DINAMICA - a new model to simulate and study landscape dynamics

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DINAMICA - a new model to simulate and study landscape dynamicsBritaldo Silveira Soares-Filho a, Gustavo Coutinho Cerqueira b, Cássio Lopes

Pennachinc

a Department of Cartography - [email protected], phone: 5531 34995417, fax: 553134995415, b Remote Sensing Center - [email protected], Federal University of MinasGerais, Av. Antônio Carlos, 6627 – 31270-900, Belo Horizonte, MG – Brazilc Intelligenesis do Brasil Ltda - [email protected], Av. Brasil 1438, 1505, BeloHorizonte, 30140-003 -Brazil______________________________________________________________________

Abstract

This paper reports the development of a new spatial simulation model of landscape

dynamics - DINAMICA. This model was initially conceived for the simulation of the

Amazon Landscape dynamics, particularly the landscapes evolved in areas occupied by

small farms. For testing its performance, the model was used to simulate the landscape

change patterns produced by the Amazonian colonists in clearing the forest, cultivating

the land, and eventually abandoning it to give birth to the ecological processes of

vegetation succession. The study area is located in the northern part of the state of Mato

Grosso, Brazil, which represents a typical Amazonian colonization frontier. To validate

the model, it was run for two sub-areas of the colonization region, using an eight year

time span, starting in 1986. The simulated landscape maps were compared with the

observed landscapes using the multiple resolution fitting procedure and a set of

landscape structure measures, including fractal dimension, contagion index and the

number of patches for each type of landscape element. The results from validation

methods for the two areas have shown a good performance of the model, indicating its

appropriateness for the study and simulation of spatial patterns created by landscape

dynamics in Amazonian colonization regions occupied by small farms. Possible

applications of the DINAMICA model include the evaluation of landscape

fragmentation produced by different architectures of colonization projects and the

prediction of a region’s spatial pattern evolution according to pre-defined transition

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rates. As contributions to the art of landscape dynamics modeling, the development of

DINAMICA model presents: 1) multi-scale vicinity-based transitional functions, 2)

incorporation of spatial feedback approach to a stochastic multi-step simulation

engineering, and 3) the application of logistic regression to calculate the spatial dynamic

transition probabilities.

Keywords: landscape change; cellular automata; simulation model; DINAMICA;

Amazonian landscape dynamics

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1. Introduction

A landscape can be considered a result of a succession of states evolving across time

(Forman and Godron, 1986). Consequently, its constant evolution can lead to

remarkable changes in the environment which may produce enormous ecological

impacts. Therefore, there is a need for characterization of the complex of mechanisms

and agents involved in this dynamics to better understand it and thenceforth to try to

predict the possible paths of a landscape evolution and its future ecological

implications.

To achieve this goal it is necessary to unveil the processes that rule landscape

changes at several spatial and temporal scales, considering that this set of processes is

comprised of local agents, regional forces, and international geographic patterns.

Furthermore, this study requires advanced analytical tools specially designed to analyze

and reproduce, in a computer environment, the spatial patterns resulting from landscape

changes (Turner, 1989; Turner and Gardner, 1990; Sklar and Costanza, 1990). These

methods will in turn enable the formulation of reliable models capable of simulating the

evolution of spatial phenomena, such as landscape changes.

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Simulation models have become a top research topic in many areas of study. The

importance of simulation models, as a new investigation device, is attributed to its

capacity of multiplying our individual imagination and thereby permitting groups of

individuals to share, interchange, and improve mental models of a certain common

reality, independently of its complexity (Lévy, 1998). Thus, simulation models can be

envisaged as a heuristic device useful to test hypothesis about landscape evolution under

several scenarios, which can be translated as different regional social-economic,

political, and environmental frameworks. In light of the outcome of the model, a better

conservation strategy or management plan can be selected by confronting the alternative

results produced by different simulation inputs. Hence, simulation models, which

realistically reproduce spatial land change patterns, are required today to quantitatively

evaluate complex environmental issues at local, regional, and global scales (Steyaert,

1993).

In a historical view, it can be said that the spatial framework of Landscape Ecology

studies provided the bases for the development of a new class of models that attempts to

describe and predict the evolution of ecological attributes in sub-units of area with

distinct localization and configuration (Baker, 1989). These models aim at integrating

diverse temporal and spatial scales to represent ecological system dynamics at the

landscape level (Sklar and Costanza, 1990). As a result, several researchers have

dedicated themselves to the development of landscape dynamics simulation models,

thus contributing to a diversity of approaches, which can be found in works such as

Turner (1987, 1988), Wilkie and Finn (1988), Parks (1990), Southworth et al. (1991),

Dale et. al. (1993, 1994), Flamm and Turner (1994), Gilruth et al. (1995), and Wear et

al. (1996).

