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CHAPTER 5. MODELING CROP ROOT GROWTH AND FUNCTION

CHAPTER 5. MODELING CROP ROOT GROWTH AND FUNCTION

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114



BETTY KLEPPER A N D R. W. RICKMAN



activities of specific root pathogens. This chapter describes some of the

ideas and approaches that are being taken in developing root growth

models for incorporation into ecosystem-level crop models.



II. EARLY MODELS

Most early root growth models were developed to provide a “root sink”

to absorb the soil water or nutrients lost from the soil profile. They contained little specific information on the root system itself.

If one assumes that root length density profiles can be used to express

the root sink, then one appropriate model has been a simple exponential

distribution of roots with depth (Gerwitz and Page, 1974). This empirical

model is sufficient for many crops and gives a simple mathematical formula

to calculate the root sink activity at any soil profile depth. However, under

management with intermittent rainfall, such models do not predict observed root profiles. For example, Fig. 1 shows the root length density

profile for cotton roots in soil profiles that were either well watered or

allowed to dry (Klepper er al., 1973). An exponential decrease of roots

with depth would describe fairly adequately the roots in the wet profile, but

not in the dry one.

Unfortunately, root sink activity is not always proportional to the root

length density profile (Reicosky et al., 1972), making it difficult to provide

root data appropriate for use in water uptake models. The lack of agreement of observed rooting with a macroscopic (root sink) description of

root function and the additional lack of fit with empirical exponential root

distributions have led to the need for describing root systems at the microscopic level. The first attempts at the microscopic approach presented the

root as a cylinder surrounded by a concentric cylinder of soil. Root length

density was obtained from root observations or empirical distributions

with depth and various estimates of water or nutrient uptake were computed using appropriate diffusion coefficients.

The level of our knowledge of root systems is such that we no longer

have to resort to direct measurement or to these empirical models to

provide estimates of root length density changes to local soil properties.

Researchers have proceeded to generate biologically based models that

account for root physiology. Some of these models allow computations of

root growth and decay to respond dynamically to shoot physiological

activity and to changing soil conditions at different depths in the soil profile

(e.g., Huck and Hillel, 1983).



MODELING CROP ROOT GROWTH AND FUNCTION



115



ROOT DENSITY ( cm/cm3)

0.0



n



0.6



W



x

!3

a

w

n 1.2

July



1.8

1



I



I



We1 I - w a t e r e d



I



I



I



Profile



I



Drying Profile



FIG. 1. Root length density profiles for cotton plants in well-watered and drying soils.

After Klepper et d.(1973).



Ill. DESIRABLE MODEL FEATURES

Figure 2 shows the desired output from a root growth model for use in a

model of root function. The top panel of Fig. 2 shows the time-averaged

root length densities for each depth for a month during the growing season.

These data come from a drying experiment on cotton (Gossypiurn hirsuturn) at the Auburn Rhizotron (see Table 5 of Browning et al., 1975).

In the rhizotron, nondestructive root counts on glass viewing surfaces

were made every other day. From the slopes of these graphs in Fig. 2

we can calculate that the average daily change rate over all depths was

0.0081 m.m-3.sec-' (0.07 ~ m . c m - ~ . d a y - ' ) ; it ranged from 0 to

0.028 m.m-3.sec-' (0.24 ~ m . c m - ~ - d a y - ' )For

. a 0.1-m depth increment

under 1 m2 of land surface, this result means that an average change in

length of 70 m of root per day was detectable by the nondestructive



116



BETTY KLEPPER AND R. W. RICKMAN



!iiV

DAY 6



DAY 16



DAY 26



RLD (crn/crn')

RLO (crn/crn')

RLD (crn/crn')

0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5



0 120

W

a

150



180



FIG.2. Root length density at five depths over a 30-day period in the growing season. Data

are from Browning et a / . (1975).



techniques used in this rhizotron experiment. The line graphs (Fig. 2,

bottom) shown for three dates in the growing season represent the usual

sampling frequency of the most intensive field trials (every 10 days). These

data illustrate the inability of such infrequent sampling to capture root

growth rates for model validation. The figure demonstrates the necessity

of frequent sampling to calibrate and validate root growth models.

Designation of the spatial arrangement of roots with respect to the crop

row and the soil profile should be relatively flexible in root growth models

to allow for studies involving plow pans, straw layers, high-fertility zones

from band placement, and other special treatments. For most purposes,

however, horizontal layers 0.1 to 0.3 m thick have been used in a onedimensional geometry. The detailed assortment of root systems into twodimensional arrays of cubes 1 cm on a side (Lambert et al., 1976; BarYosef et d , 1982) is useful if differentiation is made of the roots near the

crop row and of their interaction with banded fertilizers or other amendments.



