A Dynamic Model of Household Decision Making and Parcel
Level Landcover Change in the Eastern Amazon
Tom P. Evans*1
Aaron Manire*
Fabio de Castro*2,3
Eduardo Brondizio3,4
Stephen McCracken3
*
Center for the Study of Institutions, Population and Environmental Change
1
Department of Geography
2
School of Public and Environmental Affairs
3
Anthropological Center for Training and Research in Global Environmental Change
4
Department of Anthropology
Indiana University
Corresponding Author:
Tom Evans (evans@indiana.edu)
Department of Geography
Student Building 120
Indiana University
Bloomington, IN 47405
April 13, 2000
Abstract
The region around Altamira, Brazil, located in the Eastern Amazon, has experienced rapid landcover
change since the initiation of government sponsored colonization projects associated with the construction
of the Trans-Amazon Highway. The thirty years since colonization (1971) have been marked by a net loss
of forest cover and an increase in the amount of cultivated/productive land, particularly for pasture and
annual/perennial crop production. This research presents a parcel-level model of landcover change for
smallholders in the Altamira study area. The utility of specific land-use activities is calculated to identify
those land-uses that are most optimal at each time point and labor is allocated to these activities based on
the availability of household and wage labor. The model reports the proportion of the parcel in the
following landcover classes at each time point using a one year interval: mature forest, secondary
successional forest, perennial crops, annual crops and pasture. A graphical user interface is used for
scenario testing, such as the impact of high/low (population) fertility, the increase of out-migration to urban
areas, or changes in cattle and crop prices. The model shows a rapid reduction in the amount of mature
forest in the 30 years following initial settlement, after which the parcel is composed of a mosaic of
secondary succession, pasture and crops. The nature and rapidity of this landcover change is the function
of a variety of household and external variables incorporated in the model. In particular, the model
produces different landcover compositions as a function of demographic rates (fertility, mortality) and
agricultural prices.
Keywords: landcover change, simulation, deforestation
Acknowledgements
The research described in this paper is the product of many institutions and team researchers. A larger set
of projects conducting research in the Altamira study area is supported by NIHCHD (9701386A), NSF
(SBE 9896014) and NASA (NCC5-334) funding. Emilio Moran, Andrea Siqueira and numerous Brazilian
collaborators have led the research behind this set of projects. Emilio Moran provided helpful comments
during the construction of this model. Institutional support from the Center for the Study of Institutions,
Population and Environmental Change (NSF; SBR 9521918) is gratefully acknowledged.
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1. Introduction
The Brazilian Amazon has undergone tremendous landcover change in the past forty years.
In particular, the introduction of the Trans-Amazon highway and subsequent colonization of
territory in close proximity to the highway has led to large scale social and biophysical change in
parts of the Amazon. Much of the area where the most rapid landcover change has occurred has
been part of government sponsored colonization projects where individual parcels are surveyed
and then allocated to colonists. These areas are composed of mature forest prior to settlement and
subsequently transformed to a mosaic of pasture, cultivated lands and different stages of forest
regrowth associated with fallowed agricultural land. A substantial amount of research has been
focused on the Brazilian Amazon given its importance to global geo-chemical cycles and rich
species diversity. Regional level analyses have documented the spatial extent of deforestation
and attempted to link this deforestation to regional population changes (Skole and Tucker 1993).
Household level analyses have focused on micro-scale factors contributing to landcover change
including parcel soil characteristics, household income and demographic structure (Brondizio et
al. forthcoming; McCracken et al. forthcoming; Moran et al. forthcoming).
There is a wide range of processes affecting landcover change in the Amazon including
social, biophysical, economic and institutional components (Moran 1981; Walker and Homma
1996). Thus the data collection requirements to examine the process of landcover change are
considerable (McCracken et al. 1999). This is particularly true of spatially explicit datasets where
each component to the statistical model must be georeferenced to be integrated in a spatial
information system. Household social surveys provide in-depth information at the level at which
land-use decisions are made but require large teams of researchers due to travel time requirements
and the complexity of the survey instruments. Multi-temporal remotely sensed imagery can
provide a continuous spatial coverage of landcover change, but the data processing and field
validation requirements necessary to obtain a higher order landcover classification is
considerable.
1
Dynamic modeling provides a means by which these landcover change processes can be
examined and different scenarios tested from a systems perspective (Costanza et al. 1993; Dale et
al. 1993; Voinov et al. 1999). These models can be calibrated and validated using a combination
of primary data from field data collection and from existing literature to develop a tool whereby
different simulations and scenarios may be tested. This paper presents a dynamic model of
household decision making and landcover change at the parcel level for Altamira, Brazil. The
purpose of this model is to identify those factors that are important components to the process of
landcover change and to test a variety of scenarios or conditions for their impact on landcover
change. While the long-term predictive ability of any model is limited for various reasons (such
as unforeseen shocks to system or dramatic changes in technology), as a tool dynamic models can
provide considerable insight into the complex interactions operating to affect landcover change.
