Study of Complex Systems in the Northern Ecuadorian Amazon: Linking People and the Environment through Cellular Automata (CA) and Agent Based Models (ABMs) to Study Land Use/Land Cover Dynamics in a Frontier Setting

Biocomplexity views landscapes as complex systems, consisting of interactions of human and natural processes, in which landscape patterns are important emergent properties of complex dynamics. Spatially-explicit modeling approaches such as Cellular Automata (CA) and Agent Based Models (ABMs) are highly suited to the study of landscape dynamics and how landscape patterns form and evolve through interactions with heterogeneous places, environments, and actors. These models allow us to develop candidate explanations for specific landscape patterns, spatially simulate landscape patterns, examine likely future scenarios of change, and examine endogenous factors and exogenous shocks that can alter trajectories of landscape change resulting in possible shifts in the composition and spatial structure of the landscape.

CA models belong to a family of discrete, connectionist techniques used to investigate fundamental principles of dynamics, evolution, and self-organization. CA models are examples of mathematical systems constructed from many simple identical components that together are capable of complex behavior. CA approaches can be used to develop specific models for particular systems, and to abstract general principles applicable to a wide variety of complex systems. CA models do not describe a complex system with complex equations (e.g., differential equations, multilevel statistical modeling), but allow the complexity to emerge from interactions of basic building blocks of systems (e.g., individuals and households represented at the cell level) that follow simple rules.

The essential properties of a CA are: a regular n-dimensional lattice is where each cell of the lattice has a discrete state, and a dynamical behavior described through growth or transition rules. These rules describe the state of a cell for the next time step, depending upon the states of the cells in the defined spatial neighborhood. The essential components of a CA model are: (1) the cell -- the basic element of a CA that is capable of storing defined states, (2) the lattice, or cells arranged in a spatial matrix, and (3) neighborhoods defined by growth or transition rules that perform changes to the state of the cells depending upon neighboring cells and their conditions. Four classes of behavior are recognized in CA models: fixed, periodic, chaotic, and complex.

Agent based models examine the basic characteristics and activities of individual agents (e.g., individuals or households) as the basic building blocks. An agent based model may have multiple copies of the same type of agent, e.g. multiple copies of one type of plant or human actor, or multiple copies of multiple agents of different types, e.g. households, individuals, and government agencies. Agents differ in important characteristics. Their interactions may be dynamic, in that, the characteristics of the agents change over time as the agents adapt to their environment, learn from experiences through feedbacks, or "die" as they fail to alter behavior relative to new conditions and/or factors. The dynamics that describe how systems change are generally nonlinear, sometimes even chaotic, and seldom in any long-term equilibrium. Agents may be organized into groups of individuals or into nested hierarchies that may influence how the underlying system evolves over time. They are emergent and self-organizing in that macro-level behaviors emerge from the actions of individual agents as agents learn through experiences and change and develop feedbacks with finer scale building blocks.

In the context of understanding landscape change, i.e., LULC change, agents can include land owners, farmers, management agencies, and/or policy making bodies, all of whom make decisions or take actions that affect land-cover patterns and processes. By simulating the individual actions of many diverse actors, and measuring the resulting system behavior and outcomes over time (e.g., the changes in patterns of land cover), ABMs can be useful tools for studying the effects on processes that operate at multiple scales, organizational levels, and their effects.

ABMs have a number of strengths that contrast with traditional methods for modeling landscape change. In addition to the richer behavioral representations afforded by ABMs, because an ABM is a dynamical system, it can incorporate positive and negative feedbacks, such that the behavior of an agent has an influence on the subsequent behavior of other agents. These feedbacks can be used to represent the endogeneity of various driving forces of landscape change. By taking into account their commonalities and differences in structure, function, and evolution across time and space, ABMs and experimentation offer the possibility of considerable insights into system dynamics and behaviors. Agent based experiments provide flexibility and considerable analytical power to examine pattern and process relations, including policy issues.

A complexity theory analysis of LULC change at frontier settings, using a CA approach, aims at understanding feedbacks and changes in state space through nonlinearities, and in relation to a dynamic and coupled human-natural system. As seen in frontier environments, LULC change patterns are not random, but self organized around development fronts that are shaped by geographic accessibility into the region and the constraints of resource endowments.

The tropical rainforest of northeastern Ecuador (Figure 1) is an area of complex interactions among a number of important and diverse stakeholders -- (a) spontaneous colonists who have in-migrated from other regions of the country and settled on household farms; (b) newly emerging communities and market centers that have consolidated services, offer off-farm employment to colonists, and affect land use/land cover (LULC) through direct and indirect ways; (c) indigenous people who follow traditional practices, but are affected by the rise of commercial agriculture, oil production within their historical territories, and a transition to a consumer-based economy; (d) oil exploiters who have built roads and laid pipelines for petroleum extraction in colonist and indigenous areas; and (e) conservation and protected areas established by the government to impeded development and retain biodiversity in a rapidly transforming frontier environment. The greatest changes on the land are those created by agricultural colonists following in the wake of oil exploration, who gained access on roads that made isolated areas accessible for development. However, interactions among the groups and the regions that they’ve settled are complex, because feedbacks between spatial patterns and rates of change are known to occur at advancing fronts of settlement and land development that have implications for LULC patterns.

Our agent based model (ABM) recognizes autonomous decision-making entities (agents - households), an environment through which agents interact, rules that define the relationship between agents and their environment, and rules defining the sequence of actions in the model. Complex adaptive systems are self-organized systems that combine local processes to produce holistic systems. Macro-level behaviors "emerge" from the actions of individual agents as they learn through experiences and change and develop feedbacks with finer scale building blocks as agents. Our modeling approach integrates five sub-systems: demographic system, agricultural systems, labor and mobility system, cultural system, and uncertainty system (Figure 6). We are guided by the Multi-Phasic Response Theory in which land use/land cover change is the spatially-explicit response of a set of household adaptations to the changing socio-economic conditions and environmental factors. In addition, the Household Life Cycle is used to assess the stages of needs and development at the household level including (1) young parents who recently arrived in the area initiate forest clearings for subsistence crops, (2) parents with growing children become engaged in the cultivation of cash crops and pasture, (3) older parents with teenage children are related to a decrease in the cultivation of annuals and an increase in cattle raising and secondary vegetation, (4) pasture and perennial crops dominate with increasing proportions of secondary forest as parents age and children reach young adulthood, and (5) children begin to leave the household or subdivide the farm. We have generated the model using Re-Past software and JAVA programming. Figures 7-9 are Re-Past screen captures for years 2, 18, and 28 of the spatial simulation. The model is designed to examine household decision-making and land use/land cover dynamics.