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In spite of the contribution of the aforementioned works, environmental dynamics

modeling is still a very difficult task, considering the fact that it requires the knowledge

of several ecological mechanisms and processes which are often unknown (Nyerges,

1993) or too complex to be represented by means of the present technology. Thus, the

development of landscape dynamics simulation models still poses a great challenge to

science.

The aim of this paper is to contribute to the development of landscape dynamics

modeling, describing the conception and operation of a new spatial simulation model –

DINAMICA - which is designed to simulate the genesis and development of land

change spatial patterns. This model was initially conceived for the simulation of the

Amazon Landscape dynamics, particularly the landscapes evolved in areas occupied by

colonists - farm properties smaller than 100 hectares. For testing its performance, the

model was used to simulate the landscape change patterns produced by the Amazonian

colonists in clearing the forest, cultivating the land, and eventually abandoning it to give

birth to the ecological processes of succession. The study area is located in the northern

part of the state of Mato Grosso, Brazil, which represents a typical Amazonian

colonization frontier.

DINAMICA belongs to a new class of models which incorporates many of the

concepts embedded in previous researches, as aforementioned, and introduces

cybernetic properties of a typical cellular automaton model, based on the ideas of works

such as White and Engelen (1993, 1994, 1997), Wagner (1997), Wu (1998), and White

et al. (2000 a).

With new propositions, the DINAMICA model involves a multiple time step

stochastic simulation with dynamic spatial transition probabilities calculated within a

cartographic neighborhood. Its engineering employs special functions designed to

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reproduce cartographically the dimensions and forms of landscape patches. For the

model parameterization, logistic regression is applied to indicate the areas most

favorable for each type of transition. The data used in this analysis were obtained

mainly from satellite imagery.

2. Methods

2.1. Model structure

As mentioned by White et al. (2000 b), a cellular automaton can be considered as a

dynamical type of spatial model in which the state of each cell in an array depends on

the previous state of the cells within a cartographic neighborhood, according to a set of

state transition rules. According to White et al. (2000 b), a conventional cellular

automaton consists of:

1) a Euclidean space divided into an array of identical cells;

2) a cell neighborhood of a defined size and shape;

3) a set of discrete cell states;

4) a set of transition rules, which determine the state of a cell as a function of the states

of cells in the neighborhood;

5) discrete time steps with all cell states updated simultaneously.

Generally designed to simulate landscape changes, DINAMICA embodies the above

concepts by using a sequence of specially developed algorithms, which are described in

following text (Fig.1).

The model data

The software uses as its main input a landscape map (land-use and cover map), e.g.,

a thematic map obtained from satellite imagery. Yet, as input, the model employs

selected spatial variables which are structured in two cartographic subsets according to

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their dynamic or static nature. It generates, as output, simulated landscape maps (one for

each time step), the spatial transition probability maps, which depict the probability of a

cell at a position (x,y) to change from state i to state j, and the dynamic spatial variable

maps. In other words, the model receives a set of raster data cubes and outputs new

ones.

For running the simulations, the model works in phases, each one having its own

parameters:

1) the number of time steps;

2) the transition matrix, being the rates fixed within the phase;

3) an eventual saturation value for each type of landscape element;

4) the minimum sojourn time for each type of transition before a cell changes its state;

5) the coefficients of the logistic equations applied to calculate each spatial Pij;

6) the percentage of transitions executed by each transitional function together with its

options.

Each phase has fixed parameters; consequently the software can be run using

multiple phases, each one consisting of several time steps.

The calculation of the dynamic variables

As aforementioned, a subset of variables used in the simulation is static. These

variables need to be calculated only once before the simulation starts; then they are

stored in a raster data cube. They can comprise any type of environmental data, e.g., the

spatial variables used in this work (Fig. 1).

Another subset of variables is dynamic, which means that it needs to be calculated

before each iteration of the software program. These variables are represented by maps

showing the distances from a cell, in a particular state, to the nearest cell in a different

state of the landscape elements presented in the main input (the landscape map) and the

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landscape element's sojourn time. As a consequence, there will be one map of distances

and one of sojourn time for each landscape element.

The distance calculation procedure consists of computing, in a first step, the frontier

cells for each landscape element patch, whose locations are stored in a 2D tree. In a

second step, the landscape map is again scanned to calculate the Euclidean distance

between the null cells (a different state cell) to the nearest frontier cell stored in the 2D

tree. The sojourn time maps are calculated by adding one time unit for the non-changed

cells after each iteration.

The sojourn time can be used in two ways. First, it can be applied to restrict a

change only after a cell has remained in a given state for a specified period of time.

Second, it can also be used to derive transitions which are considered deterministic,

based only on the sojourn time, such as the evolvement of secondary forests from the

regeneration areas which have reached a certain age.

