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II. Geometrical Description of the Root System
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
Lv = 2m
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
THE CONFIGURATION OF THE ROOT SYSTEM A N D NUTRIENT UPTAKE
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,
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
K. P. BARLEY
work reflects attitudes set at a time when only coarse and arduous
methods were available.
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.
Order of root
1st order lateral
2 x 10-2
2nd order lateral
1 x 10-2
3rd order lateral
No. per cm of root
of next higher order
Length (cm) per
C.C. of soil
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
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,
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
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
Values of Lv (Root Length per Unit Volume of Soil) for Plants in the Field
Cereals (oats, rye, wheat)
Tea (Camellia sinensis)
Source of data
Dittmer (1938); C. Walter
Torssell et al. ( 1968)
Pavlychenko ( I 942)
Dittmer ( I 940)
Barua and Dutta (1961)
Bowen ( I 964)
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.
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
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,
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.