GENETIC MANIPULATION OF THE COWPEA



145



(2n=4x=32) revealed enhanced resistance to the wilt fungus Verticillum

alboatrum in protocloned and callicloned populations (Latunde-Dada,

1983; Latunde-Dada and Lucas, 1983, 1988). Some of the genotypes in

these populations exhibited differences in gross morphology and ploidy. It

was also possible, through the incorporation of toxic metabolites of the

fungus V . albo-atrum into plant growth media, to select tissues and plantlets that were incrementally more resistant to this wilt fungus than the

unselected populations of the parental variety Europe (Latunde-Dada and

Lucas, 1988). Similar results on cellular selection have been reported in

the interaction between maize and Helminthosporium maydis (Gengenbach

and Green, 1975; Gengenbach et al., 1977), oilseed rape and Phoma lingam

(Sacristan, 1982), potato and Phytophthora infestans (Behnke, 1979,

1980), and sugarcane and Helminthosporium sacchari (Nickell, 1977).

The underlying causes of genetic somaclonal variation include, among

others, polyploidy , chromosome rearrangements, point mutations, somatic crossovers, transposable elements, and rearrangements and recombinations among cytoplasmic organelle genomes (Orton, 1984). These

events may be visualized as mitotic accidents that constitute a means of

generating biological diversity. It remains possible to harness this powerful mode of evolution in extending further the gene pool of the cowpea and

enhancing its adaptability to the challenges of the Rain Forest Belt of

Nigeria, in particular, as well as elsewhere.



CULTURE

B. EMBRYO

Mention has been made of the problem of sexual incompatibility barriers

among species of the genus Vigna. A determined assessment of this constraint suggests the need for techniques that in breaking and circumventing

these barriers, will aid the exploitation of gene transfer from dissimilar

species into Vigna unguiculata. Three techniques of plant tissue culture,

namely, embryo culture, somatic hybridization, and transformation, are

suggested for this task.

The methods of embryo culture have made possible the in uitro crosspollination and fertilization of flowers, and the rescuing as well as nurturing of the resulting hybrid proembryos and embryos, which rarely survive in natural crosses. Examples abound of successful interspecific

hybrids obtained via embryo culture, including the crosses Brassica oleracea X B . campestris (Nishi et al., 1959; Snell, 1978) to produce Brassica

napus in higher frequencies, and Nicotiana tabacum X N . rependa, N .

stocktonii, and N . nesophila (Reed and Collins, 1978). In these cases the

possibility has been expressed (Brettell and Ingram, 1979) for the transfer



118



BETTY KLEPPER AND R. W. RICKMAN



with statistical distributions is perfected, the location of roots in the soil

will no longer be routinely assumed to be horizontally uniform. It should

become possible to quantify the degree of exploration of variously structured soil profiles by tap, modified tap, and fibrous root systems (Logsdon

et al., 1988; Logsdon and Allmaras, 1989).

The validation of detailed physiologically based root growth and function models is very labor-intensive. With minirhizotron techniques

(Taylor, 1987), root length density evaluations can be done more frequently than with coring techniques, but validation of most root growth

models is still feasible only at intervals of every few days. Consequently,

relatively long time steps of a day or two are probably adequate for root

growth models. However, some aspects of root function models (water or

nutrient uptake) may require shorter time steps because the diurnal transpiration pattern imposes a diurnal pattern on water uptake rates.



IV. MODEL COMPONENTS

A. ROOT CLASSIFICATION

Early models merely generated root length density profiles and made no

differentiation as to age or root type. However, we need models that

distinguish between long-lived roots such as taproots, which function

primarily as transporting roots during most of their life span, and the

shorter-lived roots that serve primarily absorptive functions. In many

models, it is possible to keep track of age classes of roots because discrete

lengths of root at each depth increment are generated each day (Diggle,

1988). The mix of root age classes is sensitive to antecedent soil conditions. For example, the root system shown in Fig. 1 for the drying profile

on July 29 would have a high proportion of old roots in the top half of the

profile and a high proportion of young roots in the bottom half, but the

well-watered profile would have a more even distribution of young and old

roots because roots were being generated throughout the profile at approximately the same rate at which they were decaying. Thus, age distribution

patterns are dynamic and models should be sufficiently sensitive to capture this aspect of rooting patterns.