The calculation of the transition rates and quantities

The transition rates are passed on to the program as a fixed parameter within a given

phase (Fig. 2). As their values represent a percentage of transition, it is necessary to

calculate the amount of cells to be changed by each specified transition during an

iteration, which is done by multiplying the number of cells of each landscape element

occurring in a time step by the transition rate. To be used for projection purposes, the

software also incorporates a parameter, called Saturation Value, which forces the

stopping of the transition i to j, when the number of cells in state i reaches a minimum

value. This effect takes into account the asymptotic shape of the diffusion curve (Fig.

3), and it is calculated by using the following equation:

Rate’ (ij) = Rate(ij)*(M-v)/(M+v) (1)

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where M is a landscape element percentage area remaining at a time and v is the

minimum area that a landscape element will remain.

The calculation of the spatial transition probabilities

The spatial transition probabilities are calculated for each cell in the landscape raster

map and each specified transition. The method selected employs a general politomic

logistic equation in the form of:

)()()(

)(

...)/),((

VnGiVGiVjGi

VjGi

eee

eVyxjiP ⇒⇒⇒

⇒

+++=⇒ 21

(2)

where V is a vector of the k spatial variables, measured at location x,y and represented

by V1xy, V2xy, ..., Vkxy, and each Gij(V) is calculated by the following equation:

xykijkxyijij VVVGij ,,,,,)( βββ +++= K110 (3)

An approach to estimate the coefficients of the equations Gij(V), and consequently

the influence of each selected variable on the transitions, is by using logistic regression.

With respect to the application of this method, it is worth mentioning that the transitions

are what must be modeled, instead of the state frequencies. Thus, these regressions

model the chances of a cell to change to one of the states, chosen along the line of the

transition matrix, or to remain unchangeable (Fig. 2).

The result of this procedure is a set of maps; each depicting the probability of a cell

to change to another state. According to the current cell state, one of the spatial

transition probability maps stored in the output cube data will be picked up to be used

by the transitional functions (Expander and Patcher).

The transitional functions

A relevant issue to be considered with regard to landscape simulation models,

especially the mosaic structured models, refers to the neighborhood influence in the

transition probabilities and, consequently, in the landscape patch dynamics. One way in

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which the DINAMICA software deals with this matter consists in splitting the cell

selection mechanism into two processes. The first process is dedicated only to the

expansion or contraction of previous landscape patches, and it is called Expander

Function. In turn, the second process is designed to generate or form new patches

through a seedling mechanism, and this function is called Patcher Function.

The combination of the two processes is shown in the equation bellow:

Qij = r*(Expander Function) + s*(Patcher Function) (4)

where Qij stands for the total amount of transitions of type ij specified per

simulation step and r and s represent respectively the percentage of transitions executed

by each function, being that r + s = 1.

Varying the proportions of transitions executed by the two functions, the simulation

outputs can be made to approximate the structure of a landscape.

Both of the previously mentioned functions employ a stochastic selecting

mechanism. The applied algorithm consists in reading firstly the landscape map to pick

up the cells with higher probabilities and arranged them orderly in a data array. In

sequence, the selection of cells takes place randomly from top to bottom of the data

array (the internal stochastic choosing mechanism can be loosened or tightened

depending on the degree of randomization desired), storing at the end the locations of

the selected cells. In a second step, the landscape map is again scanned to execute the

selected transitions. In this way, it is guaranteed that there will be no bias from the

reading of the landscape map, which it is always done sequentially from the top left of

the raster.

The previously described procedures are used in both transitional functions. For

each function, the software controls the iteration number needed to accomplish the

amount of specified transitions. In the event that the Expander function does not realize

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the amount of desired transitions, after a limited number of iterations, it passes on to the

Patcher Function a residual number of transitions, so that the total number of transitions

always reaches an expected value. As a result, the final landscape map will only need to

be evaluated with regard to its spatial configuration, since the distributional model will

be coincident to that of the reference landscape.

The Expander function

The Expander algorithm is expressed in the following equation:

If nj > 3 then P'(ij)(xy) = P(ij)(xy) else P'(ij)(xy) = P(ij)(xy)* (nj)/4 (5)

where nj corresponds to the amount of cells of type j occurring in a window 3*3. This

method guarantees that the maximum Pij' will be the original Pij, whenever a cell type i

is surrounded by at least 50% of type j neighboring cells (Fig. 4).

Despite the fact that DINAMICA is a mosaic structured model, it can work using

this function with the concept of landscape patches, which are either contracted or

expanded depending on the type of transition.

The Patcher function

The Patcher function aims at reproducing the actual landscape structure, impeding

the formation of tiny single cell patches, which would probably occur if only a simple

cell allocation process were used.

