Dynamic simulation model of land use changes

Agriculture, Ecosystems and Environment 85 (2001) 145–161
A dynamic simulation model of land-use changes in
Sudano-sahelian countries of Africa (SALU)
N. Stéphenne∗,1, E.F. Lambin
Department of Geography, University of Louvain, Place Louis Pasteur 3, B-1348 Louvain-la-Neuve, Belgium
Abstract
This paper presents a simulation model to project land-cover changes at a national scale for Sudano-sahelian countries. The
aim of this study is to better understand the driving forces of land-use change and to reconstruct past changes. The structure
of our model is heavily determined by its spatially aggregated level. This model represents, in a dynamic way, a simplified
version of our current understanding of the processes of land-use change in the Sudano-sahelian region of Africa. For any
given year, the land demand is calculated under the assumption that there should be an equilibrium between the production and
consumption of basic resources derived from different land-uses. The exogenous variables of the model are human population
(rural and urban), livestock, rainfall and cereals imports. The output are the areas allocated to fuelwood extraction, crops,
fallow and pasture for every year. Pressure indicators are also generated endogenously by the model (rate of overgrazing and
land degradation, labour productivity, average household “budget”). The parameters of the model were derived on the basis of
a comprehensive review of the literature, mostly of local scale case studies of land-use changes in the Sahel. In agreement with
farming system research, the model simulates two processes of land-use change: agricultural expansion at the most extensive
technological level, followed by agricultural intensification once some land threshold is reached. The model was first tested at
a national scale using data from Burkina Faso. Results simulate land-use changes at two time frequencies: high frequency, as
driven by climatic variability, and low frequency, as driven by demographic trends. The rates of cropland expansion predicted
by the model are consistent with rates measured for several case studies, based on fine spatial resolution remote sensing data.
© 2001 Elsevier Science B.V. All rights reserved.
Keywords: Land-use change; Land-cover change; Sahel; Desertification; Modelling
1. Introduction
Understanding the role of land-use in global envi-
ronmental change requires historical reconstruction of
past land-cover conversions and/or projection of likely
future changes. While, at a local scale, part of these
historical data can be generated from direct or indi-
rect field evidence (e.g. old vegetation maps, aerial
∗ Corresponding author. Tel.: +32-10-47-4477;
fax: +32-10-47-2877.
E-mail address: stephenne@geog.ac.ucl.be (N. Stéphenne).
1 FNRS Research Fellow.
photographs, high temporal resolution pollen stud-
ies), at a regional scale, the reconstruction of past
land-cover changes has to rely on backward projec-
tions using land-use change models (Klein Goldewijk
and Battjes, 1997). Such models rely on an under-
standing and simulation of the interactions between
drivers of land-use change.
The objective of this paper is to present a dyna-
mic simulation model of land-use changes in the
Sudano-sahelian countries of Africa (SALU). The
specific purpose of this model is to generate backward
and forward projections of land-use change over sev-
eral decades at a national scale. The Sudano-sahelian
0167-8809/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved.
PII: S0167-8809(01)00181-5

146 N. Stéphenne, E.F. Lambin / Agriculture, Ecosystems and Environment 85 (2001) 145–161
region has undergone changes in land-cover over the
last decades (Little et al., 1987; Bolwig, 1995). It
is still very much debated, however, whether these
changes are related to short-term climate fluctuations
or longer-term anthropogenic impacts (Nicholson,
1989; Hellden, 1991; Hulme, 1996). Several authors
have suggested that “desertification” in the Sahel
has caused a change in regional climate (Xue and
Shukla, 1993). One possible application of the out-
put of our model, if generated over a large region,
is to investigate the impact of land surface changes
on regional climate. This can be achieved by con-
ducting experiments with general circulation models
(GCMs) at a coarse spatial resolution. The structure
of our model is heavily determined by this coarse
resolution. The model represents, in a dynamic way, a
simplified version of the current understanding of the
processes of land-use change in the Sudano-sahelian
region.
2. Background
The backward or forward projection of land-use
changes can be performed using two main categories
of models (Lambin, 1997): (i) empirical models based
on an extrapolation of the patterns of change observed
over the recent past, with a limited representation of
the driving forces of these changes, and (ii) dynamic
simulation models based on a thorough understanding
of the processes of land-use change. Empirical models
integrate landscape variables and proximate causes of
change in a data-rich spatial context. However, they
can only provide short-range projections (5–10 years
at most) due to the dynamic character of land-use
change processes.
Longer range projections require, first, a good un-
derstanding of the major human causes of land-use
changes in different geographical and historical con-
texts. It also requires an understanding of how climate
variability affects both land-use and land-cover. Such
understanding is gained through a collection of local
scale case studies on land-use dynamics, which high-
light how people make land-use decisions in a specific
situation. A generalised understanding of the drivers
of land-use change, that can be linked to regional scale
patterns of change, is gained through a comparative
analysis of these case studies.
The knowledge gained through these case studies
supports the development of simulation models of
land-use changes that represent the dynamics of driv-
ing forces operating at regional to global scales. These
models include a representation of the processes link-
ing driving forces to changes in land-use allocation.
They have to cope with issues such as technological
changes, policy and institutional changes and changes
in economic system. On this basis, regional scenarios
can be generated to simulate possible future land-use
changes or for identifying land-use patterns with
certain optimality characteristics satisfying simulta-
neously various economic, social and environmental
goals.
In this study, we reviewed a large number of
published case studies of land-use dynamics in the
Sudano-sahelian region, compared and generalised
these case studies to identify the dominant driving
forces, processes and parameters values of land-use
change in the region, and represented these processes
in a simulation model using a combination of sim-
ple, equilibrium equations and knowledge rules. The
regional focus of the study on the Sudano-sahelian
region means that we could represent region-specific
processes of land-use change.
3. Model structure
The exogenous variables of the model are human
population (rural and urban), livestock population,
rainfall and cereals imports. New values of these
exogenous variables are defined every year from
the Faostat database (FAO, 1995) and the global
monthly precipitation dataset gridded at 2.5◦ lati-
tude by 3.75◦ longitude resolution (Doherty et al.,
1999). These exogenous variables are driving yearly
changes in land-use allocation. These land-uses gen-
erate different resources for the population: fuelwood
in natural vegetation areas, food for subsistence and
market needs in cropland and fallow, livestock in
pastoral land. These different land-uses compete
for land. Note that these land-use categories do not
strictly coincide with land-cover types. In this model,
the land-use classes “fuelwood extraction areas”
and “pastoral lands” refer to a variety of vegeta-
tion cover types such as woodlands, savannahs or
steppes.

