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Agroforestry Systems 61: 221236, 2004.
2004 Kluwer Academic Publishers. Printed in the Netherlands.221
Ecological interactions, management lessons and design tools in tropicalagroforestry systems
L. Garca-Barrios1,
and C.K. Ong2
1El Colegio de la Frontera Sur, Mexico. Carretera Panamericana y Perisur (s/n); San Cristobal de las Ca-
sas, Chiapas, Cp.29290 Mexico; 2World Agroforestry Centre, P.O. Box 30677, Nairobi, Kenya; Author for
correspondence: e-mail: lgarcia@sclc.ecosur.mx
Key words: Growth resources, Indices, Predictive understanding, Roots, Simulation models, Treecrop interactions
Abstract
During the 1980s, land- and labor-intensive simultaneous agroforestry systems (SAFS) were promoted in the trop-
ics, based on the optimism on tree-crop niche differentiation and its potential for designing tree-crop mixtures using
high tree-densities. In the 1990s it became clearer that although trees would yield crucial products and facilitate
simultaneous growing of crops, they would also exert strong competitive effects on crops. In the meanwhile,
a number of instruments for measuring the use of growth resources, exploratory and predictive models, and
production assessment tools were developed to aid in understanding the opportunities and biophysical limits of
SAFS. Following a review of the basic concepts of interspecific competition and facilitation between plants in
general, this chapter synthesizes positive and negative effects of trees on crops, and discusses how these effects
interact under different environmental resource conditions and how this imposes tradeoffs, biophysical limitations
and management requirements in SAFS. The scope and limits of some of the research methods and tools, such as
analytical and simulation models, that are available for assessing and predicting to a certain extent the productive
outcome of SAFS are also discussed. The review brings out clearly the need for looking beyond yield performance
in order to secure long-term management of farms and landscapes, by considering the environmental impacts and
functions of SAFS.
Introduction
Traditional low-input agricultural systems involving
trees have been designed and managed for centuries
by poor peasants around the world, and are still con-
spicuous in the tropics. During the past century, land-
use intensification, agroecosystem simplification and
other social changes have undermined the functional-
ity of many of these low-inputsystems, and confronted
peasant agriculture with enormous sustainability chal-
lenges (Nair 1998; Garca-Barrios and Garca-Barrios
1992; Garca-Barrios 2003). In the past two decades,
great expectations have been set on the promotion of
traditional and novel agroforestry practices as a means
for slowing down or reversing such trends, once it
became clear that high-input strategies promoted by
development agencies had failed to be adopted and/or
to deliver benefits to smallholders (Sanchez 1995).
Where there is still scope for fallow agriculture in the
tropics, sequential agroforestry systems such as en-
riched fallows have been proposed; where land-use
intensification and fragmentation is more severe, the
bet has been on simultaneous agroforestry systems
(SAFS) such as alleycropping, alley farming, parkland
systems and trees on field boundaries.
During the 1980s, alleycropping was promoted
throughout the tropics as a sustainable option for low-
input agriculture. By the 1990s it was recognized
that the density, management intensity and envir-
onmental scope of new tree-based SAFS had been
pushed too far. It became clear that introducing trees
in croplands was in some cases like walking on a
razor-edge because trees provide peasants with both
crucial products and strongly facilitate crops, but can
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deeper roots than crops. Trees are perennial and there-
fore: a) they eventually explore a relatively large space
and can substantially modify their biophysical envir-
onment to their benefit, b) they are better adapted to
resist cyclic environmental harshness and to use and
recycle resources when it is more efficient to do so,
and c) they commonly have a canopy and a root systemin place when crops starts growing (Ong et al. 1996).
Mature trees in SAFS can have the following
positive effects on crop fields:
1. They can add considerable amounts of organic mat-
ter to the soil and slow down its decomposition rate,
improving soil fertility and physical structure. Trees
roots can stabilize loose soil surfaces, which together
with tree litter cover, reduces erosion (Young 1997).
They recover leached nutrients from deep soil or bed-
rock layers inaccessible to crops (Rao et al. 1998).
Trees can make more phosphorus available via mycor-
rizha and fix important amounts of nitrogen, which can
be transferred to the crops via shoot and root prunings
(Giller 2001).