This function employs a device which searches for cells around a chosen location

for a combined transition. This is done firstly by electing the core cell of the new patch

and then selecting a specific number of cells around the core cell, according to their Pij

transition probabilities, for the combined transition (Fig. 5). As an example of the

application of this function, the new deforested patches, produced by the simulations in

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this work, are set to be equal to an area, about 5 hectares, equivalent to the yearly forest

cleared by a typical Amazonian colonist.

For each phase of the simulation, the percentage of the amount of transitions is set

for each of the aforementioned functions. Yet to avoid infinite loops, a maximum

number of iterations for the Expander Function is specified. The number of successful

transited cells is subtracted from the total number desired, and the remaining number is

passed on to the following function.

Both described functions also incorporate an allocation device which is responsible

for locating the cells with the highest transition probabilities for each ij desired

transition. This function stores these cells and organizes them for subsequent selection.

In this process, each newly selected cell will form a core for a new patch or an

expansion fringe, which is still needed to be developed by the use of the transitional

functions.

The size of the new patches and the expansion fringes are set up according to a

lognormal probability distribution; this implies that as input it is necessary to specify the

parameters of this distribution represented by the average size and the variance of each

type of new patch and expansion fringe to be formed.

The software interface

The DINAMICA software was written in object oriented C++ language and its

present version runs on 32 bits Windows system. All the DINAMICA model

parameters are set by using its graphical interface before they are saved to a script file.

This makes easier for users to understand and operate the software as well as to check

for input inconsistencies. Besides outputting the raster cubes, the software also

produces a log file which reports the numbers per types of transitions achieved after

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each step of its execution. The DINAMICA software, including the manuals and the

database of the test areas, can be accessed via internet on: www.csr.ufmg.br.

2.2. Test performance

The test site and its land change conceptual model

For testing its performance, the software was applied to simulate the landscape

changes of a typical Amazonian frontier colonization region, located in the Northern

state of Mato Grosso, Brazil (Fig. 6). The occupation of this region began to evolve at a

large scale at the end of the seventies, with the installation of several colonization

projects, consisting mainly of colonist from rural cooperatives of Southern Brazil.

Within this region, two sub-areas were selected for testing the simulations (Fig. 6).

Those areas, known as Terra Nova (140,870 hectares) and Guarantã (127,480 hectares)

correspond respectively to subsets of colonization projects, which are occupied by

colonists: farm properties smaller than 100 hectares.

The landscape changes produced by the Amazonian colonists in clearing the forest,

cultivating the land, and eventually abandoning it to give birth to the ecological

processes of succession, can be simplified for the study region in four landscape

elements (states) and six transitions according to the conceptual model illustrated in Fig.

7.

The simplification of the conceptual model can be justified by the fact that most of

the deforested areas in this region are occupied by pastures in several stages of use and

abandon. Furthermore, it can se said that the crops, despite a few exceptions found in

the region, are seen only as an initial stage of the forest-pasture conversion process.

With respect to this model, if we consider that the transitions regeneration to

secondary forest and secondary forest to mature forest are deterministic, based solely

on the sojourn time of the vegetation succession, we can reduce the model’s transition

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matrix to 9 elements, of which only six occur in reality. Notice, in this case, that the

transition matrix will reduce to a vector, since the other transitions are complementary.

Thus, the simulations will deal only with the transitions: forest-deforestation,

deforestation-regeneration, and regeneration-deforestation.

In effect, this taxonomic simplification does not compromise the model, considering

that it was not initially conceived to focus on the current land uses of these regions, but

the spatial configuration arising from the forest fragmentation and the forest recovery of

the abandoned areas.

The time span for running the model

The time span chosen for running the model encompassed eight years and was

divided into two periods: 1986 to 1991 and 1991 to 1994. These periods correspond to

distinct phases of the regional landscape dynamics. The first phase shows a slower

annual deforestation rate as a consequence of the gold rush, which took place in the

region and attracted colonists to work in the alluvial mines (known in Brazil as

garimpos) instead of cultivating their lands. The second phase corresponds to the

decline of the gold rush and is characterized by more intense land changes provoked by

the return of the colonists to cultivate theirs lands as well as by the increase in pressure

for land holding due to internal migration from the mining areas.

In this way, three TM/Landsat images were selected to characterize the distinct

phases of the landscape dynamics: the first one acquired in June, 1986, corresponding

to a short time after the beginning of the Landsat-5 operation; the second in June,

1991, the most intensive phase of the garimpo, and the third in May, 1994, concomitant

to the field work. The satellite images were classified in order to generate the

multitemporal maps, which depict the distribution of the landscape elements: forest,

deforestation, and regeneration. The three resulting landscape maps were cross-

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tabulated to produce the transition matrices for the two periods of analysis (Table 1).

Subsequently, these matrices were derived by means of the Markovian chain property

(Equation 6) to give the annual transition rates, because the simulations were set to run

in time steps of one year.