N. Stéphenne, E.F. Lambin / Agriculture, Ecosystems and Environment 85 (2001) 145–161 147
For any given year, the land demand is calculated
under the assumption that there should be an equi-
librium between the production and consumption of
resources. This assumption drives the land-use allo-
cation for every yearly time step. In other words, the
offer of food and energy resources derived from the
areas allocated to the different land-uses must satisfy
the demand for these resources by the human and an-
imal populations, given the exploitation technologies
used at a given time. The second assumption is that
the study area, i.e. a country or an eco-climatic region
within a country, is geographically homogeneous. As
the model is not spatially explicit but only predicts
aggregated values of land-use change, spatial hetero-
geneity is not taken into account. Furthermore, the
study area is closed, except for food imports.
The model is programmed with STELLA, a mod-
elling language with a graphic interface which has
been widely used for developing simulation models
(Costanza et al., 1990; Woodwell, 1998). The name of
this model is SALU (SAhelian Land-Use model).
4. Computation of demand for different land-uses
The competition between the different land-uses
takes place within the national space, which is finite
U = Veg + Past + Crop (1)
where U is the used area, Veg the fuelwood extraction
area, Past the pastoral land and Crop the cropland,
all quantities being in ha. The difference between the
national space and the total used area is the unused
area
UN = N − U (2)
where UN is the unused area in ha and N the na-
tional area in ha. The unused area correspond to the
same land-cover types as pastoral lands and fuelwood
extraction areas. It is the area of these land-cover
types that would not need to be used for grazing
or fuelwood collection given the demand for related
resources and given a certain land-use intensity. The
total demand for land in a given year is the sum of
demands for cropland and pastoral land
landd = Cropd + Pastd (3)
where landd is the land demand, ∆Cropd the annual
variation in cropland demand and ∆Pastd the annual
variation in pastoral land demand, all quantities being
in ha. The demand for land for specific land-uses is
computed on the basis of a set of equations described
below.
4.1. Pastoral land
In the pastoral land, the equilibrium assumption
requires that the consumption of forage is equal to
the biomass production. As, in the Sudano-sahelian
region, pastoralism is mostly extensive, biomass
production relies on the natural productivity of grass-
lands. Thus
BiomPy ∗ Pastd = Liv ∗ BiomC (4)
where BiomPy is the biomass productivity in
tonnes/ha, Liv the livestock population in equivalent
tropical livestock unit (TLU) and BiomC the con-
sumption in biomass per head in tonnes/equivalent
TLU. TLU is a conventional stock unit of a mature
zebu weighting 250 kg (Boudet, 1975). One TLU
corresponds to one cattle, one horse, five asses, 10
sheeps or 10 goats (Pieri, 1989). We assume that
biomass productivity in Sudano-sahelian grasslands
only depends on rainfall (Le Houérou and Hoste,
1977). This is described by the following statistical
relationship between dry matter (DM) biomass and
rainfall, taken from ground measurements by Breman
and de Wit (1983)
BiomPy = 0.15 + 0.00375R (5)
where R is the annual average of rainfall in mm.
Given its natural biomass productivity, a sufficient
area is allocated to pastoral land to produce the
biomass required to feed the livestock population,
which is determined exogenously (FAO, 1995). The
consumption of biomass measured per cattle equiv-
alent (TLU) is estimated at an average value of
4.6 tonnes/year based on the following reasoning. The
average dietary requirements of a TLU are 6.25 kg of
DM per day (Le Houérou and Hoste, 1977; Behnke
and Scoones, 1993; de Leeuw and Tothill, 1993).
The consumable forage of grasses is only one-third
of the above-ground biomass (Penning de Vries and
Djitèye, 1982; de Leeuw and Tothill, 1993). But