2. Although trees can increase the potential soil water-
holding capacity, they have variable and conflicting
effects on the actual water volume available in the
treecropsoil system: Rainfall intercepted by the can-
opy that evaporates without reaching the soil can be as
much as 50% when tree density is high (Ong et al.
1996). Yet, reduced soil evaporation by tree shade can
help offset such losses as long as rainfall is lower than
700 mm per annum (Ong and Swallow 2004). Trees
can eventually increase infiltration but this strongly
depends on slope and soil characteristics (Ong andSwallow 2004). In general, tree presence produces a
net increase in total water used by the system (Ong
and Swallow 2004).
3. Tree shade can reduce leaf temperature and evap-
orative demand experienced by crops, increasing the
latters water productivity (i.e., g of dry mass per g of
water transpired). The net shade effect is more positive
(or less negative) when the annual crop is a C3 plant
which is normally light saturated in the open, so partial
shade may have little effect on assimilation or even
be beneficial (Ong 1996). This improvement in con-
version efficiency is relatively modest when compared
to the effect described in the previous point (Ong and
Swallow 2004).
4. Tree hedgerows provide protection against wind and
runoff (Rao et al. 1998.).
5. Trees can reduce weed populations and change
weed floristic composition towards less aggressive,
slow growing species (Leibman and Gallandt 1997).
6. Little is known about the complex and sometimes
conflicting effects of trees on pest and disease con-
trol, but Schroth et al. (2000) and Rao et al. (2000)
providecomprehensive reviews on the topic. Increased
pest and disease incidence has often been observed
directly at the treecrop interface. Trees increase air
humidity, which favors microorganisms, provide shel-ter for herbivores (insects, birds, and small mammals),
which damage the crops, and reduce pest and disease
tolerance of competition-stressed crops. Trees them-
selves can be more susceptible to pest and disease
attack when sown at densities and spatial arrange-
ments uncommon to their natural environments. Yet,
tree hedges have the potential to slow down windborne
pests and diseases, to act as repellants, and to attract
natural enemies; recent evidence is provided by Girma
et al. (2000).
On the other hand, with increase in density of trees,
their size, and/or ability to capture resources in SAFS,
they can exert strong competition for light, water and
nutrients, and reduce annual crop yields beyond the in-
terests of farmers if improperly selected and managed
(Garca-Barrios 2003). Nevertheless, weak competi-
tion is possible under certain circumstances such as
the following:
1. Tree roots can potentially reach below the crop root
zone, and thus they can use water accumulated deeper
in the ground when the crop is growing; after the crop
is harvested, they can use whatever residual available
water is found in the crop root zone; and they can
use any additional rain which falls outside the crop
growing season (Ong et al. 1996). It is important tostress that trees used in SAFS do not always have deep
pivotal roots, and that mixed and superficial tree root
architectures are common (van Noordwijk et al. 1996).
Moreover, if water recharge below the root zone is
infrequent and/or nutrients are superficial, most trees
will tend to develop or redirect their roots to the upper
soil layers (Rao et al. 2004) and only a few species
will develop roots that can reach relatively deep water
tables. Consequently, there seems to be less scope for
vertical root complementarity than originally thought
(Sanchez 1995; Ong and Swallow 2004).
2. Some deciduous tree species used in SAFS in semi-
arid regions such as Faidherbia albida exhibit reverse
phenology: they produce their leaves and demand
water only during the dry season, while their litter
provides nutrients and their trunk and bare branches
cast a light shade over crops during the rainy season
(Rao et al. 1998).
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itive and negative effects explicitly, and without con-
sidering resource distribution and use. An extensive
literature has been developed on this matter during
the past 40 years (Vandermeer 1989). A number of
competition- and productivity indices have been de-
veloped and their scope, limitations, and pitfalls dis-
cussed (Connolly et al. 2001; Williams and McCarthy2001). Most productivity indices have been developed
for two species intercrops. They assume that the
farmer is interested in finding whether combinations of
both crops in the same field can outperform the corres-
ponding sole crops. We will give a very brief account
of how crop and tree yields relate separately to their
net intra and interspecific interactions by developing a
graphical analysis of a hypothetical and generic SAFS.
We will then discuss the simultaneous assessment of
crop and tree yields.