Other root classifications may be of use in modeling. The distinction of

the seminal and crown roots of cereals is important because of the difference between these two root types in time of appearance and in potential

depth of rooting (Elkins, 1987). Distinctions among axes and first- and

second-order branch roots may have some use if they are explicit in a



MODELING CROP ROOT GROWTH AND FUNCTION



119



model because the higher-order branches are often ephemeral absorbing

roots and main axes and sometimes first-order laterals are the central

transporting roots. Distinctions among roots functioning in transport and

absorption have proven necessary in water extraction models that specify

axial resistances to transport through roots (Klepper et al., 1983).

One useful approach would be to organize roots into the three classes

shown in Fig. 3. One class (A) is the downward-growing main taproots,

axes, or early branches that take over downward-growing dominance from

a taproot and serve primarily as transporting roots during most of their

existence. Although these vertical roots certainly go through an absorbing

phase early in their life span and may absorb some materials throughout

their lives, their most significant function in plant physiology is in the

transport of materials absorbed by younger, smaller branch roots. The

second class (B) is first-order lateral roots, which may be horizontal or

vertical in their growth direction and often grow at an angle for a distance

of several centimeters before turning downward. Their function may be

either transport or absorption depending on their age and the species being

studied. Finally, the third class ( C ) of roots is second-order and higherorder laterals that are primarily absorptive and ephemeral. Unfortunately,

available data sets for classifying roots into these categories are rare.



A - Vertical axis



B



-



First-order laterals



C



-



Higher-order laterals



MODIFIED

TAPROOT

SYSTEM



STRICT

TAPROOT

SYSTEM



y



F I BROUS SYSTEM



*B



A

A



A



A



FIG.3. The three classes of roots as applied to a strict taproot system, a modified taproot

system, and a fibrous system.



120



BETTY KLEPPER AND R. W. RICKMAN



This classification system works well for monocots, which have root

systems composed of a series of downward-growingaxes. At germination

the radical usually grows vertically downward. The radical is followed by

other axes from successive nodes on the plant. These axes grow for a short

distance at successively increasing angles from the vertical and then turn

downward to vertical. Below the 0.3 m depth most cereal axes are vertically oriented if soil conditions permit. The net result of this pattern of axis

production and growth is that successive axes explore wider and wider

cylinders of soil as the season progresses.

Figure 4 shows photographs of wheat roots excavated from the field

using a 0.17 x 0.17-m-square sampling tube (Belford et al., 1986). A side

was removed from the tube and 2-cm sections of soil were washed out,

leaving 2-cm horizontal layers of soil in place to hold the roots in their

original relationship to one another. The A roots are the main vertical axes

that connect to the culms. The B and C roots are thinner and shorter and

presumably are primarily absorptive. There is a tendency for roots of

grasses to be less ephemeral than those of dicots (Huck and Hillel, 1983).

Dicotyledonous root systems of annuals are generally of two types:

taprooted and modified taprooted (Fig. 3). The taprooted plant has one

central root that grows vertically and explores ever-deeper layers of soil as

the season progresses. This taproot undergoes secondary growth and may

become woody. In some taprooted species at least, the B roots grow

horizontally or at an angle to the vertical for a time and then turn downward (Stone et al., 1983; Stone and Taylor, 1983). They may undergo

secondary growth to become transporting roots.



B. ROOTGROWTHPARAMETERS



FOR MODELING



Figure 5 shows a hypothetical example of the information available from

a root growth model with the three classes of roots distinguished and with

the age distributions for roots in each of those classes at each depth. This

output would provide more definition of root condition, age, and origin

than that currently available in models describing uptake of materials from

soils. Furthermore, the root length density profile breakdown into classes

could be verified in the field because the root types have morphological

criteria as their primary defining property.

Some modelers would like to use root diameters to calculate root surface

areas for each class. That calculation could be incorporated into the

preceding output by assigningan average diameter for each class and/or by

generating a root diameter in response to local soil conditions. Generally

axes have larger diameters than first-orderlaterals, which in turn are wider



MODELING CROP ROOT GROWTH AND FUNCTION



121



FIG.4. The top meter of field-grown wheat root systems showing orthogonality of the

axes and branches except for the upper 0.3 m, which has a conical arrangement.



122



BETTY KLEPPER AND R. W. RICKMAN



FIG. 5. Theoretical output from a root growth model with root length densities divided

into the three classes of root (A, B, and C), with the age distribution of each root class shown

in the bar graphs below.



than higher-order laterals, but the actual diameters encountered reflect

plant species, plant conditions, and local soil conditions, thus making

assignment of fixed diameters to each class of questionable validity. Also

monocot axes often slough off their cortex, making their diameter smaller

as they age. In dicots, secondary growth occurs and the diameters of A and

B roots change over the season.