The model presented here is designed to be run for a 30-100 year period representing multiple
generations for the household. The model simplifies many elements of landcover change but
includes enough complexity that important relationships between labor, resources and landcover
can be observed.
2. Altamira, Eastern Amazon
Altamira located in the Xingu Basin of the Brazilian Amazon, is an old riverine town that
experienced government directed large-scale colonization starting in 1971 (Moran 1981). Parcels
are rectangular lots of approximately 100 ha (500 m x 2000 m), with the 500 m boundary
adjacent to the road to maximize the collective access for all parcels and there is relatively little
variance in the size of parcels (~100 ha). This land settlement pattern has resulted in the
documented ``fishbone'' pattern of settlement and deforestation found in many but by no means
all parts of the Brazilian Amazon (Moran et al. 1994).
During the initial wave of colonization (ca. 1971), each household was given a single parcel
in exchange for little, if any, capital. Subsequent waves of colonization also have seen households
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allocated a single parcel, although as time passed land acquisition required more capital due to the
emergence of a land market reflecting the area's development and farm improvements (e.g.
buildings, cleared forest, pastures). To date there is no evidence that parcel fragmentation exists
in the Altamira study area and relatively little land consolidation. In other words, there has been
little change in the originally established parcel boundaries since the time of initial colonization.
While the initial wave of colonists needed very little capital to purchase rights to a parcel,
parcels on which there have been improvements (e.g. land cleared for pasture, buildings) can be
sold by first generation colonists for substantial amounts. Households must save in order to make
the substantial investment needed to acquire land for their children. The most common pattern is
for children to acquire their own land for cultivation rather than to inherit fragments of their
parent’s parcels. Land prices and the resistance to land fragmentation encourage second
generation colonists to seek land in frontier areas far from their relatives.
After 25 years of settlement, 61% of the Altamira study area remains in primary forest
(Brondizio et al. forthcoming). About half of the deforested area from 1970 to 1996 remains in
production (pasture, annuals, perennials) in 1996 and the other half has been taken over by
secondary forests and fallows (Brondizio et al. forthcoming). The land that has transitioned from
cleared land to secondary succession includes lands where farmers perceived agricultural
production to be marginal due to initial conditions of the soil or by successive years of cultivation
and associated soil nutrient depletion. Of the area in production, 50-80% of the landcover is in
pasture (Brondizio et al. forthcoming). There seems to be a clear association between the
percentage of a property in pasture and the absence of above-average soils. As the amount of
nutrient rich alfisols increases, the percent of the property in pasture declines and the area in
cocoa and sugar cane increases (Moran et al. forthcoming).
The data show consistent deforestation trajectories across cohorts with marked oscillation
reflecting changes in the larger political economy (Brondizio et al. forthcoming). Farmers
deforest steadily in the beginning stages of settlement to establish cultivatable land (Brondizio et
-3-
al. forthcoming; Dale et al. 1993; Leite and Furley 1985). After this initial clearing there is an
increase in pasture and perennial crop land while landholders maintain a modest amount of land
for annual crop production (rice and beans).
3. Modeling Land Use in the Amazon
Land-use dynamics have been the focus of a large body of research in the Brazilian Amazon
(Dale et al. 1993; Dale et al. 1994; Moran et al. 1994; Walker and Homma 1996). Dale et al.
(Dale et al. 1993) developed a dynamic model of regional-level landcover change for Central
Rondônia, Brazil an area that is characterized by the same fishbone settlement pattern as
Altamira. Their model (Dynamic Ecological – Land Tenure Analysis (DELTA)) uses different
scenarios to determine the impact of different land-use systems on carbon release and habitat
fragmentation at the parcel level and then aggregates the individual parcel results up to a regional
level model (Dale et al. 1994). In particular, the model compares the landcover composition and
pattern as a result of two land-use strategies: 1) a system typical of that observed in the study area
where forest is initially cleared for annual and perennial crops followed by pasturing, and 2) a
cultivation system where there is a greater diversity of crops and farmers receive no income from
cattle production. Each land-use system is given specific landcover characteristics and the model
produces a regional scale representation of landcover pattern and composition in addition to an
accounting of the impact of modeled landcover changes on carbon sequestration and species
habitat. The DELTA model predicts that a more diversified system of land management can
reduce carbon release and increase the productivity of the land over time (Dale et al. 1993).
In addition to land-use strategies, the DELTA model predicted that soil and vegetation
conditions would affect the landcover composition as a result of their affect on crop yields and
forest regrowth rates (Dale et al. 1993). Factors external to the parcel have also been observed to
affect landcover, including distance to markets, transportation accessibility and market prices
(Dale et al. 1993; Walker and Homma 1996). In particular, road conditions can vary dramatically
-4-
between the rainy and dry season, affecting crop choice. For example, one method of
ameliorating the impact of poor road conditions is to substitute land-uses that produce goods that
require less frequent access to markets (e.g. cattle production). Perhaps more importantly, the
fishbone settlement pattern is characterized by some parcels being adjacent to the primary road
(first line), while parcels that were surveyed and settled in subsequent waves of colonization are
more often located on feeder roads that are in relatively poor condition or farther from the closest
market along the primary road. The net result is that subsequent waves of settlers have greater
travel times to market than settlers who were part of the initial settlement wave.