Consider the crop and tree sole stands in Fig-
ure 1(a) and (b). Both are sown at their optimum sole
crop densities (N.), i.e., the number of individuals
per unit area which produces the maximum possible
yield (Y.) in that surface. These parameters result
from the reasonably hyperbolic relation between sole
crop yields and sole crop plant densities (Willey and
Heath 1969) depicted in Figure 1d and are a direct
consequence of net intra-specific interactions. In our
example, the sole crop stand parameters are Nc = 6
and Yc = 6, while the sole tree stand parameters are
Nt = 2 and Yt = 18. Intra-row plant distances are the
same for both crops. In the treecrop mixture depicted
in Figure 1c, every sixth crop row has been substituted
with a tree row. As a consequence, the crop density inmixture (nc) is 5 and the tree density in mixture (nt) is
1. In other words, nc = 5/6*Nc and nt = 1/2*Nt. For
simplicity, we will assume that both tree competition
and facilitation on the crop can be present, and that
no tree pruning is practiced so that facilitation results
from other mechanisms. Crop plants nearer to the tree
are generally smaller as they experience more compet-
ition (see Figure 1c), but here we consider the average
plant performance within the unit area.
Different crop yield outcomes in mixture (yc) are
possible; they are shown in Figure 2a. An interesting
starting point is case 3, where yc = 5/6*Yc, i.e., mix-
ture crop yield is reduced in the same proportion as
crop density. The average crop individual has the same
weight in sole crop and intercrop, which means that
the average net effect of a tree on crop plants matches
the net intra-specific effect of the average crop indi-
vidual in the sole stand. Considering the asymmetry
in tree and crop sizes, this seems highly unlikely, un-
less it results from very weak tree competition due
to high resource complementarity, or from facilitation
almost compensating competition. In case 4, either
tree competition is zero (perfect complementarity) or
facilitation exactly compensates competition, because
in this case, yc equals the yield expected for five
plants per unit area in the sole crop (here we make theassumption that given a near-optimum crop density,
particular plant arrangement has little effect). In case
5, the crop stand experiences enough net facilitation to
match the maximum sole crop yield, and in case 6 to
surpass it. In case 1 and 2 the average crop plant ex-
periences significant net competition and crop yields
are strongly reduced.
A similar analysis is possible from Figure 2(b),
for the trees performance in mixture; the roles are
simply inverted. Cases 1 and 2 are highly unlikely,
unless strong crop allelopathy effects on young trees
are present. The most probable outcome is somewhere
between case 3 and 4. Cases 5 and 6 are not realistic,
given asymmetry between tree and crop.
Of course, the crop and tree yield outcomes in our
example will be coupled and depend on one another
such that not all outcome combinations make sense.
Some possible combinations are depicted graphically
in Figure 3. In more general terms, each specific
spatio-temporal mixture design for a given pair of
plant species in a given environment produces a pair of
coupled yields. The set of coupled yield outcomes of
all possible designs (which include all sole crop yields
as well) is called a yield set (Vandermeer 1989); the
subset of points which constitute the exterior envelopeof this set is called the production possibility fron-
tier (PPF; Ranganathan and De Wit 1996); (Figure 4
presents a possible yield set and PPF for our hypothet-
ical SAFS). A PPF can be analyzed to compare sole
and mixed crop outcomes and to find the optimum
mixed crop designs according to different biological
and economical performance criteria. An example of
such criteria is the land equivalent ratio (LER), defined
as (yc/Yc) + (yt/Yt). A LER> 1 means that there
mixture is advantageous because more land would
be required to obtain yc and yt by sowing each spe-
cies separately as sole crops. (For further details on
LER and other mixture performance indices, see Van-
dermeer 1989). A few scores of yield pairs can be
obtained through field experiments, while more thor-
ough yield set and PPF constructions can be aided by
experimentally fitted models. Simple analytical mod-
els have been developed for this purpose, which only
consider global population densities and render final
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Figure 1. Schematic representation of the yield vs. density relation of a tree-crop mixture, and its corresponding sole crops stands. Bar areas
represent the aboveground biomass of the individual plants. (a) sole crop stand; (b) sole tree stand; (c) tree-crop mixture; (d) sole stand yield
vs. density relations.