Modelers of carbohydrate partitioning factors need information on the

daily carbohydrate requirements for a growing root system. For each

monocot root class, a root lineal density (weight per unit length) can be

assigned and the carbohydrate needed to produce each length of root

calculated. Respiratory losses are more difficult to assess since they vary



MODELING CROP ROOT GROWTH AND FUNCTION



123



both with root diameter class and with root age. Nevertheless, the ideal

root growth model should account for respiratory losses within the root as

well as for the losses of organic compounds exuded from the root and

respired by rhizosphere organisms.

For those models that use the number of rneristems to partition carbohydrates (Charles-Edwards, 1984), it would be useful to keep track of the

number of meristems at each depth for each class of root. The number and

location of meristems and zones of elongation would also be of interest to

researchers concerned with root-pathogen interactions since young root

tips are a point of attack for certain microorganisms such as Pythium

(Cook and Haglund, 1982), whereas older surfaces are more subject to

other organisms such as Fusarium (Skipp et al., 1982).

Finally, some models require information on distance to the nearest

neighbor to calculate the sphere of influence of the root. The formula

(Barley, 1971) relating average distance between neighbors (4to the root

length density (Lv),



d



=



4 (Lv)-‘I2



would probably suffice. However, this formula does not take into account

the fact that roots tend to follow preferential paths (old root channels,

worm holes, natural fractures in the soil) and tend to be clumped rather

than random in distribution (Wang et a f . , 1986).

It would also be desirable to retain some of the developmental relationships of root axes and their branch lengths so that the “plumbing” of the

root system is explicit in the model. This is relatively easy to simulate but

very difficult to validate. Laborious excavations and root-washing

schemes are required (Belford et al., 1986).

C. ROOT-SOILRELATIONSHIPSI N GROWTH

Elongation rates of roots in soils depend on many factors, some of which

have major impact and others of which are less important. Physical factors

include soil strength, soil oxygen diffusion rate, soil temperature, and

water potential. Chemical factors include soil pH, activities of certain ions

such as aluminum, borate, and calcium, soil osmotic potential, and soil

fertility. Basic concepts for use in modeling cell elongation were discussed

by Lockhart (1965) and modified for roots in soil to include soil resistance

to root penetration by Greacen and Oh (1972). The driving force for

elongation is the turgor pressure in the expanding cells of the elongation

zone. Resisting this are constraints in the cell wall and the constraint of

soil. These concepts can be simplified to the following relationship:



124



BETTY KLEPPER AND R . W. RICKMAN



1dL

=



L dt



(b(P-Y-M)



where



L is root length (m),

(b is wall extensibility (S'aMPa-'),

P is turgor pressure (MPa),

Y is the minimum turgor required for expansion (MPa), and

M is the resistance of soil to root penetration (MPa).

Very little is known about the influence of environment, plant age, and

other factors on (b, P, and Y, but most modelers of root growth in soil

concentrate on the M term and assume that 4, P, and Yare constant.

Since most crop models are intended for use in agricultural soils where

toxic materials are not present at sufficient concentrations to influence

root elongation and where tillage and other management history has provided adequate fertility and minimal soil compaction problems, it may be

possible to simplify the modeling of root elongation rate with respect to soil

properties at least for some cropping situations. For example, assume that

the principal factor that changes during the growing season is soil water

content. Because it is possible to relate soil strength to soil water content

for the specific soil profile being modeled, it is possible to calculate root

elongation rate as a function of soil strength, which could be determined

separately for each depth increment from the soil water budget. It would

be possible to use separate relationships for each depth increment, but in

practice it is probably only necessary to specify the plow layer, any

compacted zones, and the profile below the traffic-compaction zone. One

property that could be specified for each layer might be the probability of a

root encountering a low-strength spot in the soil. A high presence of old

root and worm channels would raise this probability, for example. Although this profile simplification would not take care of acid subsoils or

other common problems, it would be adequate for many agricultural soils.

A more sophisticated approach has been taken by Jones and associates

(Jones, 1990). They account for changes in soil resistance to root penetration based on soil texture, water content, bulk density, aeration, and

temperature.

The branching rate (number of branches per unit length of parent root) is

also difficult to model because it varies both with local soil properties and

with general plant vigor. Local pockets of nutrients such as P and N

(Drew, 1975;Maizlich et al., 1980)can influence the branching rate considerably, as can local soil water content and aeration. Realistic ranges of



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