ( 1968)



1



20

4



Pavlychenko ( I 942)

Dittmer ( I 940)



4

1

0.5



Barua and Dutta (1961)



2

0.8



Bowen ( I 964)



0.4



crops, and values as great as 3000 cm-1 have been reported for perennial

grasses (Newman, 1969).

The great abundance of roots in topsoils under established crops or

pastures needs to be emphasized strongly. In the author’s laboratory

values of LV ranging from 30 to 50 cm-1 have been found repeatedly in

the top 10 cm of grassland soils. In their examination of the density of

root intercepts on polished sections of a sandy loam, Barley and Sedgley

(1961) found that the roots of Italian ryegrass, Lolium rnultiflorum Lam.,

were remarkably closely spaced. The half distance between axial parts

of neighboring roots - those occupying contiguous polygons -was only

1.5 mm at 2 cm depth. Abundant root hairs reduced the distance between

the roots to even smaller values.

111.



Nutrient Transference in the Soil



The processes by which nutrients are transferred through the soil to

plant roots -diffusion, and convection with or without a significant degree

of dispersion-have been described in detail by S. R. Olsen and Kemper



168



K. P. BARLEY



(1968). Here we comment on several salient points and state the relevant

differential equations in order to define generalized terms and symbols.

It has been shown empirically that nonconvective transfer of ions and

salts in the soil can be described by diffusion equations (Patil et al., 1963;

Phillips and Brown, 1964), and we may profitably define the diffusive

conductivity for anions, cations, or salts by



f = -k, Bdcldr,



u =0



(4)



+



wherefis the flux density in the r direction (moles cm-2 sec-l), k, is the

diffusive conductivity (cm2 sec-l), 8 is the volumetric water content (we

assume that the soil is isotropic), c is the concentration of the substance in

a suitably defined equilibrium solution (moles cmP3),r is the radial distance from the axis of the root (cm), v is the apparent velocity of water

through the soil (cm sec-l).

When diffusion and convection occur simultaneously, solutes undergo

hydrodynamic dispersion, and this tends to accelerate transfer down concentration gradients. In published theories it is assumed that dispersion

is unimportant at the rates of water flow found around plant roots, so

that diffusive and convective fluxes are additive. However uncertainty

still exists about the actual values of v around the roots, and about

the significance of dispersion, particularly when the flow is radial. When

dispersion is unimportant we may write



In the absence of sources or sinks, we find from Eq. ( 5 ) and the continuity requirement, a(c6)lat = -div f, that



Most ion species react with the soil during transference. When the reaction can be regarded as being instantaneous and reversible -this

assumption is tenable for readily exchangeable ions -and provided there

are no other sources or sinks,



where y = dc'/dc is the slope of the reaction or adsorption isotherm and

c' is the concentration of all labile (reactable or exchangeable) forms of



the substance considered per unit volume of the soil.



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