production from shrubs and trees, and crops residues
also take part in the biomass consumption of the
livestock (Le Houérou and Hoste, 1977). Pieri (1989)
evaluates this part to one-third of the total con-
sumption. However, this fraction does increase with
scarcity of pastoral land and intensification. Initially,
the model estimated the total DM biomass required
to satisfy the average biomass consumption of live-
stock as 6.25 kg ∗ 365 ∗ 3 ∗ 2
3 = 4.6 tonnes/year.
TLU. The factor 3 accounts for the consumable frac-
tion of above-ground biomass and the factor 2
3 for
the contribution of grasses to the consumption. In
the intensification phase (see below), the later factor
becomes 1
3 (i.e. 2
3 of the consumption is based on
crop residues). The demand for pastoral land is thus
computed endogenously per Eq. (4). Whether this
demand will actually be satisfied will depend on the
competition with the other land-uses.
4.2. Cropland
In cultivated land, food crops for the subsistence
needs of the rural population, are separated from crops
which are commercialised. The subsistence demand
for food crops depends on the rural population and its
basic consumption requirements. The crops which are
commercialised consist mainly of food crops for the
subsistence needs of the urban population, but may
include some cash crops (e.g. cotton). The part of the
production which is commercialised on local markets
generates an income for farmers. The food crops that
are commercialised also depends on cereal imports,
which are assumed to complement the consumption
of the urban population only. The model defines the
demand for cropland as
1. Food crops for the subsistence needs of the rural
population
CropY ∗ CropSd = Poprur ∗ FoodC (6)
where CropY is the crop yield in kg/ha, CropSd
the cropland demand for subsistence in ha, Poprur
the rural population in inhab, and FoodC the food
consumption per capita in kg/inhab.
2. Food crops for the subsistence needs of the urban
population
CropY ∗ CropMd = (Popurb ∗ FoodC)
−CImp (7)
where CropMd is the cropland demand for market
in ha, Popurb the urban population in inhab, and
CImp the cereal imports in kg. The basic consump-
tion of the population is estimated at an average
value of 300 kg of grains per inhabitant, includ-
ing losses at different stages of grain processing.
Local-scale studies in the Sudano-sahelian coun-
tries estimate an average of 250–375 kg of millet
and sorghum production to feed an average per-
son during 1 year (Raynaut, 1985; Lambin, 1988;
Bolwig, 1995). In these countries, the diet is com-
posed by cereals for up to 83% (FAO, 1998) to
90% (Claude et al., 1991) of the total consumption.
About 20% of the harvested grain is lost by shelling
and wastage, or is kept for seeds (Bolwig, 1995).
Estimates of the actual consumption per capita
vary between 230 kg (Claude et al., 1991), 200 kg
(Boulier and Jouve, 1990), and 180 kg (Gueymard,
1985). Based on minimum diet requirements of
2182–2470 kcal for an average person (Banque
Mondiale, 1989), and knowing the caloric supply
of cereals (Ministère de la Coopération, 1984) and
the conversion factor between production and ac-
tual consumption, we estimate an average value of
cereal consumption of 360 kg/inhabitant.
In Eqs. (6) and (7), rural and urban populations, and
cereal imports are exogenous variables derived from
FAO (1995). Crop yield is defined as a linear func-
tion of rainfall (Vossen, 1988; Sicot, 1989; Ellis and
Galvin, 1994; Larsson, 1996). Groten (1991) defines
the relationship between millet production and annual
rainfall as
CropY = 0.91 ∗ R (8)
The cropland area includes fallow
Crop = CropSd + CropMd + Fal (9)
where Fal is the fallow area. At the most extensive
level of cultivation, corresponding to a pre-intensifica-
tion stage (see below), the crop-fallow cycle is 2 years
of fallow for 1 year of cultivation (i.e. cultivation
frequency (CF) = 2 (dimensionless)) (Ruthenberg,
1976). The crop-fallow cycle is modified endoge-
nously under population pressure (see below).

4.3. Fuelwood extraction area
The Sudano-sahelian population uses fuelwood har-
vested from natural vegetation areas as its main energy
source. These areas also provide a number of other
ecological services: biodiversity conservation, source
of natural food and pharmaceutical products, wildlife
for hunting, hydrological balance, etc. Therefore, in
the model, fuelwood extraction areas are treated dif-
ferently than cropland and pastoral land. It assumes
that the fuelwood extraction areas can be reduced on
an annual basis by the expansion of cropland and pas-
toral land. The vegetation cover types where fuelwood
extraction takes place need 20 years to be reconsti-
tuted if they are left unused. Moreover, not all natural
vegetation areas can be destroyed. Actually, the local
population will always protect a certain fuelwood ex-
traction area: minimum area to satisfy some of the fu-
elwood requirements for domestic consumption, forest
reserves, national parks, sacred forests, inaccessible
forests or forests with a high incidence of tse-tse flies
or onchocerciasis. Some authors already noted that,
at the exception of critical situations, one generally
observes a sustainable use of natural vegetation re-
sources in the Sudano-sahelian region (Benjaminsen,
1993; Ite and Adams, 1998). If fuelwood needs
exceed the wood production through natural regrowth
of vegetation, rural households will turn to other
energy sources.
The demand for fuelwood is estimated as
VegPy ∗ Vegd = Poprur ∗ FuelCrur
+Popurb ∗ FuelCurb (10)
where VegPy is the productivity in fuelwood in m3/ha,
Vegd the demand for fuelwood extraction area in ha,
FuelCrur the rural fuelwood consumption per capita
in m3/inhab, and FuelCurb is the urban fuelwood con-
sumption per capita in m3/inhab. Wood consumption
and productivity in fuelwood are estimated from the
literature. Local-scale studies and regional surveys
in the Sudano-sahelian region estimate that 90% of
the energy needs of households are covered by wood
(USED, 1985). An average person uses a minimum
of 1 kg of fuelwood per day (Lambin, 1988), using a
conversion factor of 750 kg/m3 (CTFT, 1989). Some
studies establish that the consumption needs vary
from 0.5 to 1 m3/inhab∗year (USED, 1985; CTFT,
1989). Rural and urban consumptions of fuelwood
are slightly different. In the model, the fuelwood con-
sumption is 0.65 m3 per inhabitant on average for the
rural population. It rises to 0.85 m3 per inhabitant on
average for the urban population. The productivity
in woody biomass in Sudano-sahelian savannahs is
estimated at an average value of 0.75 m3/ha (Pieri,
1989; Yung and Bosc, 1992). In reality, this value
ranges from around 0.1 to 2 m3/ha∗year depending
on rainfall, vegetation cover and soil type.
Initially, all unused land is covered by natural
vegetation
Vegi = N − Crop − Fal − Past (11)
where Vegi is the initial natural vegetation area in ha.
The fuelwood demand is thus easily satisfied. As the
energy demand increases (with population growth)
and the offer for fuelwood decreases (due to agricul-
tural expansion at the expenses of fuelwood extraction
areas), a threshold is reached at which a minimum
fuelwood extraction area is conserved
If Veg − (Landd − UN) > Vegd, then veg
= (Landd − UN), else veg = 0 (12)
where ∆veg is the annual variation in fuelwood
extraction area in ha. This minimum fuelwood ex-
traction area is defined such that it satisfies a certain
proportion of the fuelwood requirements for do-
mestic consumption of the population (Vegd) at the
time when this threshold is reached, i.e. the demand
for fuelwood extraction areas defined in Eq. (10).
Once this threshold is reached, the population has
to satisfy an increasing fraction of its energy needs
through alternative sources such as kerosene. A stan-
dard family in Senegal buys for 3600 FCFA/month,
or 4320 FCFA/year∗person, of alternative energy
(Legendre, 1997). A World Bank report on West Africa
(quoted by Jensen, 1997) estimates the alternative
energy consumption in Senegal at 84,000 TOE/year
(tons of oil equivalent (TOE) = 41.8 GJ). The aver-
age cost of energy substitution per inhabitant and
per year is estimated at 4320 FCFA per approxi-
mately 0.01 TOE. This represents a substitution cost
of 66,900 FCFA/m3 to replace fuelwood by kerosene
(6 m3/TOE, CTFT, 1989)
EnergC = (Ford − For) ∗ VegPy ∗ FuelS (13)