1−= HHVP tt (6)

where P is the original transition matrix, H and V are its eigenvector and eigenvalue

matrices, and t is a fraction or a multiple of its time span.

The input variables

The multitemporal landscape maps were used with cartographic ancillary data to

point out the most important spatial variables and their weights of influence on the

analyzed transitions. The logistic regression method was used in this procedure; its

outcome consists in the spatial transition probability maps. As aforementioned, these

maps represent the chances of a cell, with coordinates x and y, and in a state i, to change

to another state. In synthesis, these variables are used to incorporate, in the simulation

analysis, the colonists’ decision rules about where they cultivate their lands and

eventually abandon them; as well as the ecological processes and natural barriers to the

recovery of the forest landscape.

The spatial variables used in this work to calculate the spatial transition probabilities

are soil, vegetation, distance to rivers, distance to main roads, distance to secondary

roads, altitude, slope, distance to forest, distance to deforested areas, distance to

regeneration patches, and the urban attraction factor. This last variable is evaluated

through a gravitational model, which involves the sum of the inverse of distances, raised

to the second power, from a rural area cell to all cells classified as urban. A detailed

description of the method used to calculate the spatial transition probabilities is reported

by Soares-Filho et al. (2000).

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The cell map resolution was chosen to be equal to 100 meters, taking into account

the average size of the regeneration patches – the smallest occurring patches - which

correspond to 3.76 hectares for the selected areas. This resolution results in data arrays

consisting of 360 per 400 cells for Guarantã and 664 per 484 cells for Terra Nova.

2. Model calibration

As the DINAMICA transitional functions present many calibration possibilities, the

software needed to be run several times in order to adjust the parameters of these

functions. For this purpose, a set of simulation series was run adopting the empirical

transitions rates, as shown in Table 1, and varying the mixture of the transitional

functions – Patcher and Expander, as well as the expected mean patch size of each

landscape element. In this manner, the effect produced on the simulated landscape

structures by these varying parameters was tested. To evaluate the results, the simulated

landscapes were measured by using a set of landscape quantitative indices, including

fractal dimension (double fractal dimension), contagion index and the number of

patches for each type of landscape element (McGarigal and Marks, 1995).

From the graphs in Fig. 8, it can observed that as the proportion of transitions

executed by the Patcher function grows at the expense of the Expander function, the

contagion index decreases while the fractal dimension and the number of patches of the

landscape elements increase. When the patcher process prevails over the Expander

function, the patches become smaller, more fragmented, and consequently showing a

higher fractal dimension and a less connectivity, as indicated by the lower contagion

index. In turn, as the expected mean patch sizes are set larger, the contagion index

increases and the fractal dimension and the number of patches decrease, as a result of

forming more core areas.

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As main observation attained from these graphics, we can assert that the mixtures of

these transitional functions show a predictable behavior with regard to the simulated

landscape structures, thus leading us to conclude that an optimized solution for a

particular landscape can be achieved by means of defining a certain combination of

these functions together with their parameters.

Subsequently, a new set of simulations was performed to approximate the simulated

landscapes to the ones of Terra Nova and Guarantã. Still, in this calibration phase, some

coefficients of the logistic equation had to be slightly modified to account for

interactions resulted by the effect of using multiple time steps and transitional functions,

which were not considered by the logistic regression analysis. As a consequence, the

urban attraction factor coefficient had to be diminished, since it was added to the effect

of the Expander function to provoke an extreme concentration of the deforestation

around the urban centers. The simulation input data for the best achieved results for

both areas are presented in Table 2 and Table 3.

3. Results and discussion

Since DINAMICA has a stochastic structure, the final obtained models were run

twenty times for each area, using the best adjustment achieved (Tables 2 and 3 and Fig.

9). To validate the simulations, the simulated landscape maps were compared with the

observed landscapes using the set of landscape indices previously mentioned - fractal

dimension, contagion index and the number of patches for each type of landscape

element - plus the multiple resolution fitting procedure (Turner et al., 1989).

The results from the validation methods for the two areas are presented in Table 4.

They show that the simulations were able to reproduce the contagion indices with an

average deviation of 10.7% for Terra Nova and 6.9% for Guarantã.

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In turn, the fractal dimension of the landscape elements were reproduced with a

maximum average deviation of 2.8% for Terra Nova and 10.8% for Guarantã.

For Terra Nova, the simulation model matches from 93.9% to 95.6% the numbers of

landscape element patches. For Guarantã, the numbers of deforestation and regeneration

patches attained, respectively, an average approximation of 97.1 and 94%. On the other

hand, the simulation did not approximate the number of forest patches for the Guarantã

sub-area, where the average deviation exceeded 183%.