Figure 2. Sole stand yield vs. density relations and some possible yield outcomes (16) after mixture with the other species. (a) Crop yields;
(b) Tree yields. See text for further explanation of mixture outcomes.
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biomass or yield (e.g., Ranganathan and De Wit 1996).
Spatially explicit, individual-based plant growth mod-
els have also been developed. They require empirical
growth and competition parameters and render yields
at any growth stage for any spatio-temporal design
(e.g. Garca-Barrios et al. 2001). Both models need
to be re-parameterized in different environments.
Quantifying the effects of positive and negative
interactions separately
The idea to separate and quantify positive and negative
tree effects on crop yield in SAFS was formalized by
Ong (1995) in the simple equation:
I = F + C (1)
where I is the overall interaction, i.e., the percentage
net increase in production of one component attribut-
able to the presence of the other component, F is the
fertility effect, i.e., the percentage production increase
attributable to favorable effects of the other component
on soil fertility and microclimate, and C is the compet-
ition effect, i.e., the percentage production decrease
attributable to competition with the other component
for light, water and nutrients. The I value is based on
total area, including that occupied by trees; therefore,
a positive I value means net increase in total crop yield,
irrespective of crop population in mixture relative to
that of sole crop (Rao et al. 1998). In alleycropping
systems, the measurement of F and C has been accom-
plished with four treatments: Co = sole crop; Cm =
sole crop + mulch from pruned trees; Ho = crop +
tree with mulch removed; Hm = crop + tree with itsmulch. The equation then becomes
I = (Cm Co) (Hm Cm) (2)
The competition term can also be calculated as (Ho
Co) or, more conveniently, as the average of (Hm
Cm) and (Ho Co). This equation motivated the ana-
lysis of numerous previous alleycropping experiments
and the establishment of new ones (Ong 1996). Un-
fortunately, few proved to have these four treatments
and/or the appropriate experimental designs and field
display. Nevertheless, successful positive and negative
separation in a few experiments made evident, among
others, the following important facts (Sanchez 1995;
Ong 1996; Rao et al. 1998; Ong et al. 2004): 1) Strong
tree competition is more conspicuous than originally
thought; 2) high tree growth rates and tree biomass, in-
tuitively associated with the potential for a significant
fertility effect are also strongly related with tree com-
petitiveness, so tradeoffs between both interactions are
high; 3) positive and negative component effects are
very site specific and change with the environment .
After a modification by Ong (1996), the equation
evolved to (Rao et al. 1998):
I = F + C +M + P + L + A (3)
where F refers to effects on chemical, physical andbiological soil fertility, C to competition for light, wa-
ter and nutrients, M to effects on microclimate, P to
effects on pests, diseases and weeds, L to soil con-
servation and A to allelopathy effects. The benefit of
Equation (3) is that it encapsulates a comprehensive
overview of the possible effects involved. However, as
emphasized by the authors, many of these effects are
interdependent and cannot be experimentally estim-
ated independently of one another. Limitations have
been identified for this approach (Ong et al. 2004):
1) due to interdependence, the individual terms most
likely will give a sum that exceeds I, such that the rel-
ative importance of each term cannot be established. 2)
It cannot predict delayed effects and long-term trends.
3) It is not meant to predict the consequences of mov-
ing from one environment to another, as it does not
explicitly consider growth resource capture and use,
and their interaction (e.g. water x P interaction in P-
fixing soils). Cannell et al. (1996) attempted to clarify
the resource base of Ongs equation but did not make
plant interaction with resources sufficiently explicit.
Mechanistic research may be necessary to understand
SAFS functioning and performance over time and/or
in different environments.
Methods that explicitly consider growth resources
Positive and negative interactions between plant spe-
cies largely depend on how the latter affect each
others ability to capture and use growth resources.
The principles of light, water and nutrient capture
and use efficiency first applied to sole crop growth
analysis and modeling have been extended to inter-
cropping and agroforestry research in the past decade.
The field has seen enormous advances in the gather-
ing of relevant experimental data, theory development,
modeling capability, and construction of very sensitive
instruments for measuring direct above- and below-ground resource flow and capture (Black and Ong
2000). They have also made evident the challenges for
studying these processes in multispecies systems, and
the limitations of some basic idealized and simplified
assumptions about the relation between plant growth
and resource capture and use efficiency.