4. Model Description
The model presented in this paper differs from the DELTA model in that each land use
activity is assigned a specific utility based on 1) the labor and economic resources available to the
household and 2) the expected benefit from that land use activity based on crop and cattle prices.
Labor is allocated to specific land-use activities based on these relative utilities; landholders seek
to maximize their financial income by allocating labor to the those activities that they perceive
will provide the greatest financial return on their labor investment. In other words, the land-use
system chosen by the household is a product of the model structure rather than an input to the
model. The simulation is designed to be run over approximately seventy years using a one year
time step. Landholders can select multiple land-use decisions (e.g. cut primary forest for annuals
production, convert annuals to pasture…) in one year, but there is only one decision making
round per year. At the beginning of the model run the entire parcel is composed of mature forest
simulating the settlement of a previously uncultivated area. Field data shows that the majority of
parcels in the Altamira study area vary in size between approximately 90 and 110 ha. A parcel
size of 100 ha is used for the model runs presented here based on a 500m x 2000m rectangular
area. The model may easily accommodate alternative parcel sizes by adjusting the initial size of
mature forest at the beginning of the model run.
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The model is organized into the following sectors representing the major processes affecting
landcover change: demography, household economics (finances and prices), land-use decision
making, labor allocation, and institutions. Figure 1 shows a conceptual diagram describing how
the main model components are related in the model structure. The interactions between each of
these sectors result in specific land management decisions that affect the landcover sector where
the landcover composition of the parcel is tracked. These landcover decisions result in clearing
of forested land, fallowing of agricultural land, and the transition from one type of agricultural
production to another. These landcover changes result in changes in the landcover composition
of the parcel. Landcover class proportions are reported for the entire parcel and thus there is no
representation of the landcover pattern within the parcel (e.g degree of fragmentation, number of
patches). Currently the model assumes that biophysical parameters are homogenous within the
parcel, such as soil fertility, topography and hydrography.
The model consists of a labor allocation framework whereby landholders invest labor and
resources in specific activities to either maintain land already under one activity (e.g. perennial
crop production) or convert area in one land-use to another land-use (e.g. the conversion of
mature forest to annual crop production). While there is a clear distinction between land-use and
landcover in Altamira (e.g. successional forests can either be used for agroforestry, non-timber
forest production, or simply abandoned agricultural land), the model presented here has a one-toone correspondence between each land-use activity and a corresponding landcover class. The
area (ha) in each land use is reported in single year intervals, showing the landcover composition
over time and the types and proportions of landcover transitions that have occurred during the
model run. The model is run for an individual parcel given a set initial household composition,
but multiple model runs can be aggregated to provide a regional scale representation of landcover
change. However, in order to more properly model a regional scale representation of landcover
change, various parcel characteristics affecting land-use would need to be included such as
-6-
transportation accessibility measures and soil characteristics to represent the variable of soil
conditions in the Altamira study area.
4.1. Demography Sector
The demographic sector controls human fertility, mortality and migration events for members
of the household (Figure 2). The age and sex composition of the household is represented using
the following demographic groups: children (0-14), adult males (15-64), adult females (15-64)
and seniors ( 65). This breakdown was constructed to account for the different contributions
that household members (men, women, children) make to household, farm wage labor and offfarm wage labor activities.
While dynamic models typically represent fertility, mortality and migration as rates, the
model presented here uses probabilities to initiate specific demographic events (e.g. a birth, an
adult male migrating to an urban area). Rather than having continuous flows in and out of the
demographic stocks, there is a specific probability of a birth, death or out-migration from each
demographic stock at each time period based on fertility, mortality and migration rates which can
be adjusted by the model user.
i
Bt   Pi
Equation 4.1
1
Where :
Bt = Birth events during year t
i = Number of adult females in household
Pi = Random number generated for individual i;
0 if
Pi below user specified fertility rate, 1 if above
This method was chosen so that each of the demographic groups would be represented by
integers rather than as continuous variables or fractions of people. With these representations,
-7-
more logical behavior can be depicted for specific demographic events. For example, if there is a
single adult female in the household, there can be a specific probability that she will either leave
the household or that an adult male will join the household. Likewise, birth events can be more
precisely controlled as a function of the number of adult males and females in the household and
the prevalence of out-of-marriage births. Such controls partially exist in the model, and will be
more elaborately integrated with subsequent versions. Children start at age 0 and are moved to
the adult male or adult female stocks based on a sex ratio based probability value. Female
fertility rates are not age dependent except that women less than 15 years old and more than 65
years old have no birth rates.