where EnergC is the energy cost in FCFA, FuelS the
fuel substitution cost in FCFA/m3.
5. Processes of land-use changes
In agreement with farming system research, includ-
ing the work of Boserup (1965), the model simulates
two processes of land-use change: agricultural expan-
sion at the most extensive technological level, fol-
lowed by agricultural intensification once some land
threshold is reached.
5.1. Agricultural expansion and deforestation
Expansion of cultivation can take place into previ-
ously uncultivated area or by migration into unsettled
areas without involving any change in the technolog-
ical level of agriculture. Agricultural expansion thus
leads to deforestation or to a regression of pastoral
land. Pastoral land can also expand into natural vege-
tation areas and cropland. Expansion of cropland and
pastoral land is driven by two sets of factors: changes
in human and animal population, which increase the
consumption demand for food crops and forage, and
interannual variability in rainfall, which modifies land
productivity and therefore increases or decreases pro-
duction for a given area under a pastoral or cultivation
use. If rainfall decreases in a given year, farmers are
expected to compensate the decrease in yield by an
expansion of the area under use. If rainfall is above av-
erage, farmers use a smaller portion of land to produce
the same amount of food, thanks to the higher yields.
In this case, some fields are abandoned, all other things
being equal. This (temporarily) unused area becomes
available for another land-use, or for expansion of
cropland or pastoral land in a subsequent year. Expan-
sion of cropland and pastoral land in unused land is
associated with a lower environmental cost than in the
case of deforestation. The effects of demographic and
rainfall changes can concur or be opposed.
5.2. Agricultural intensification and decrease of
pastoral land
Once the expansion of cropland and pastoral land
has occupied all unused land, and once fuelwood ex-
traction areas have reached their minimal area, the land
is saturated. In that case, another process of land-use
change would take place
If UN < Landd and if for = 0,
then CF < 0 and past < 0 (14)
where ∆for is the annual variation in fuelwood
extraction area in ha, ∆CF the annual variation in
CF (dimensionless) and ∆past the annual variation in
pastoral land in ha.
Additional demand for food crops will result
mainly in agricultural intensification with livestock
being increasingly fed on crop residues, but also, in
a lesser way, in expansion of cultivation in pastoral
land. Intensification is defined as the substitution of
capital, labour or technology for land in order to
produce more on the same area. In Sudano-sahelian
agriculture, intensification mostly takes place as a
shortening of fallow cycle, compensated by the use
of labour and agricultural inputs such as organic or
mineral fertilisers to maintain soil fertility (Sanders
et al., 1990; Diop, 1992; Gray, 1999). Because of
deficiencies in output and input data, the crop-fallow
cycle is used as a proxy variable to measure intensi-
fication (following Boserup, 1965 and Turner II and
Brush, 1987). This indicator is expressed by the ratio
between fallow area and cropland
CF =
Fal
(CropSd + CropMd)
(15)
fal = ( Cropd ∗ CF1961)
−((Landd − UN) ∗ (1 − r)) (16)
where ∆fal is the annual variation in fallow area in
ha, CF1961 the CF in 1961 and r the ratio of pastoral
land to cropland . These two last indicators are di-
mensionless. Part of the additional demand for food
crops will also lead to the expansion of cultivation
in pastoral land. Actually, the economic value of the
output per unit of area is much higher for cultivated
fields than for pastoral land in an extensive system (de
la Masselière, 1984; Okoruwa et al., 1996). The exact
proportion of additional food demand which is sat-
isfied by intensification of cultivation and expansion
of cultivated fields in pastoral land is set arbitrarily at
80% for the former and 20% for the later.
The increase in livestock population combined
with shrinking pastoral lands (due to agricultural