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Figure 3. Coupled tree and crop yields in mixture. Points 16 represent the six crop yield cases depicted in figure 2(a), and reasonable associated
tree yields. Three additional outcomes are included: in A, tree excludes crop; In B crop excludes young tree through strong allelopathy. In C
allelopathy effect on tree is milder. The slope of the dashed line indicates the intensity of the slightly negative crop effect on tree biomass. Stars
are maximum sole crop yields, and the line that crosses them represents all outcomes with a land equivalent ratio (LER) = 1. Above this line,
LER > 1.
A central tenet of mechanistic plant-plant interac-
tion analysis has been that, according to the Law of
the Minimum (Blackman 1905), as long as a resource
is the most limited, growth depends linearly on the
capture of this resource. If eventually another resourcebecomes the most limiting, the formers concentration
ceases to have an effect and the latter dictates growth.
As a consequence, biomass production (W) should be
easily modeled as the product of the capture of the
most limiting resource, and the efficiency with which
the captured resource is converted into biomass (Mon-
teith et al. 1994; Ong et al. 1996). The conversion
efficiency of the limiting resource is considered to be
conservative for a given species for a given environ-
ment, and the growth response of the plant is attributed
to the increased capture of the resource. Research
data (e.g., Demetriades-Shah et al. 1992; Black andOng 2000) and theoretical developments (Kho 2000;
Ong et al. 2004) have shown that: 1) Usually sev-
eral resources are limiting, in which case the relation
between biomass production and the capture of one
single resource should be viewed as a correlation, not
a causal relation that can be readily modeled. 2) The
variation in conversion efficiencies between environ-
ments is larger than that between species; therefore
such efficiencies are more determined by the environ-
ment than by species. 3) Plants alter the availability
of resources simultaneously and thus conversion ef-ficiencies by changing resource limitation. Moreover,
the most limiting resource for a species can differ
in sole system and mixture. 4) Efficiencies should
be studied and modeled in relation to the availabilit-
ies of the other resources, and treated as variables in
process-based models. 5) Dynamic simulation models
for different resources should be linked.
In recent years, different resource-based model-
ing approaches have been developed and/or used to
explore or predict how tree-environment-crop inter-
actions (and the productive performance of SAFS)
change when environmental resource availability ismodified. Some relevant examples are cited below:
The mulchshade model
Tree canopies in alleycropping provide N-rich mulch
but reduce radiation available for crops. The net tree
effect should then be a function of at least three
factors: 1) the trees mulch:shade ratio (MSR), 2) the
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Figure 4. A yield set and Production Possibilities Frontier for the hypothetical tree-crop mixture presented in figures 1 (c). Thin solid lines
result from fixing a global density and modifying the crop-tree proportion; thick dashed line from fixing a tree-crop proportion and modifying
global density. The thick solid line is the production possibility frontier, and the area under it is the yield set. The thin dashed line represents all
outcomes for which LER = 1.0, and the black dot on the PPF is the tree crop mixture which renders the highest attainable LER value.
importance in the particular environment of nitrogen
supplied by mulch, expressed as a Nsoil: Nmulch ra-
tio (NNR), and 3) tree row distance as a surrogateof tree leaf area index. Van Noordwijk (1996) de-
veloped a static-analytical alleycropping model, which
links these species attributes and management factors,
and produces explicit algebraic solutions. The simple
MSR offers a basis for comparing and selecting tree
species. The equation variables and parameters require
a lengthy explanation; here we are interested only in
discussing the type of results it delivers. The model
predicts that at low soil fertility, where the soil fer-
tility improvement due to mulch can be pronounced,
there is more chance that an agroforestry system im-
proves crop yields than at higher fertility where the
negative effects of shading will dominate. Moreover,it defines combinations of MSR and NNR for which
some alleycropping systems should be expected to
work (Figure 5a). Although not validated with em-
pirical data, it has been parameterized for typical
alleycropping tree species in order to estimate their
optimum hedgerow density at different Nsoil values
(Figure 5b). The mulch/shade model provides use-
ful insights, but does not incorporate the interactions
between resource dynamics, and crop and tree growth.Incorporating these elements extends the model bey-
ond what can be solved analytically and into the realm
of dynamic simulation models.