Each demographic group has their own mortality rate that is based on UNDP data (United
Nations Development Program 1999). The child mortality rate was based on an adjusted infant
mortality rate from UNDP data sources for Brazil. We are currently searching for more detailed
mortality data for the Amazon region. These demographic rates are levers that can be adjusted by
the model user for specific scenario testing (e.g. constant fertility over time, declining fertility,
declining mortality). Crude birth rates (CBR) in the region were relatively high in the 1970’s
(CBR = 40), but the crude birth rate has been steadily declining in recent years (CBR = ~25).
Infant mortality rates have also declined rapidly over the past 30 years. Model users can specify
high or low fertility scenarios as well as a declining fertility or mortality scenarios.
Rural-urban migration has become an increasingly important process in the region. The
Atlamira study area is named for the town of Altamira located along the Trans-Amazon highway
and that serves as a center of commerce for the colonists. Surveyed parcels along the TransAmazon extend 120km west of the Altamira town location with the earliest settled parcels being
closest to the town. As the urban economy of Altamira develops, more opportunities are
available for urban wage labor, particularly for young women as household laborers. In terms of
labor activities, women participate primarily in the cultivation of household annual and perennial
crops rather than as wage labor for other landholders (e.g. land clearing, burning). Thus,
-8-
migration to the town of Altamira provides women with a means of generating income that would
otherwise not be possible on the farm. The model incorporates these wage labor opportunities by
allowing the wage labor rate to be set by the model user. Scenarios can be run where there is a
high demand for wage labor (high hourly wage) or low demand for wage labor (low hourly
wage). The impact of remittances from household members who have permanently moved off
the parcel is currently unknown, but is hypothesized to be modest by researchers familiar with the
study area. While the model allows for such remittances to be incorporated into the model
scenarios, the model runs presented in this paper do not include this factor.
4.2. Economic Sector
Household consumption and expenditures are controlled by the economic sector.
This sector affects landcover primarily in that the amount of capital available to the
household affects their ability to hire wage labor. Equation 4.2 shows the individual
contributions to household income. Wage labor is used for land-use activities requiring
large amounts of labor in short periods of time. Examples include crop harvest, forest
clearing and burning cleared vegetation.
I t  ct  st  it  at
Where :
Equation 4.2
I t = Total income during year t
ct = Income from cattle sales during year t
s t = Income from social security during year t
it = Wage labor income during year t
at = Income from agricultural crops in year t
Households receive agricultural income from cattle and crop sales. Crop prices are defined
by the model user according to the major crop types (perennial, annual) and are measured in gross
-9-
profit per hectare per year. These prices are treated exogenously in the model. The primary
annual crops grown in the study area are rice and beans, and the income for annuals represents an
aggregate measure based on a combination of these two crops on one hectare in one year. The
most common perennial crop present in the Altamira study area is cocoa, while there are lesser
amounts of coffee and sugar cane. Another source of income for some families is the
Brazilian social security system that was initiated during the last decade.
The model
represents this as a lever that can be turned on or off or to test different social security
scenarios (e.g. presence/absence of social security, different social security allocation
rates).
The main household expenditures are cattle purchases, household consumption and
institutional penalties (see Equation 4.3). Households expend capital based on the
number of members in the household and an estimated per capita household consumption
representing costs such as food, clothing, medicine and education. Certain institutional
factors can decrease net household income such as property taxes or land regulatory
penalties both of which can be controlled by the model user. Expenditures for crops are
incorporated into the net income price/ha for each crop type.
Et  ct  pt  Ft  et
Where : C
Equation 4.3
= Household consumption (based on household size)
= Expenditures from cattle purchases
pt
Ft = Institutional fees and penalties
et = Wage labor expenditures
- 10 -
4.3. Decision Making Sector
The decision making sector is the main mechanism affecting landcover change outcomes in
the model and is affected by each of the other model sectors. This decision-making sector
allocates labor to specific activities that affect the conversion of land from one land-use to
another and the preservation of land in its current state. The utility of each possible activity or
decision is calculated at each time point based on the expected economic gain from that activity.
Using these relative utilities, labor is allocated to specific activities that are then translated into an
area conversion measure based on the labor consumption per unit area for that activity.
4.3.1. Utility Calculation
There are three main types of land-use activity on the parcel: 1) the conversion of one landuse to another land-use, 2) the preservation/maintenance of one land-use to the next time step,
and 3) the abandonment of a specific land-use activity (e.g. the transition of cultivated or
otherwise productive land to initial secondary succession through fallowing). The complete set of
possible activities (including landuse activities resulting in landcover change) is provided in
Table 1. Estimated labor consumption for each of these activities was obtained from field notes
and estimates from field researchers familiar with the study area. Labor consumption units are
person weeks necessary for that activity on one hectare for one year. Conversion and
maintenance activities require labor allocation, while no labor is required for the cessation of an
activity and subsequent transition to initial secondary succession.