expansion) will result in partial sedentarisation of
livestock, with greater reliance on crop residues
for consumption, and overgrazing on pastoral land
(Sinclair and Fryxell, 1985; Hellden, 1991). Seden-
tarisation is modelled by an increase in the share of
crop residues in livestock consumption (2
3 of biomass
consumed, see above). The modelling of overgraz-
ing is described below. There are few reported in-
stances of intensification of livestock grazing in the
Sudano-sahelian region. Practices such as artificial
fertilisation, livestock stabling and cultivation of fod-
der crops are unusual in this region (Le Houérou and
Hoste, 1977).
6. Endogenous pressure indicators
Agricultural intensification leads to a decrease in
labour productivity and requires the use of organic
or chemical inputs. A shortening of the fallow cycle
without input use would deplete soil fertility. Several
“pressure indicators” are generated endogenously by
the model: labour productivity, agricultural input use
as a function of the average household budget, main-
tenance of soil fertility in cultivated fields, and rate of
land degradation in pastoral land due to overgrazing.
These indicators are symptoms of changes in the sys-
tem and can be interpreted to identify some sustain-
ability thresholds, which might affect decision-making
processes by farmers and pastoralists.
6.1. Labour productivity
Labour productivity is defined by the output per
hour of labour, or the income per unit of time invested
(Stomal-Weigel, 1988). In the intensification process,
labour productivity decreases because the increase in
labour input is more than proportional than the produc-
tion increase (Bonnefond and Couty, 1988). Estimat-
ing the time allocated to agricultural work is difficult
due to differences by gender and age, varying labour
efficiencies, seasonal distribution of tasks, and inher-
ent difficulties in labour time estimation. The model
defines the labour quantity as the number of hour per
day allocated to agriculture per rural worker. This time
allocated to agricultural work is proportional to CF, as
a proxy for intensification:
LabourQy = a + b ∗ CF (17)
where LabourQy is the labour quantity in hours in
agricultural work/day∗inhab, and a and b are dimen-
sionless parameters. From several studies in Africa
(Cleave, 1974; Raynaut et al., 1988; Stomal-Weigel,
1988), an average labour time allocated to agriculture
is 200 h per year per inhabitant under an extensive
farming system, i.e. with a CF of 2. The highest
level of agricultural intensity found in West African
agriculture, i.e. with a CF of 0.5 (Ruthenberg, 1976;
Raynaut, 1985), is characterised by an addition of
4 h per day of farming work (Netting et al., 1993).
Based on this reference, we estimated empirically the
parameters of the above relationship (a = 5.833 and
b = −2.667). Labour productivity is then computed
by the ratio between the agricultural output and the
amount of labour performed by the rural workers for
a given year. Agricultural output is measured by the
cultivated area multiplied by the average crop yield.
LabourPy =
Crop ∗ CropY
Poprur ∗ LabourQy ∗ 365
(18)
where LabourPy is the labour productivity in kg/hour
of work.
6.2. Agricultural input use and household budget
When the length of fallow decreases, farmers intro-
duce technological inputs to maintain soil fertility. By
reference to a detailed study in Senegal (Diop, 1992)
and various other studies in West Africa (Retaille,
1984; Raynaut, 1985; Claude et al., 1991; Seini et al.,
1995), an average cost is 24,000 FCFA for agricultural
inputs per agricultural exploitation in the first stage
of the transformation of shifting cultivation systems
into permanent farming (Boserup, 1965; Ruthenberg,
1976). The fallow is substituted by mainly natural fer-
tilisers and selection of seeds, with only a minor use
of mechanisation (Diop, 1992). The mean farm size
in Senegal is estimated at 4.5 ha (Ancey, 1977; Little
et al., 1987; Pieri, 1989; Saul, 1991). The model esti-
mates the necessary investment in agricultural inputs
per hectare to maintain the yield level on the entire
cultivated area. We assume that the cost of inputs per
hectare in Senegal and other Sudano-Sahelian coun-
tries are equal. This quantity of inputs (mostly fertilis-
ers) is expressed in monetary value (cost of inputs)
InputC = Crop ∗ InputP ∗ (CF1961 − CF) (19)

where InputC is the input cost in FCFA and InputP
the input price in FCFA/ha. To maintain fertility, the
agricultural inputs must compensate the decrease in
fallow time. If farmers are not able to afford this cost,
e.g. because their monetary income would be too low,
then a decrease in soil fertility in cropland takes place
(Traoré and Galley, 1979). The model computes this
degradation of soil fertility by comparing the invest-
ment in agricultural inputs to the shortening of the
fallow (see below).
The ability to invest in agricultural inputs depends
on the household budget, which is computed as the
difference between incomes and expenses. The share
of production sold on the market generates incomes
from which one subtracts the cost of the substitutes
for fuelwood and the cost of agricultural inputs. Food
demand of the urban population defines the amount
of food crops sold on the market. However, this also
depends on cereal imports (an exogenous variable)
which are used to feed urban population. The monetary
value of food crops sold on the market (50 FCFA/kg)
is computed from average market prices for millet and
sorghum (Bonnefond and Couty, 1988)
HhInc = (Crop − CropSd) ∗ CropY
∗50 FCFA/kg (20)
where HhInc is the household income in FCFA. Note
that several studies reveal that non-farm activities rep-
resent an important part of the income in rural regions
of West Africa (Reardon et al., 1988; Staatz et al.,
1990). Since, these activities do not modify directly
land-use, they are not represented explicitly in the
model. There is just a fixed income from non-farm
activities which is added to the income generated
from the sale of food crops on urban markets.
The household income is in part used to acquire
agricultural inputs, provided that such inputs are
needed (i.e. provided that the farmers have entered
in the intensification phase). Only a fraction of the
household income can be allocated to acquiring in-
puts, as there are a number of other needs (housing,
clothing, taxes, leisure, etc.). Based on empirical
studies, the model considers that the maximum share
of the income which is allocated to buying agricul-
tural inputs is 13% (Retaille, 1984; Diop, 1992; Seini
et al., 1995). If the cost of the required inputs is in-
ferior to this value, the land fertility is maintained. If
the cost of inputs exceeds this threshold, a decline in
soil fertility is taking place. Indeed, the rate of soil
fertility decline depends on the amount of inputs that
are used in relation with the fallow cycle.
6.3. Maintenance of soil fertility of cultivated fields
A shortening of the fallow cycle and an insufficient
use of agricultural inputs reduces soil fertility of fields
and, therefore, has a negative impact on crop yields.
The model estimates this soil degradation as a dimen-
sionless indicator
Deg =
2 − CF
2
+
InputC − Invest
InputC
(21)
where Deg is the dimensionless indicator of degrada-
tion and Invest the investment in FCFA. In the absence
of any fallow and fertilisers, yields decrease by 20%
after 4 years of permanent cultivation (Pieri, 1989).
In extensive farming systems in African savannahs,
4 years is the usual time limit to put the land into
rest (Pieri, 1989; Olsson and Rapp, 1991; Guyer and
Lambin, 1993). We extrapolate this rate of yield
reduction to establish a linear relationship between
the period under continuous cultivation and yield
decrease, in the absence of any agricultural inputs
CropYt
CropYt−1
= 1 − (0.05 ∗ y) (22)
where y is the number of years under continuous culti-
vation (dimensionless). The slope of this relationship
varies between two extremes: (i) fertility maintenance
through either adequate fallow cycle or input use and
(ii) rapid loss of soil fertility due to continuous cul-
tivation and no input use. A combination of reduced
fallow and inadequate fertility conservation methods
would lead to a moderate rate of yield reduction,
described by
CropYt
CropYt−1
= 1 − (0.05 ∗ y ∗ Deg) (23)
6.4. Land degradation in pastoral land due to
overgrazing
To model the process of overgrazing, the carry-
ing capacity concept is used for the sake of simpli-
city (Bartels et al., 1993). It is defined here as “the