The multiple resolution fitting procedure evaluates the model spatial adherence to

the reference landscape with regard to the equal number of occurring equivalent cells

within a specified cell neighborhood, which is defined by a window size that is

considered a spatial resolution (Turner et al., 1989). The idea of using this procedure

consists in not discarding models which do not exactly match considering only a cell by

cell comparison, but show a good spatial approximation within a certain cell vicinity. In

this manner, the multiple resolution fitting procedure showed that the average simulated

landscape of Terra Nova started with a spatial fitting of 82.4% for the highest resolution

of 100 meters, and reached a fitting of 90% for a window size of 1800 meters. In turn,

the average simulated landscape of Guarantã showed a fitting of 63.6% at its highest

resolution, which reached 80% for a window size of 1400 meters (Fig. 10).

With respect to the achieved spatial adjustments, it is worth mentioning that

deforestation spreads throughout the region, generally from the road network, thus

being strongly influenced by the colonization project architecture. In this way, the lower

spatial fitting achieved for Guarantã sub-area can be explained by the fact that many

land invasions occurred in the central part of this region, deforesting an area originally

designed to be a collective forest reserve. Consequently, this process could not be

modeled by this specific simulation due to the lack of information about where the

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squatters would open the roads. This situation did not take place in the Terra Nova area,

where the simulation achieved a much better spatial adjustment.

Finally, we can mention that the low adjustment obtained for the number of forest

patches for the Guarantã sub-area could be, in part, explained by the high sensitivity of

this index, which can be drastically affected by any small change in the spatial

arrangement of the cells (Fig. 11).

3. Conclusions

The simulations were performed by using spatial data which could be obtained

mainly from satellite imagery. In view of this fact, it can be said that the achieved

results are encouraging, especially considering the fallible character of environmental

prediction. Moreover, the convergent results of both areas indicate that application of

the DINAMICA model can be transposed to investigate the landscape dynamics of other

Amazonian areas occupied by colonists, as long as some initial conditions are known.

Thus, this model can be applied to these Amazonian areas to describe the spatial

configuration arising from the forest fragmentation and the forest regeneration of the

abandoned areas. In this manner, DINAMICA deals with the effects of the deforestation

and regeneration processes on the fragmentation and recovery of the original forest

habitats. Thenceforth, the following issues can be addressed to the DINAMICA model:

− Which deforested areas will become secondary forests?

− What will be the spatial configuration of the landscape elements in a given future

time?

− What will be the ecological consequences of that landscape structure?

− Where will the forest fragments remain?

− How can the architecture of a colonization project influence the development of a

landscape, especially forest fragmentation?

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As DINAMICA focuses on the development of spatial patterns produced by land

change, this makes the software useful to investigate many other types of environmental

dynamic phenomena, considering the fact that its transitional functions can be adapted

to replicate different landscape structures and to work with any spatial resolution or at

diverse cartographic scales. Futhermore, DINAMICA can model any type and any

number of transitions as well as embrace any span of time, divided into any number of

time steps and phases with pre-defined transition rates. It can also incorporate, by means

of the logistic equations, any kind and number of data to calculate the spatial transition

probabilities. Still, the DINAMICA software can handle substantive large data arrays

with a good performance. The eight-step simulations executed for testing the model

took only six to seven minutes using a standard 400 MHz PC.

Therefore, the main contributions of the DINAMICA software to the art of

landscape change modeling can be mentioned as:

1) The development of multi-scale vicinity-based transitional functions;

2) the incorporation of spatial feedback approach to a stochastic multi-step simulation

engineering;

3) the application of logistic regression to calculate the spatial dynamic transition

probabilities.

In light of this development, DINAMICA presents us with new application

possibilities which will permit us to test hypothesis on how the many facts involved in

landscape evolution interact. Hence, this software can be envisaged as an investigation

device useful to decision makers to foresee the evolution of the spatial pattern of a

region, according to a particular environmental planning or caused by some type of

human occupation.

4. Acknowledgements

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The authors thank the project “Land use and Health in Amazon”, carried out by

CEDEPLAR-UFMG and coordinated by Dr. Diana Sawyer, for the financial support of

this work, and John Di Fiore for the proficient review of this paper.

5. References cited

Baker, W.L., 1989. A review of models of landscape change. Landscape Ecology, 2:

111-133.

Dale, V.H., O’Neill, R.V., Pedlowski, M., Southworth, F., 1993. Causes and effects of

land-use change in central Rondônia, Brazil. Photogrammetric Engineering and

Remote Sensing, 59: 997-1005.

Dale, V.H., O’Neill, R.V., Southworth, F., Pedlowski, M., 1994. Modeling effects of

land management in the Brazilian Amazonian settlement of Rondônia. Conservation

Biology, 8: 196-206.