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“From” land use
“To” land use
Type
Labor
(Person-weeks/ha/yr)
Annuals
Perennials
Pasture
Mature Forest
Annuals
Annuals
Annuals
Perennials
Perennials
Pasture
Secondary Succession
Secondary Succession
Annuals
Perennials
Pasture
Annuals
Perennials
Pasture
Secondary Forest Succession
Pasture
Secondary Forest Succession
Secondary Forest Succession
Annuals
Pasture
M
M
M
C
C
C
C
C
C
C
C
C
3
2
1.5
7
3
2.5
0
2.5
0
0
6
4.5
Table 1. Labor consumption for land-use activities (see Appendix A for notes).
The overall utility of each activity at a specific time step is a function of the return on labor
investments for that landuse activity over the previous five years. This model structure mimics
the process of how households ‘learn’ what are the optimal landuse activities over time. The
individual factors that affect the utility over time are labor availability and prices for cattle and
crops. The actual utility for each activity is the ratio of financial return per hectare to labor
invested per hectare. Prices are held constant for the model runs presented here. However, given
data on crop and cattle prices over time, these prices can change during the course of the model
run allowing changes in relative crop prices to affect land use decisions.
Households may choose to maintain a current landuse activity or convert some of their parcel
in one landuse to another landuse. At each time step the utility of maintaining each landuse
activity and the utility of converting each landuse activity to each other activity is calculated.
Maintaining a landuse requires a labor maintenance cost. Converting an area from one landuse to
another requires a conversion cost (i.e. labor weeks require to clear forest for annuals production
per hectare) and a maintenance cost of the “to”-landuse. The model distributes the cost of landuse conversion according to an expected duration of the new land-use.
- 12 -
There are four general types of utilities calcuated. The first and simplest is the utility
involved in maintaining land in it’s current landuse. This utility is simply the ratio of the
financial return per hectare for that landuse to the labor required to maintain that hectare in that
landuse for one year. The second type of utility is the conversion of land in one landuse that does
not require labor maintenance (e.g. forest or secondary forest) to a landuse activity that does
require labor. An example would be converting a hectare of forest to annuals crop production. In
this case, the utility of this landuse conversion is the ratio of the financial return per hectare for
one hectare of annuals to the sum of the conversion cost of forest to annuals and the labor
maintenance cost for annuals crop production. The third type of utility calculation is the
conversion of landuse in one labor requiring activity to another landuse activity that also requires
labor. The utility of this type of conversion is a function of the difference in financial return for
each landuse, the labor required for each landuse activity and the conversion cost from one
landuse to another. The last type of utility is the abandonment of a landuse activity requiring
labor to a landuse that does not require labor. An example would be the abandonment of
perennial crop production and subsequent succession of secondary forest vegetation.
A household can select multiple landuse activities and landuse changes at each time
point. In other words, households to not allocate all of their available labor to a single
landuse activity. Rather, a risk aversion parameter is used that increases or decreases the
likelihood that a household will diversify their landuses. This risk aversion parameter
can be adjusted by the model user at the beginning of the model run. If this parameter is
set very high, households will select only the landuse with the highest utility. If the
parameter is set relatively low, the household will allocate labor to a larger set of
landuses. The total available household and wage labor is then allocated to each of the
selected landuse activities based on their relative utilities. For example, assume the
following two activities are selected for a specific time step: 1) the conversion of mature
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forest to annuals, and 2) the conversion of annuals to pasture. If the utility for the
conversion of mature forest to annuals is twice the utility for the conversion of annuals to
pasture, then two thirds of the labor available at that time step will be allocated to the
mature forest to annuals activity. The size of the areas converted or maintained in
different landuses will not necessarily be proportional to their specific utilities because
each landuse conversion consumes different amounts of labor. When there is inadequate
labor necessary to maintain the existing landuse activities, land is abandoned based on the
landuse with the lowest utility.
4.4. Landcover Change Sector
Each household land-use activity is associated with a specific landcover class and each landuse change involves the removal of land from one landcover class or stock to another. The
following land-use/landcover classes are used in the model: mature forest, secondary forest
succession, annuals, perennials and pasture. A variety of annual crops are grown in Altamira.
The most common are beans and rice which are diet staples and grown by all households in some
quantity. The annuals class here represents land that is rotated often, every 2-3 years, and is a
combination of different crops. The pattern observed in Altamira is for recently cleared land to
be put into some type of annual crop until yields decline. Common perennial crops in Altamira
include coffee, cocoa and to a lesser extent sugar cane and these crops are most often harvested
using wage labor. In contrast to annuals, perennials are cultivated for 6-8 years before yields
decline to the point where the land is allowed to fallow.