stocking number supported without range degrada-
tion, with livestock being well and taking weight”
(Boudet, 1975). Depending on ecoclimatic zones, pas-
toral exploitation systems, estimates of average car-
rying capacity vary from 10 ha/TLU in drier years to
3.5 ha/TLU in normal years (Boudet, 1975; Penning
de Vries and Djitèye, 1982). Actual measurements
of carrying capacities are 2 ha/TLU (Horowitz and
Salem-Murdock, 1993) and 1.25 ha/TLU (Boulier and
Jouve, 1990). Overgrazing is defined by the stocking
outnumbering the carrying capacity. Tolerance levels
are estimated in the literature from 160 to 200% of the
carrying capacity (Picardi and Seifert, 1976; Bartels
et al., 1993).
The model represents a transhumant pastoral sys-
tem where, beyond a certain threshold, plant biomass
decreases proportionally to the increase in animal
biomass. As the expansion of pastoral land is limited
by other land-uses, an increase in livestock population
on shrinking pastoral land decreases land produc-
tivity. The model compares the maximum carrying
capacity (1.25 ha/TLU) to the available pastoral land
and its stocking rate
Overg =
Liv − (Past/CC)
Past/CC
(24)
where Overg is the dimensionless indicator of over-
grazing and CC the carrying capacity (1.25 ha/TLU).
This high value of carrying capacity accounts for
herds mobility and for the pastoral strategy of min-
imising the understocking. Once the actual stocking
rate is larger than this carrying capacity, a process
of rangeland degradation is set up. Empirical data
in the “Mare d’Oursi” (Burkina Faso) reveal that an
overstocking of 36% reduces land productivity by
30% (Claude et al., 1991). Other authors (Penning de
Vries and Djitèye, 1982) suggest that these figures are
grossly overestimated given the resilience of Sahelian
ecosystems, and that the relationship between plant
and animal biomass is negatively asymptotic. Actu-
ally, estimating quantitatively dryland degradation is
almost an impossible task. In the absence of any other
published quantitative study, and to be conservative,
we adopted arbitrarily a value of only 10% of the
land productivity reduction estimated by Claude et al.
(1991) in response to overstocking. This is thought to
better account for the ecological resilience of range-
lands and for the adaptive strategies of pastoralists.
This figure is extrapolated to a linear function where
the level of overstocking determines the slope of the
relation between biomass productivity and rainfall
If
Liv − (Past/CC)
Past/CC
≥ 0, then BiomPy
= 0.15 + 0.00375R,
If
Liv − (Past/CC)
Past/CC
< 0, then BiomPy
= 0.15 + b ∗ R with b = d + c(Overg),
If Liv =
Past
CC
, then d = b = 0.00375,
If
Liv − (Past/CC)
Past/CC
=
0.36
0.30
∗ 10 = 12,
then b = 0 and c =
−0.00375
12
where b, c and d are statistically derived parameters
(dimensionless). The relation becomes
BiomPy = 0.15 + (0.00375
−0.0003125(Overg)) ∗ R (25)
7. Dynamic character of the model
Fig. 1 represents the overall structure of the model.
This includes: (i) the exogenous driving forces of
land-use changes, (ii) the competition for land-use al-
location, (iii) the different phases of land-use changes
and (iv) the pressure indicators. Table 1 summarises
the values of the main parameters of the model and
their sources, and Table 2 lists the variables. The
model is dynamic in the sense that it includes multiple
interactions between processes, feedback loops and
endogenous changes in “phases” of land-use change
corresponding to different levels of farming tech-
nologies. For example, the processes leading to land
degradation link agricultural intensification, average
household income, commercialisation, rural and urban
demand for food products, cereal imports, etc. (Fig. 2).
Land degradation is thus the result of complex inter-
actions between numerous factors. In no way it can be
reduced to a simple population–degradation relation-
ship. It can only be predicted using a dynamic, system
approach.