Integrated water, nutrient and light simulation models
in agroforestry systems
In the late 1990s complex agroforestry simulation
models and user platforms were constructed for ex-
ample, WaNuLCAS (van Noordwijk and Lusiana
1999) and HYPAR (Mobbs et al. 2001), and they are
still undergoing development, parameterization, and
validation. These two models are process-based and
have a useful level of spatial structure. Both require
weather databases and a considerable number of soil-
and plant parameters as inputs. WaNuLCAS is quite
elaborate in its soil sub-models and HYPAR in its can-
opy sub-models. They are too complex to allow a use-
ful description here, but excellent specifications and
user manuals are available. Once proper inputs and
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Figure 5. Some of the results obtained by van Noordwijk, (1996) with the mulch and shade model. (a) shows combinations of MSR and
NNR for which some hedgerow systems should be expected to work, given two different values of N mulch. P, C and L stand for estimatedMSR values for Peltophorum dasyrrachis, Calliandra calothyrsus and Leucaena leucocephala, respectively. (b) shows predicted optimum
tree density in an alley cropping system for five tree species (Peltophorum dasyrrachis, Erytrina poeppigiana, Gliricidia sepium, Leucaena
leucocephala and Calliandra calothyrsus) as a function of Nsoil. Tree density is expressed in linear meters of hedgerow per hectare. Species
parameters were estimated empirically and are reported in van Noordwijk, (1996), table 3.2.
parameters are in place, these models can be powerful
tools for systematically exploring the possible con-
sequences of diverse management practices and of
one or more resource gradients, before engaging in
costly and time consuming experiments and product-
ive projects. Van Noordwijk and Lusiana (1999) used
WaNuLCAS to model grain- and wood production,
water use, water-use efficiency and N limitation for
a wide range of annual average rainfall conditions
(240 mm to 2400 mm) in parkland systems with dif-
ferently shaped trees; an example of their results is
presented in Figure 6a and 6b. As yet, no experi-
mental data set exists on the same agroforestry system
at the same soil but widely differing rainfall condi-
tions, so they used data and parameters from different
sources and from theoretical assumptions. Model res-
ults generally agreed with conclusions derived from
experimental evidence (Breman and Kessler 1997).
Similar conclusions were reached with the HYPAR
model about the effect of climatic gradients on tree-crop interactions and productive outcomes (Cannell
et al. 1998).
Complex process-based models are potentially
powerful tools but have their own limitations and
pitfalls; they are expected to confront problems of
parameter estimation, validation and input gathering
similar to or more severely than those found in sole
crop physiological models (Aggarwal 1995; Hakan-
son 1995). These models can be used with caution
in order to gain insight about management practices
and about the consequences of theoretical assump-
tions; their outputs should be constantly confronted
with empirical results and farmers experience.
A general treeenvironmentcrop interaction
equation for predictive understanding of SAFS
Kho (2000) has developed a simple but powerful ana-
lytical model in which the overall tree effect on crop
production is explained as a balance of (positive and
negative) relative net tree effects on resource availabil-
ity to the crop. We will describe here some of its basic
features, consequences and applications. When trees
are introduced in a crop field, they simultaneously
change the availability of several resources in the en-
vironment of the crop, some for the better and somefor the worse. Notwithstanding the Law of the Min-
imum stated earlier, it has become clear that not one
but many resources can limit growth simultaneously
and that the degree to which a resource affects produc-
tion at a given level is dependant on the availability of
the other growth resources (Kho 2000). Consequently,
the relation between a given resource and production
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Figure 6. Some of the results obtained by van Noordwijk and Lusiana (1999) with the WaNuLCAS model for grain and wood production, for
a range of annual rainfall conditions in an hypothetical agroforestry system where trees provide N-rich mulch. For comparison, the sole crop
and sole tree stand are grown also. (a) shows a gradual shift from water to N as the major factor limiting crop production as rainfall increases.