The model assumes that mature forest covers the entire parcel at the beginning of the model
run. As land is cleared for agricultural production and fallowed it is moved into a series of stocks
representing different stages of forest regrowth. One simplification of the model is that previous
landuse does not affect subsequent forest regeneration rates. In accordance with the land
- 14 -
management practices found in Altamira, land with less than 10 years of forest regrowth is not
cleared for agricultural production. A proportion of each secondary succession class is moved to
the next stage of forest regrowth at each time step, eventually reaching the mature forest state.
This model structure results in a dynamic landscape where land is moved from one landuse class
to another of the several decadal run of the model. The pattern of forest clearing and
abandonment is captured in the different stocks used to represent labor consuming landuses and
different stages of forest regrowth. The actual landscape in Altamira is characterized by a mosaic
of different landuses within a parcel with varying degrees of landcover fragmentation. The model
presented here represents this compositional structure by the different stocks of landcover
representing different landcover classes. As landuse conversion activities
4.5. Institutional Sector
A variety of institutional factors affect land management in the study area. In particular,
landholders are required to have at least 50% of their land in forest (mature forest or advanced
secondary succession). This requirement is only loosely enforced, but landholders face a penalty
if caught violating this regulation. While only a limited set of scenarios are presented in this
paper, different scenarios can be run representing the enforcement of this penalty as well as
varying fines associated with the violation of the regulation. There is currently only a loosely
based property tax in the study area, and no property tax existed at the time of initial settlement.
The model user can adjust this property tax value through the graphical user interface.
Crop and cattle prices affect the utility of different land-uses and these prices can be adjusted
for different model runs. Crop prices represent the income for one hectare of land under annuals
or perennials production while cattle prices represent the purchase and sale of one head of cattle.
Prices can be set to run a low or high price scenario or to represent declining and increasing
prices through the model run. The model currently has no allowance for varying crop yields as a
function of labor inputs, agricultural inputs or soil conditions.
- 15 -
5. Model Validation
The model was validated using landcover classifications for the Altamira study area derived
from aerial photography from 1970, Landsat Multi-Spectral Scanner (MSS) satellite data from
1978 and Landsat Thematic Mapper (TM) satellite imagery from 1985 and 1996 (McCracken et
al. 1999). The 1970 and 1978 data were interpreted to produce a classification of mature forest
and non-forest land. Non-forest land is considered to be agricultural land, pasture land, and
young forest regrowth. Landcover boundaries visible in the 1970 aerial photography were
digitized and then converted into a raster cell representation to be integrated with the raster-based
satellite imagery. The 1985 and 1996 satellite images were processed to produce a classification
with the following landcover classes: mature forest, bare ground (including land cleared for
agriculture), pasture, water, and three stages of forest regrowth. These raster data were resampled
to a cell size of 80m and overlayed with a vector layer of 367 parcel boundaries (INCRA Instituto Nacional de Colonização e Reforma Agrária) registered to the same coordinate system
and projection as the landcover data (see Figure 5). These parcel boundaries were used to
generate parcel level landcover composition statistics for the 1970, 1978, 1985 and 1996 time
points. Brondizio (forthcoming) reports approximately 60% of the mature forest remains in the
Altamira region today, approximately 30 years after colonization. However, this figure
represents several waves of colonization while the validation data here uses a set of parcels that
were colonized with the first wave of settlement and thus represent 30 years of modification.
Figure 6 shows the mean percent forest on parcels for 30 model runs and for the 367 parcels
based on the multi-temporal landcover classifications (tails indicate +/- one standard deviation
from the mean). This figure indicates that the percent mature forest from the observed data
matches the model data for 1996 (approximately 25 years after colonization), while the model
overestimates the amount of mature forest in 1985. This discrepancy in 1985 is due to the fact
that the model runs are initiated with a standard family household composition for all families,
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one child, one male adult, one female adult and one senior. The household composition of the
first wave of colonists is unknown and therefore children were assumed to be one year old at the
beginning of the model run. Therefore, there is a 15 year lag to the time where the children reach
reproductive age (and children are parsed into the male and female adult pools based on the
defined sex ratio) and all children are incorporated into the adult labor pool. It is hypothesized
that this lag is responsible for the underestimation of deforestation in 1985. In addition, the
model does not incorporate access to credit as a model parameter. Credit allows landholders to
hire wage labor for labor intensive tasks, such as clearing land for pasture. The availability of
credit is an example of an institutional factor that is not included in the model but likely affects
landcover changes in the Altamira study area.
The variance in model results increases with time because of the human fertility probability
used in the model. At each time point each adult female is given a birth probability based on the
user-defined crude birth rate for the model run. Thus, there is relatively little variance between
parcels in the amount of mature forest for the first 10 years of the model run since these variations
in human fertility do not have land-use outcomes until children reach the adult pool (thereby
increasing the pool of household labor). However, as there is more variability in household
composition (especially in the adult male and adult female groups) there is a greater likelihood of
variation in household activities, explaining the larger variances after approximately the 20th
model run year.
