dinamica—a stochastic cellular automata model designed to simulate the landscape dynamics in an Amazonian colonization frontier
Introduction
A landscape results from a succession of states evolving over a period of time (Forman and Godron, 1986). Consequently, its constant evolution can lead to remarkable changes that may produce enormous ecological impacts. Hence, to better understand the natural and human-induced processes of landscape changes, landscape ecologists have focused on the development of dynamic simulation models, which attempt to replicate the possible paths of a landscape evolution and thereby evaluate future ecological implications. Baker (1989) and Sklar and Costanza (1990) bring detailed reviews on landscape dynamics modeling. An utmost class of dynamic models consists of those specially designed to analyze and reproduce, in a computer environment, the spatial patterns resulting from landscape changes. Spatially explicit simulation models attempt to describe and predict the evolution of ecological attributes in sub-units of area with distinct localization and configuration (Baker, 1989). Moreover, 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, spatially explicit simulation models can be used to test hypotheses about landscape evolution under several scenarios, which can be translated by different 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. Therefore, simulation models, which realistically reproduce spatial patterns, are required to evaluate quantitatively complex environmental issues at local, regional, and global scales (Steyaert, 1993).
Recent advances in high performance computers at a low cost plus the advent of specific languages for spatial simulation modeling, e.g. SME (Maxwell and Costanza, 1997a, Maxwell and Costanza, 1997b), EcoSim (Lorek and Sonnenschein, 1998), and SELLES (Fall and Fall, 2001), have fomented the development of a plethora of spatially explicit models applied to a wide variety of studies, such as epidemic propagation, land-use and land-cover change, forest dynamics, fire spreading, coastal ecosystem dynamics, and population dynamics. Although, spatially explicit simulation models are increasingly becoming hybrid-complex to be definitely classified into a unique category, except for the application purpose, their dominant modeling approach generally relies on three major paradigms: individual-based, process-based, and space-oriented cellular automata model.
Individual-based simulation attempts to mimic individual processes of movement, behavior, birth, growth, and death according to species information, such as genotype, age, history, and location. Examples of individual-based models are given by FORMOSAIC (Liu and Ashton, 1998) and the model of Lett et al. (1999), which simulate forest dynamics, and the model of Congleton et al. (1997) applied to describing the winter kill of deer.
Large-scale process-based simulations model the role of physical and ecological processes in regulating or modifying the landscape patterns. Examples of these models are given by CELSS (Costanza et al., 1990) that simulates coastal marsh dynamics, ELM, a model designed to predict the landscape response to different water management scenarios in the Everglades, FL (Fitz et al., 1993), and the Patuxent Landscape model, which simulates ecological processes on a watershed by modeling ecological and economic interactions (Voinov et al., 1999). In a broad sense, these models comprise a two-dimensional array, in which each cell contains a complex dynamic simulation model, like the General Ecosystem Model. The flows, which can be of energy, material, species, and information, are modeled within each cell's model and horizontally between adjacent cells.
The third category, cellular automata model, consists of a regular n-dimensional array of cells that interact within a certain vicinity, according to a set of transition rules. Thus, in a cellular automata model, the state of each cell in an array depends on its previous state and the state of cells within a defined cartographic neighborhood, all cells being updated simultaneously at discrete time steps. The algorithm used to make the cells interact locally is known as the cellular automata local rule (Sirakoulis et al., 2000).