At low rainfall levels, tree competition for water dominates over positive effects of N supplied by tree mulch. (b) Because of crop competition,
tree yield is lower in the SAFS stand than in sole tree stand.
is not linear but asymptotical when other resources are
held constant. As a particular resource becomes lessavailable in relation to others, its influence on produc-
tion becomes greater and in this last sense it becomes
more limiting. The limitation of a resource Ai (i.e.,
Li) can be formally defined as the ratio between the
slope of the production response curve (at a given re-
source level) and the average use efficiency of that
level of resource by the crop; it is therefore a rel-
ative non-dimensional term. Li can also be defined
(more intuitively) as the relative change in production
in response to a relative change in resource availabil-
ity (Kho 2000), which corresponds to the definition of
elasticity in economic theory. Kho 2000 has fruitfully
applied Eulers law from economics to demonstrate
that the sum of limitations (or elasticities) of all growth
resources ( Li) should reasonably be equal to 1.0 if
the so called constant return to scale assumption holds.
De Wit (1992) shows agricultural data supporting this
latter assumption of proportional relation of output to
input.
As a consequence of the previous arguments, when
trees interact with a crop, the expected relative cropyield change (dW/W) should be equal to a weighted
sum of the relative changes induced by the tree on
each resource Ai; the weights should be the Lis which
result from the particular balance of resources in the
specific environment. This leads to the equation:
dW/W=
n
i=1
(dAi/Ai) Lii (4)
In short, each resource contributes to the relative
change in production proportionally to its degree of
limitation and proportionally to its relative change in
availability. From Equation (4), Kho (2000) derivesEquation (5), which predicts the relative change in
crop production (I, as in Ong 1995), as a function
of tree effects on resource availability and of resource
balance in the particular environment considered:
I=
n
i=1
Li Ti (5)
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Figure 7. Trees influence crop production through altering (the balance of) resource availabilities to the crop. Each rectangle represents a
different resource: water (W), nitrogen (N), phosphorus (P) and radiation (R). The height of each shaded area relative to the height of the
rectangle represents the relative change in availability of the resource (Ti). The width of each shaded area relative to the total width represents
the limitation of the resource in the tree-crop interface (Li). The sum of positive and negative shaded surfaces relative to the total surface of therectangle represents the overall tree effect I expressed as fraction of sole crop production. The figures show possible tree effect balances of an
alley cropping technology in a humid climate. A) on nitrogen deficient soils, B) on acid (phosphorus deficient) soils, C) on nitrogen deficient
soils with nitrogen fertilizer (applied to the alley crop and the sole crop), and D) on acid soils with phosphorus fertilizer (applied to the alley
crop and the sole crop). The relative net tree effects on availability of each resource (Ti) are equal in AD; only the environments (i.e. resource
limitations Li) change, and explain the different overall effects (I). Source: Ong, et al., 2004.
where
Ti =Ai
Ai=
Ai;multi Ai;mono
Ai;mono(6)
Ti is the relative net change in availability of resource
i because of the tree, Ai;multi is the availability of re-
source i to the crop in the SAFS and A i;mono in thesole crop. Robust estimations of L and T values for
a particular SAFS and environment can be obtained
experimentally and/or derived from the literature fol-
lowing relatively simple methods which are described
and applied by Kho (2000) and Kho et al. (2001).
The relation between resource balance and limit-
ation combined with Equation (5) leads to two rules
that can be viewed as counterparts of classic crop
production principles (Kho 2000): 1) The greater the
availability of a resource in the environment, the smal-
ler is its share in the overall tree-crop interaction. 2)
The greater the availability of other limiting resources
in the environment, the greater is the share of a re-
source in the overall tree-crop interaction. These rulesare helpful for predicting the performance of a SAFS
technology when it is extended to another environment
and for developing a SAFS technology. For example,
Kho (2000) showed that for the alleycropping tech-
nology the net effect of the alleys on the availability
(to the crop) of the resources light, water, and phos-
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233
phorus is most likely negative, and that for nitrogen
it is most likely positive. Consequently, in a (sub-)
humid climate on nitrogen- deficient soils, the overall
alleycropping effect is most likely positive, because
of the high limitation for the positive nitrogen effect
and the low limitations for the negative net effects on
other resources (Figure 7A). In the same climate, buton acid soils, phosphorus is relatively less available,
which will increase the share of the negative phos-
phorus effect (rule 1) and will decrease the share of
the positive nitrogen effect (rule 2), resulting in a neg-
ative overall effect (Figure 7b). Through management
practices, the share of positive net effects can be in-
creased and the share of negative net effects decreased.