The processing of the landcover data for the 1970, 1978, 1985 and 1996 time points is
substantial, as is the registration of the INCRA parcel boundary data. Ideally a denser time series
could be used to validate the model as there may be multiple landcover changes in single areas
between the 8-10 year intervals of the observed data, however the processing necessary to
develop a denser time series is substantial. In addition, the fluctuations in crop and cattle prices
are not specifically known and the values used in this model are based on field researcher best
estimates. However, despite the use of the various estimated model parameters, the model
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landscape outcomes still reasonably match the landscape composition observed from the multitemporal landcover data.
6. Results/Scenario Testing
The success of the household through time depends primarily on the household size (labor
availability), ability to hire wage labor and prices of annual crops, perennial crops and cattle.
Adjusting model parameters allows the results of various scenarios to be compared, such as high
vs. low human fertility scenarios or changes in relative prices between crops and cattle.
Landcover composition over time can be observed for each of these model runs indicating the
land-uses conducted at each time point and, specifically, the ability of forest regrowth to keep
pace with the degree of forest clearing for various agricultural activities.
Using a crude birth rate of 40.0 mature forest declines from 100% to 0% in approximately 4550 years (Figure 7a). It should be noted that the results of individual model runs vary. Figure 7b
shows a typical high fertility model run where up to 20% mature forest remains for the 50-100
year period. In this model run there is a corresponding lack of agricultural land (annuals,
perennials and pasture). With a crude birth rate more common in developed countries (11.0-16.0)
25% mature forest remains after 60 years for most mode runs (Figure 8), presumably as a result
of the lack of labor available for the relatively high labor cost activity of clearing mature forest.
Likewise, the area of land under production (annuals, perennials, pasture) is greater under the
high fertility scenarios compared to the low fertility scenarios.
The Altamira study area has been colonized for approximately 30 years. During this period
there has been a reduction in the amount of mature forest in the study area from 100% to
approximately 60% (the amount of deforestation varies from parcel to parcel, however). Using a
crude birth rate of 27.0 the model predicts that mature forest drops to approximately 30% after
25-30 years depending on the probabilistic fertility rates in the model. After 30 years the amount
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of mature forest gradually declines to be replaced by secondary succession and a combination of
pasture, annuals and perennials in this moderate human fertility scenario.
An initial spike is seen in the model where mature forest is cleared for annuals production, a
transition observed in Altamira and Rondônia (Brondizio et al. forthcoming; Dale et al. 1993).
After this initial clearing, there is a shift to pasture and perennials and a drop in the amount of
annuals production, another landcover transition observed in Altamira (Brondizio et al.
forthcoming). Throughout the model run a small amount of area is retained in annuals
production. According to researchers familiar with the Altamira study area, landholders prefer to
keep 2-4 ha of land in annuals for subsistence (primarily beans and rice) and to a lesser extent for
sale in local agricultural markets. Under typical demographic and price scenarios the amount of
land in annuals ranges from 4-10 ha for each model run.
The model is also sensitive to the relative prices of annuals, perennials and pasture (via
cattle). Figure 9 shows a scenario where the price of perennials is inflated relative to the price for
annuals or for cattle. This results in a greater proportion of landcover in perennials production
compared to annuals and pasture over the 100 years of the model run. However, this bias towards
perennials land-use is affected by the availability of mature forest for clearing and labor. When
there is relatively little labor and plentiful mature forest, there is more pasture relative to
perennials. After there is more labor available (children enter adult pool) and less mature forest,
there is a transition to perennials production. Changing these relative prices affects both the rate
of landcover change as well as the relative proportion of each landcover class in the parcel.
Researchers familiar with the study area indicate the income from one ha of annuals and
perennials is 400 reais/yr and 450 reais/yr, respectively. Lowering the income value for annuals
reduces the proportion of the parcel in annuals, as is expected. While these observations do not
qualify as model calibrations in the formal sense, they do indicate that the model can replicate the
landcover changes observed in the Altamira study area.
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It should be noted that the figures referred to in this section are single parcel runs
representing typical results for each scenario. Because these scenarios are probabilities, it is
possible for a single parcel to have relatively high human fertility even given low fertility
parameters in the model specification. However, over the course of multiple model runs, the
aggregated results for the high vs. low fertility scenarios should demonstrate the difference
between the typical landscape outcomes for these different model specifications.
7.
Discussion
The model necessarily involves a series of simplifications of the actual complexity of
land-use activities in the Altamira study area. In particular, there is a greater complexity of landuse and landcover in Altamira than is represented by the basic classes used in the model. The
model aggregates crops into two basic classes (annuals and perennials) rather than representing
each crop individually (rice, beans, cocoa). Thus, the model is not able to predict the impact of
changes in crop prices for a single crop in its present state. Additionally, households extract
income from unmanaged forests in the form of non-timber forest products and managed forests in
through agroforestry.