Cellular automata model are becoming very popular, as they can even be found included in commercial Geographical Information Systems (e.g. Eastman, 2001), due to their easiness of implementation, ability to replicate spatial forms, and capacity to be quickly readapted to reproduce several types of dynamic spatial phenomena, such as fire spreading (Karafyllidis and Thanailakis, 1997, Hargrove et al., 2000), epidemic propagation (Sirakoulis et al., 2000), forest dynamics (Lett et al., 1999), urban growth (White et al., 2000b, Clarke and Gaydos, 1998), and land-use and land-cover change (Wu, 1998, White et al., 2000a).
dinamica falls in this last category, as it introduces cybernetic properties of a typical cellular automata model. As dinamica was applied to simulate landscape dynamics in an Amazonian colonization frontier, it can be considered, according to the classification of Kaimowitz and Angelsen (1998), as a meso-scale regional model of tropical deforestation. Therefore, with respect to its application purpose, it can be compared with other spatially explicit simulation models, such as the works of Wilkie and Finn, 1988, Southworth et al., 1991, Dale et al., 1994, Gilruth et al., 1995, Manson, 2000, and Messina and Wash (2000). For a basis of comparison, as the art of modeling is always a trade-off between realism, precision, and generality (Costanza et al., 1993), dinamica attempts to maximize precision and generality at the expense of modeling realistically the processes of change.
dinamica involves a multiple time-step stochastic simulation with dynamic spatial transition probabilities calculated within a cartographic neighborhood. As the cellular automata local rule, its core engine employs transitional functions specially designed to reproduce the dimensions and forms of landscape changes, such as the deforestation patterns produced by different agents of change (e.g. Mertens and Lambin, 1997). For the model parameterization, logistic regression is applied to indicate the areas most favorable for each type of transition, by using data obtained mainly from satellite imagery.
This model was initially conceived for the simulation of Amazonian Landscape dynamics, particularly the landscapes evolved in areas occupied by colonists—farm properties smaller than 100 ha. For testing its performance, the model was used to simulate the spatial patterns of land-use and land-cover changes produced by the colonists in clearing the forest, cultivating the land, and eventually abandoning it to the ecological processes of succession. The study area is located in the north of Mato Grosso state, Brazil, which represents a typical Amazonian colonization frontier.
Section snippets
Model structure
According to White et al. (2000b) conventional cellular automata model consists of:
- 1
a Euclidean space divided into an array of identical cells;
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a cell neighborhood of a defined size and shape;
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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 a 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
Results and discussion
Since dinamica has a stochastic structure, the final obtained models were run twenty times for each area by using the best adjustments (Fig. 9). To validate the simulations, the simulated maps were compared with the observed land-use and land-cover maps using the set of landscape indices—fractal dimension, contagion index and the number of patches for each land-use and land-cover class—plus the multiple resolution fitting procedure (Costanza, 1989).
The results from the validation methods for
Conclusions
The simulations were performed by using spatial data that were 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
Acknowledgements
The authors thank ‘Land Use and Health in Amazon’ project of Centro de Desenvolvimento e Planejamento Regional of the Federal University of Minas Gerais—and Dr Diana Sawyer, for the financial support of this work, and John Di Fiore for his proficient review of this paper. The two first authors also receive support from the Center for Applied Biodiversity Science at Conservation International.
References (45)
- et al.
A c++ implementation of an individual/landscape model
Ecological Modelling
(1997) Model goodness of fit: a multiple resolution procedure
Ecological Modelling
(1989)- et al.
A domain-specific language for models of landscape dynamics
Ecological Modelling
(2001) - et al.
A dynamic spatial model of shifting cultivation in the highlands of Guinea, West Africa
Ecological Modelling
(1995) - et al.
Simulating fire patterns in heterogeneous landscapes
Ecological Modelling
(2000) - et al.
Comparison of a cellular automata network and an individual-based model for the simulation of forest dynamics
Ecological Modelling
(1999) - et al.
FORMOSAIC: an individual-based spatially explicit model for simulating forest dynamics in landscape mosaics
Ecological Modelling
(1998) - et al.
Object-oriented support for modelling and simulation of individual-oriented ecological models
Ecological Modelling
(1998) - et al.
An analysis of anthropogenic deforestation using logistic regression and GIS
Journal of Environmental Management
(1990) - et al.
A language for modular spatio-temporal simulation
Ecological Modelling
(1997)