Fig. 1. Overall structure of the model.
Table 1
Summary of the values retained for the main parameters of the model, and literature sources from which these values where derived
Consumption parameters
Food consumption FoodC 300 kg/inhab∗year Bolwig (1995), Boulier and Jouve (1990), Claude et al.
(1991), Gueymard (1985), Lambin (1988), Netting et al.
(1993), Raynaut (1985), Reardon et al. (1988), USED
(1985)
Livestock forage consumption BiomC 4.6 tonnes/equiv TLU∗year Behnke and Scoones (1993), Boudet (1975), Claude et al.
(1991), Groten (1991), Lambin (1988), Ministère de la
Coopération (1984), Penning de Vries and Djitèye (1982),
Pieri (1989)
Fuelwood needs: urban consumption FuelCurb 0.85 m3/inhab∗year CTFT (1989), Jensen (1997), Lambin (1988), Pieri (1989),
USED (1985)
Fuelwood needs: rural consumption FuelCrur 0.65 m3/inhab∗year CTFT (1989), USED (1985)
Productivity parameters
Fuelwood productivity in
natural vegetation
VegPy 0.75 m3/year CTFT (1989), Lambin (1988), Pieri (1989), van Lavieren
and van Wetten (1990) quoted by Horowitz and Salem-
Murdock (1993), Yung and Bosc (1992)
Crop-fallow cycle/cultivation
frequency
CF 2 years/3 under crops Boulier and Jouve (1990), Claude et al. (1991), CTFT
(1989), Guyer and Lambin (1993), Pieri (1989), Raynaut
(1985), Ruthenberg (1976)
Carrying capacity CC 1.25 ha/TLU Boudet (1975), Boulier and Jouve (1990), Horowitz and
Salem-Murdock (1993), Penning de Vries and Djitèye
(1982)
Fuel substitution FuelS 66,900 FCFA/m3 CTFT (1989), Jensen (1997), Legendre (1997)

Table 2
Summary of the notations and dimensions for the main exogenous and endogenous variables of the model
Main variables Notation Dimension
Exogenous variables
Cereal imports CImp kg
Livestock Liv equivalent TLU
Rainfall (annual average) R mm
Rural population Poprur inhab
Urban population Popurb inhab
Land-use variables
Used area U ha
Unused area UN ha
National area N ha
Land demand Landd ha
Cropland Crop ha
Cropland demand for market CropMd ha
Cropland demand for subsistence CropSd ha
Fallow area Fal ha
Fuelwood extraction area (natural vegetation) Veg ha
Initial forest area Vegi ha
Demand for forest area Vegd ha
Pastoral land Past ha
Demand for pastoral land Pastd ha
Annual variation (in most of the preceding variables) D ha
Biomass productivity BiomPy tonnes/ha
Crop yield CropY kg/ha
Endogenous processes
Overgrazing Overg Dimensionless
Cultivation frequency CF Dimensionless
Cultivation frequency in 1961 CF1961 Dimensionless
Degradation Deg Dimensionless
Energy cost EnergC FCFA
Household income HhInc FCFA
Input cost InputC FCFA
Input price InputP FCFA/ha
Investment Invest FCFA
Labour productivity LabourPy kg/hour of work
Labour quantity LabourQy hours/day∗inhab
Ratio pastoral land to cropland r Dimensionless
Number of years under continuous cultivation y Dimensionless
8. Application of the model to Burkina Faso
The model was ﬁrst tested at a national scale using
data from Burkina Faso, over the period 1960–1997.
The annual rate of population growth was 2.4% in
Burkina Faso during the 1960–1990 period. Droughts
have been frequent in the Sahel over the 1972–1984
period (Nicholson, 1989; Jouve, 1991). The model
simulates changes in land-use over the study period
for all land-use categories (Fig. 3).
Results show land-use changes at two time frequen-
cies: high frequency, as driven by climatic variability,
and low frequency, as driven by demographic trends.
Concerning the short-term events, every drought
period is associated with a slight expansion of crop-
land and pastoral land in fuelwood extraction areas
(until 1988) and in unused land. Once rainfall recov-
ers to a normal level, a peak increase in unused land is
observed (e.g. in 1985, after the 1984 drought). Con-
cerning the longer term trends, a phase of expansion

Fig. 2. Dynamic interactions between the processes leading to land degradation.
of cropland, fallow and pastoral land accompanied by
deforestation first appears in 1970s and early 1980s.
At the end of this phase, deforestation is stopped, due
to constraints on the conservation of a minimum fu-
elwood extraction area. Cultivated areas and fallows
continue to increase. The area allocated to crops for
the market increases steadily, as a response to the
rapid increase in urbanisation. This increase takes
place at a faster rate than the total cropland area as
the urban population grows faster than the rural pop-
ulation. After 1983, the system oscillates between the
Fig. 3. Model simulations of land-use changes in Burkina Faso.
phases of agricultural expansion and intensification.
The first signs of land degradation in cropland ap-
pear in 1991. Degradation in pastoral land, caused by
overgrazing, appears sporadically, mostly in 1980s.
At a first glance, by reference to the literature on
land-use changes in the Sudano-sahelian countries,
this simulation is a plausible representation of the
land-use evolution in Burkina Faso. In the expansion
phase, from 1960 to 1983, case studies evidence from
the Burkina Faso provide quantitative information
mainly for the change in cropland. The rate of change