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Table 1The transitions matrices of the sub-areas for the two periods analyzed

Guarantã Terra Nova86x91 86x91

Deforestation Regeneration Forest DeforestationRegeneration ForestDeforestation 78.86 0.00 22.78 77.41 0.00 21.27Regeneration 21.14 0.00 0.00 22.59 0.00 0.00Forest 0.00 0.00 77.22 0.00 0.00 78.73

91x94 91x94Deforestation Regeneration Forest DeforestationRegeneration Forest

Deforestation 61.67 26.42 16.07 69.94 35.50 19.40Regeneration 38.33 73.58 0.00 30.06 64.50 0.00Forest 0.00 0.00 83.93 0.00 0.00 80.60

25

Table 2Logistic regression coefficients

Terra Nova sub-area - Phase 1 - - Phase 2 -DR FD DR RD FD

Constant 4.08 -1.9621 0.0246 2.788 0.043

Vegetation type 2 0 2.0793 0.3138 0 2.07

Vegetation type 3 0 2.0462 0.2 0 2.506

Soil type 2 -1.12 0 0 0 -0.7414

Soil type 3 -1.459 0 0 0 1.5237

Altitude 0 0 0.00551 -0.01304 0

Slope 0 0 0.06231 0 0

Urban Attraction -0.003 0 -7.50E-05 0 -0.00387

D. to main roads 6.78E-05 -7.32E-05 0 0 -3.24E-05

D. to secondary roads 0 -4.38E-03 0 -1.00E-03 -1.34E-04

D. to river 2.72E-04 -7.51E-05 -2.76E-04 3.99E-04 0

D. to deforestation 0 -4.39E-04 0 0 -6.07E-03

D. to regeneration 0 0 -4.51E-04 0 0

D. to forest -6.83E-03 0 -0.00271 0.00286 0

Guarantã sub-area- Phase 1 - - Phase 2 -DR FD DR RD FD

Constant 0.287 -4.083 -2.4181 -0.6259 -0.7143

Vegetation type 2 0 2.2334 0 0 1.7841

Vegetation type 3 0 1.5923 0 0 1.8828

Soil type 2 -1.4534 0 0 0 0

Soil type 3 -1.5089 0 0 0 0

Altitude 0.01638 0 0.00837 0 -0.01302

Slope 0 0 0.03744 0 0

Urban Attraction -0.00403 0.00018 0 0 0.00036

D. to main roads 3.50E-05 0 -1.23E-05 0 0

D. to secondary roads 0 -2.03E-04 0 -0.00087 0

D. to river 0 -3.44E-05 0 0 0

D. to deforestation 0 -4.32E-05 0 0 -7.72E-05

D. to regeneration -4.59E-06 0 0 0 -3.31E-04

D. to forest -4.59E-03 0 -0.00458 0 0

D. (distance). DR: deforestation-regeneration, FD: forest-deforestation, and RD:Regeneration-deforestation. d. means distance.

26

Table 3Input parameters for the best simulation results

Terra NovaDeforestation-Regeneration Regeneration-Deforestation Forest-Deforestation

Steps Expan. Mean Var. Rate S.T Expan. Mean Var. Rate S.T Expan. Mean Var. Rate S.T1 to 5 0.2 1 1 0.0391 5 0.6 3 1 0 0 0.6 5 2 0.0466 06 to 8 0.2 1 1 0.1199 3 0.6 3 1 0.1617 0 0.8 5 2 0.0696 0

GuarantãDeforestation-Regeneration Regeneration-Deforestation Forest-Deforestation

Steps Expan. Mean Var. Rate S.T Expan. Mean Var. Rate S.T Expan. Mean Var. Rate S.T1 to 5 0.8 1 1 0.0311 5 0 0 0 0 0 0.6 5 1 0.0503 06 to 8 0.6 1 1 0.1600 3 0.8 3 1 0.166 0 0.8 10 1 0.0553 0

Expan. represents the proportion of transitions executed by the Expander function,being the Patcher function complementary to the Expander. S.T represents sojourntime.

27

Table 4Landscape structures indices obtained for the average simulated landscapes* comparedwith the ones of the reference landscapes

TERRA NOVAForest Deforestation Regeneration

NP DLFD NP DLFD NP DLFD ContagionReference Landscape 791 1.45 671 1.49 2473 1.58 25.21

Simulated Landscape 764 1.41 712 1.49 2387 1.6 27.9% deviation 3.4 2.8 6.1 0.0 3.5 1.3 10.7

GUARANTÃForest Deforestation Regeneration

NP DLFD NP DLFD NP DLFD ContagionReference Landscape 507 1.39 823 1.48 2300 1.55 28.39

Reference Landscape 1438 1.48 847 1.64 2162 1.66 26.44% deviation 183.6 6.5 2.9 10.8 6.0 7.1 6.9

* n= 20, NP: number of patches; DLFD: Double fractal dimension.