Compare, for example, Figure 7b and 7d for the effect
of phosphorus fertilizer applied to both the alleycrop-
ping system and the sole crop system. External inputs
of organic or inorganic nitrogen are most likely inap-
propriate, because these will reduce the share of the
positive nitrogen effect (rule 1) and increase the share
of the negative effects (rule 2; cf. Figure 7a and 7c).
Beyond yield performance
During the past two decades, agroforestry research in
the tropics has focused, naturally, on the prospects
for higher productivity in low-input agriculture, which
are based on plot-level research just as in agronomic
research. In recent years, there is a growing realiz-
ation that recommendations based on productivity at
the plot level alone are insufficient for the long-termmanagement of farms and landscapes. Sustainability
of land use practices, a major incentive for prefer-
ring agroforestry to high input agriculture, depends
(among other things) on ensuring that the flow of en-
ergy through the agroecosystems is in close balance to
those of the natural ecosystems (Lefroy and Stirzaker
1999). Furthermore, extrapolation of results from plot
to landscape level is often flawed because they fail to
account for the lateral movement of water and soil,
which are greatly influenced by filters in the landscape
(van Noordwijk and Ong 1999).
Young (1998) argues that much of the future in-
crease in food and wood production in the humid
tropics will have to be achieved from existing land and
water resources. Therefore, future research agenda
should aim to improve the efficiency with which land
and water are currently used. One promising option
for improvements of this kind is by using agroforestry,
with the ultimate aim of achieving sustainability of
production and resource use. The principal agro-
forestry systems suited to humid tropical environments
are multistrata systems, perennial crop combinations,
managed tree fallows, contour hedgerows and reclam-
ation agroforestry (ICRAF 1996; Young 1997; Tomich
et al. 1998). These mixtures of trees and crops have
the potential to improve land management via theirability to reduce soil erosion and improve soil condi-
tions for plant growth. There is some evidence for the
utility of agroforestry systems for soil conservation,
soil organic matter maintenance, nutrient retrieval,
and nutrient recycling (Buresh and Tian 1998; Young
1997). In farming for annual crops, contour hedgerows
may provide a viable alternative to conventional con-
servation measures (Kiepe and Rao 1994). However,
despite the demonstration that such systems can dra-
matically reduce soil losses and improve soil physical
properties, the beneficial effects on crop yield are of-
ten unpredictable and insufficient to attract widespread
adoption (Alegre and Rao 1996).
Agroforestry is now receiving increasing attention
by researchers, landowners and policy makers in Aus-
tralia as a potential solution to the salinity problems
caused by the rising water-table (Lefroy and Stirzaker
1999). Replacement of the native vegetation, mainly
trees and shrubs, have resulted in a steady increase
in the water table for much of the semiarid wheat
(Triticum sp.) belt of Eastern and Western Australia,
because the vegetation has been replaced by winter-
growing crops such as wheat (Triticum aestivum),
barley (Hordeum vulgare), canola (Brassica napus),
and lupin (Lupinus spp.), which cannot fully utilizethe annual rainfall. The salinity problem is more com-
plex than that experienced in the tropics because of
the nature of the duplex soils there, which slow lateral
movement of water across the landscape and there are
few profitable tree species to replace the existing an-
nual crops. Widely spaced tree rows (10 mm to 300 m
and also called alleycropping) of fast-growing nat-
ive (e.g., Eucalyptus spp.) and exotic origin (e.g., tree
lucerne Chamaecytisus palmensis) were originally
seen as the practical alternative for solving this huge
landscape problem. As with the tropical alleycrop-
ping experience, there is a strong tradeoff between
environmental function and crop performance in the
Australian environment. Therefore, there is now a ser-
ious emphasis on identifying trees that can provide
direct value to farmers (e.g., oil malle, Eucalyptus
polybractea), as suggested by Ong and Leakey (1999)
for sub-Saharan Africa, in addition to the hydrological
function.
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designing and evaluation of complex systems needs
to be tested. Research methods are needed to derive
useful and flexible rules from adaptive management.
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