Table 3
Annual rates of land-use changes in the expansion phase from the model simulation and from literature sources
Expansion phase (1961–1983) Annual rates of change
in cropland (%)
SALU model Burkina Fasoa 4.91
Lindqvist and Tengberg (1993)
Northern Burkina Faso
1955–1974 4.87
Gilruth and Hutchinson (1990)
Fouta Djallon, Guinea
1953–1989 5.31
Raynaut et al. (1988)
Maradi, Niger Tarka
1957–1975 5.80
Magami 4.00
Sharken H. 1.40
Gourjae 2.90
Average 3.00
Reenberg et al. (1998)
Oudalan Province, Burkina Faso
1945–1955 3.44
1955–1986 1.83
Moussa (1999)
SO Niger Bogodjotou
1956–1996 2.00
Ticko 1.60
FAO (1995), Faostat — series statistics, Burkina Faso 1961–1984 1.65
a BF: Burkina Faso.
of 4.9% predicted by the model simulations is simi-
lar to the rate of change measured by Lindqvist and
Tengberg (1993) — 4.9% in northern Burkina Faso.
Over the same period, other studies throughout the
Sudano-sahelian region report cropland expansion at
annual rates from 3 to 5.8% (Table 2). Note that, the
rate of cropland expansion for Burkina Faso based on
Table 4
Annual rates of land-use changes in the period following the first occurrence of intensification (1984) from the model simulation and from
literature sources
Intensification phase (1984–1997) Annual rates of change
in cropland (%)
SALU model Burkina Fasoa 1.42
Lindqvist and Tengberg (1993)
Northern Burkina Faso
1955–1981 2.88
Gilruth and Hutchinson (1990)
Fouta Djallon, Guinea
1973–1985 11.59
Reenberg et al. (1998)
Oudalan Province, Burkina Faso
1988–1989 4.84
1989–1991 2.84
1991–1995 1.58
Moussa (1999)
SO Niger Bogodjotou
1975–1996 3.40
Ticko 2.80
FAO (1995), Faostat — series statistics, Burkina Faso 1985–1997 1.34
a BF: Burkina Faso.
the Faostat data is only 1.6%. In the period after the
first occurrence of intensification (1984), expansion of
cropland is predicted by the model to take place at a
rate of 1.4%. This is lower than the figure provided by
Lindqvist and Tengberg (1993) for northern Burkina
Faso (2.9%). Other studies in the Sudano-sahelian cou-
ntries reveal a similar range of values (Tables 3 and 4).

However, the rate of cropland expansion in Faostat
data is much lower compared to all these local studies
(1.3%).
9. Discussion
Models are always based on simplifications. In
this case, the computation of the area under pastoral
land (Eq. (5)) assumes that land management and soil
attributes do not influence biomass productivity in a
significant way. Concerning the first factor, this is an
acceptable assumption in the Sudano-sahelian region
given the extensive character of pastoral activities.
Concerning the second factor, as the model is not spa-
tially explicit, it only represents average soil attributes.
Several authors, however, caution that low availabil-
ity of soil nutrients is a more serious constraint on
rangeland production and quality than low rainfall
(Penning de Vries and Djitèye, 1982; Breman and de
Wit, 1983). The estimation of crop yield (Eq. (8)) also
ignores cropping systems, soil fertility and the dis-
tribution of rainfall during the growing season. Some
management factors are however introduced through
the crop-fallow cycle and the use of agricultural in-
puts. Improving these production functions would
increase the realism of the model but also its data
requirements.
Particular land-uses which are of a small extent
in most Sudano-sahelian countries, such as irrigated
fields or forest plantations around settlements are not
represented in the model, even though their impor-
tance for household economies can be significant.
Protection of forest reserves, which is included in
the model, is generally observed in rural regions but
the satisfaction of energy requirements for the urban
population does induce widespread deforestation in
peri-urban areas. Finally, the model uses the concept
of carrying capacity in rangelands, which has lost
currency in ecology. Critics of this concept find argu-
ments either in natural opportunistic pastoral strategies
of herdsmen to avoid understocking (Sandford, 1982),
or in the actual growth of herds beyond this capac-
ity (Bartels et al., 1993). State and transition models
(Westoby et al., 1989) and “non-equilibrium” models
(Ellis and Swift, 1988) seem to be more appropriate
to describe rangeland modifications. We are aware of
these different paradigms, but we still use the carrying
capacity concept as a simplification to model in a more
“static” way the stocking pressure on rangelands.
A number of improvements to this initial version of
the model are being considered. In the current model,
the consumption pattern is assumed to be constant.
In reality, it could shift towards more affluent diet
with an increase in level of well-being. More funda-
mentally, the model is not spatially explicit but only
predicts aggregated values of land-use change. We are
currently disaggregating the model per eco-climatic
zone within each country (e.g. mostly pastoral
Sahelian zone versus Sudanian zone dominated by
farming). This will allow varying key parameters
such as wood productivity or carrying capacity, which
can be given a different value for different ecological
zones. A more systematic sensitivity analysis of the
model to parameter values will also be conducted.
In the current version of the model, the “pres-
sure indicators” are only diagnostic indicators of the
system. In a more sophisticated use of the model,
the pressure indicators could be used in a goal pro-
gramming approach to better represent the decision
process of land managers. Actually, land managers
could express preferences for their labour productiv-
ity, their income or the conservation of their natural
environment. They could also maximise productivity
or minimise risk under certain constraints. These dif-
ferent attitudes, reflecting different values, will lead
to a different allocation of land.
We are currently testing the model for other
Sudano-sahelian countries. Currently, the study area
is closed, except for food imports. For a regional
application of the model, spatial interactions between
countries (e.g. balanced, not prescribed trade pat-
terns) should be represented. Finally, the model out-
puts are currently being validated by comparing the
land-uses projected by the model for 1992–1993 to the
land-cover map produced by IGBP-DIS from remote
sensing data, for the same years. This “validation”
only concerns the “quantity” of land-use categories
and not their location.
10. Conclusion
A simulation model which was specifically aimed
at generating simulations of land-cover changes at a
coarse spatial resolution was developed. This model

is specific to the Sudano-sahelian countries. The main
characteristic of the approach lies in the definition of
values for the parameters of the model on the basis
of a comprehensive review of the literature, mostly
of local scale case studies of land-use changes in
the Sudano-sahelian countries. New values of the
exogenous variables of the model are introduced in
the model on a yearly time step and drive changes in
land-use allocation. The model predicts endogenously
changes in the technology of farming systems. Pres-
sure indicators are also generated endogenously by the
model. The model was applied at a national scale using
data from Burkina Faso. Results simulate land-use
changes at two time frequencies: high frequency,
as driven by climatic variability, and low frequency,
as driven by demographic trends. The model predicts
an increase in land degradation in the early 1990s.
The rates of cropland expansion predicted by the
model are consistent with rates measured for several
case studies, based on fine spatial resolution remote
sensing data. In the model simulations, intensification
appears in Burkina Faso in the mid-1980s.
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