Another notable simplification is the homogeneity of biophysical characteristics within a
parcel. While parcels with relatively homogeneous soil fertility do exist in Altamira, more
commonly there are a variety of soil characteristics within a parcel introducing a constraint to the
area suitable for specific land-uses. Given the present model structure, it is possible to represent
parcels with either low or high soil fertility within a homogenous parcel, but not to represent a
parcel with different proportions of low and high fertility soils.
Mature forest is represented as forest regrowth that has been in secondary succession for
a given period of time. The model currently handles this in a relatively inelegant manner with a
small proportion of each successional class passing to the next stage of forest regrowth at each
time step. Additionally, ecologists might argue that even after eighty years of undisturbed growth
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the forest will still not have the species diversity and ecological function of primary forest
(Shukla and Sellers 1990). As noted earlier, the model does not allow forest regrowth rates to
vary as a function of previous land use and crop yields do not vary as a function of the stage of
forest growth cleared and burned prior to planting. This could be handled if each unit of land
were assigned a specific state, but given the present model structure where landcover is
represented as a series of stocks between which land passes this level of complexity would be
difficult to include.
While this model attempts to construct a simplified model of land-use activities, the
utility of this model as a predictive tool is understandably limited, particularly for long time
periods. At each time step, there is a probability that the model will misrepresent the actual
behavior of that single household. Thus, as time progresses, the likelihood that the model
actually represents the true landcover composition of a individual parcel declines. While the
long-term predictive power for simulating a single specific household in Altamira is limited,
collectively the set of model runs can be used to observe interactions operating to affect
landcover change in the region. The utility of the model can be found in understanding the
importance of different factors contributing to landcover change more than as a tool to predict
future landcover composition. Additionally, it is not possible to foresee shocks to the system that
may dramatically affect the interactions between sectors such as natural disasters, changes in
technology or introduction of new crops or cultivars. Nevertheless, the model does represent a
reasonable simulation of the existing landuse/landcover change process in Altamira.
Lastly, the model assumes that households make predictions about future prices based
solely on the prices from the previous five years. This does not allow the model to include spikes
and troughs in prices. In addition, this reliance on past price behavior assumes that households
act rationally to maximize their profit without allowing households to experiment or innovate.
With this type of modeling, innovation is perhaps the most difficult component to incorporate.
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Nevertheless, the model does show a relationship between labor, prices, land-use and landcover
that corresponds to patterns evident in the Altamira study area.
8. Conclusion
This paper presents a dynamic system model linking social and biophysical data to
simulate land-use changes in the Altamira study area. The utility of this model to predict
particular landcover outcomes is limited by the level of specification in the model. However, a
series of trends are evident from the model output. High human fertility scenarios result in more
rapid deforestation and a system where there is a higher proportion of sucessional forest growth
to mature forest over long time periods. Conversely, low human fertility scenarios indicate a
slower rate of mature forest loss compared to the high fertility scenarios. In this regard, the
implication of demographic trends (e.g., fertility and migration rates) as well as socioeconomic
trends (e.g., price change) in the land use pattern can be traced through observing the land cover
dynamics through time.
This dynamic model structure enables one to understand the process of land cover change
as a system rather than as a isolated set of dependent and independent variables. What is
particularly valuable about the process of model construction is to indicate to the researcher and
model user what factors are important to include in approaching the question of landcover
change. If a particular model run generates implausible outcomes, the model user/creator must
hypothesize about what model parameters need to be adjusted or what additional factors need to
be included in the model specification. This process of model specification can lead to insights
that would not have been gained through other research methods.
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persons
Figure 1. Model Overview
Figure 2. Demography Sector and Graphical User Interface
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Figure 3. Altamira Study area Landcover (1996) derived
from Landsat TM satellite imagery
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Percent Mature Forest
Tails indicate +/- one standard deviation
from mean for all parcels at each time point
Figure 4. Comparison of Model Runs (30) and Parcel Level (368) Mature Forest
Composition from 1970, 1978, 1985 and 1996 Landcover Classifications
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Figure 5. High Fertility Scenario
Figure 6. Low Fertility Scenario
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Figure 7. Forest Composition
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Appendix A.
Notes for Table 1:
Type M = Maintenance; C = Conversion
The labor necessary to convert one ha of mature forest to annuals is the conversion cost (mf-an)
plus the cost to maintain one ha of annuals for one year. Therefore, the utility to convert any one
land-use to another land-use is the conversion cost shown in the above table plus the relevant
maintenance cost.
Activities where the “from” and “to“ landuses are the same consume only a yearly maintenance
labor cost. Activities where the “from” and “to” landuses differ consume a yearly maintenance
cost for the “to” land-use and a conversion cost for the labor necessary to convert the area from
one land-use to another.
Mature forest can only transition to annuals because field researchers indicate that landholders
prefer to extract what productivity they can from the cleared/burned biomass from annuals
production (which benefits the most from higher fertility soils) and then let the annuals transition
to pasture or perennials.
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