28

Figure Captions

Fig. 1. Flowchart of the DINAMICA software

Fig. 2. The transition matrix for four landscape elements

Fig. 3. Hypothetical deforestation curve obtained by using the saturation function(Equation 1)

Fig. 4. Pij arrays before a) and after b) the convolution of the Expander operator

Fig. 5. The selection of cells around an allocated core cell by the Patcher function

Fig. 6. TM/Landsat of May, 1994, comprising the study region and its localization withrespect to Brazil and the state of Mato Grosso. The two selected sub-areas arecontoured in white

Fig. 7. Model of landscape changes in the study area. The indicated time spans for thetransitions “regeneration to secondary forest” and “secondary forest to forest” mayvary greatly

Fig. 8. Setting the percentage of transitions executed by each transitional function andthe mean size of the produced patches (m) to replicate the desired landscapestructure. The values of m are expressed in hectares. Graphics a to e were obtainedfor the forest-deforestation transition and graphic f for the deforestation-regenerationtransition

Fig. 9. Simulated landscape maps of Terra Nova, compared with the observed landscapemaps

Fig. 10. Results of the multiple resolution fitting for both areas. Average values for 20runs. Average fitting for Terra Nova = 0.88 and for Guarantã = 0.77

Fig. 11. Modification of the number of patches as a result of the rearrangement of asingle cell: a) two patches, b) one patch

29

landscape map static variables

Pdr

final landscape map

Pfd

Prd

Number of phases,Phase 1:• n° of time steps,• the transition matrixwithin the phase,• the saturation values,• the minimum sojourn timefor each type of transition,• the coefficients of thelogistic equations,• the percentage oftransitions executed by eachtransitional function and itsparameters:maximum number ofiterations for the expanderfunction, mean patch sizeand patch size variance.Phase 2: ..........,Phase 3: ..........,Phase n: ...........

sojourn time in state i

calculates thedynamic distances

calculates thespatial

probabilities

calculatesthe amount

of transitions

executes theExpanderfunction

executes thePatcherfunction

t = tn

END

changes the cells

distance to deforestationdistance to forest

distance to regeneration

soilvegetation

altitudeslope

distance to riversdistance to secondary roads

distance to main roadsurban attraction factor

iterates

calculates sojourn time

dynamic variables

n=N (N =maximum number of iterations)

distances to landscapeelements

transition probability mapsInput Parameters

30

44434241

34333231

24232221

14131211

31

0

10

20

30

40

50

60

70

80

90

1 5 9 13 17 21 25 29 33 37

years

% d

efor

esta

tion

deforestation

deforestation rate

saturation threshold

32

ji

i

j

33

allocated core cell

generated patch

34

TERRANOVA

GUARANTÃ

J-1Mato Grosso

BRAZIL

35

FORESTFOREST

DEFORESTEDDEFORESTEDAREASAREAS

REGENERATIONREGENERATION

SECONDARYFOREST

TIME > 90 YEARS

TIME > 20 YEARS

Dense Rain ForestOpen Rain Forest

Alluvial ForestDense SavannahOpen Savannah

Pastures in diversestages of use andagricultural areas

Young andintermediatesuccessions

36

Number of deforestation patches varying the forest-deforestation transition

600

1100

1600

2100

2600

3100

1 0.8 0.6 0.4 0.2 0%Expander to Patcher

NP

m=5

m=4

m=3

m=2

m=1

Double fractal dimension of deforestation patches varying the forest-deforestation transition

1.47

1.52

1.57

1.62

1.67


DLF

D

m=5

m=4

m=3

m=2

m=1

Number of forest patches varying the forest-deforestation transition

200400600800

10001200140016001800


NP

m=5

m=4

m=3

m=2

m=1

Double fractal dimension of forest patches varying the forest-deforestation transition

1.35

1.4

1.45

1.5

1.55

1.6

1.65

1.7


DLF

D

m=5

m=4

m=3

m=2

m=1

Contagion index varying the forest-deforestation transition

162126313641465156


% C

onta

gion

m=5

m=4

m=3

m=2

m=1

Number of regeneration patches varying the deforestation-regeneration transition

1200

1700

2200

2700

3200

3700


NP

m=5

m=4

m=3

m=2

m=1

a) b)

c)

e) f)

d)

37

deforestationregeneration

forest

TERRA NOVA 86


forest

SIMULATED 91


forest

SIMULATED 94


forest

TERRA NOVA 86


forest

TERRA NOVA 91


forest

TERRA NOVA 94

10 5 0 5 10 KM

38

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1 2 7 12 18 25 33

window size in cells

% fi

tting

Guarantã

TerraNova

39

a) b)

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DINAMICA - a new model to simulate and study landscape dynamics