Complex Systems and Emergence Gilberto Câmara Tiago Carneiro Pedro Andrade

Where does this image come from?

Map of the web (Barabasi) (could be brain connections)

Information flows in Nature Ant colonies live in a chemical world

Conections and flows are universal Interactions yeast proteins (Barabasi e Boneabau, SciAm, 2003) Interaction btw scientits in Silicon Valley (Fleming e Marx, Calif Mngt Rew, 2006)

Information flows in the brain Neurons transmit electrical information, which generate conscience and emotions

Information flows generate cooperation White cells attact a cancer cell (cooperative activity) Foto: National Cancer Institute, EUA

Information flows in planet Earth Mass and energy transfer between points in the planet

Complex adaptative systems How come that a city with many inhabitants functions and exhibits patterns of regularity? How come that an ecosystem with all its diverse species functions and exhibits patterns of regularity?

What are complex adaptive systems? Systems composed of many interacting parts that evolve and adapt over time. Organized behavior emerges from the simultaneous interactions of parts without any global plan.

What are complex adaptive systems?

Universal Computing Computing studies information flows in natural systems......and how to represent and work with information flows in artificial systems

Computational Modelling with Cell Spaces Cell Spaces Components  Cell Spaces  Generalizes Proximity Matriz – GPM  Hybrid Automata model  Nested enviroment

Cell Spaces

Cellular Automata: Humans as Ants Cellular Automata: Matrix, Neighbourhood, Set of discrete states, Set of transition rules, Discrete time. “CAs contain enough complexity to simulate surprising and novel change as reflected in emergent phenomena” (Mike Batty)

2-Dimensional Automata 2-dimensional cellular automaton consists of an infinite (or finite) grid of cells, each in one of a finite number of states. Time is discrete and the state of a cell at time t is a function of the states of its neighbors at time t-1.

Cellular Automata RulesNeighbourhood States Space and Time t t1t1

Von Neumann Neighborhood Moore Neighborhood Most important neighborhoods

Conway’s Game of Life 1. At each step in time, the following effects occur: 2. Any live cell with fewer than two neighbors dies, as if by loneliness. 3. Any live cell with more than three neighbors dies, as if by overcrowding. 4. Any live cell with two or three neighbors lives, unchanged, to the next generation. 5. Any dead cell with exactly three neighbors comes to life.

Game of Life Static Life Oscillating Life Migrating Life

Conway’s Game of Life  The universe of the Game of Life is an infinite two- dimensional grid of cells, each of which is either alive or dead. Cells interact with their eight neighbors.

Characteristics of CA models Self-organising systems with emergent properties: locally defined rules resulting in macroscopic ordered structures. Massive amounts of individual actions result in the spatial structures that we know and recognise;

Which Cellular Automata? For realistic geographical models the basic CA principles too constrained to be useful Extending the basic CA paradigm From binary (active/inactive) values to a set of inhomogeneous local states From discrete to continuous values (30% cultivated land, 40% grassland and 30% forest) Transition rules: diverse combinations Neighborhood definitions from a stationary 8-cell to generalized neighbourhood From system closure to external events to external output during transitions

Agents as basis for complex systems Agent: flexible, interacting and autonomous An agent is any actor within an environment, any entity that can affect itself, the environment and other agents.

Agent-Based Modelling Goal Environment Representations Communication Action Perception Communication Gilbert, 2003

Agents: autonomy, flexibility, interaction Synchronization of fireflies

Agents changing the landscape It is the agent (an individual, household, or institution) that takes specific actions according to its own decision rules which drive land- cover change.

Four types of agents Natural agents, artificial environment Artificial agents, artificial environment Artificial agents, natural environment Natural Agents, natural environment fonte: Helen Couclelis (UCSB)

Four types of agents Natural agents, artificial environment Artificial agents, artificial environment Artificial agents, natural environment Natural Agents, natural environment fonte: Helen Couclelis (UCSB) e-science Engineering Applications Behavioral Experiments Descriptive Model

Is computer science universal? Modelling information flows in nature is computer science

Bird Flocking (Reynolds) Example of a computational model 1. No central autority 2. Each bird reacts to its neighbor 3. Model based on bottom up interactions

Bird Flocking: Reynolds Model (1987) Cohesion: steer to move toward the average position of local flockmates Separation: steer to avoid crowding local flockmates Alignment: steer towards the average heading of local flockmates

Agents moving

Segregation Segregation is an outcome of individual choices But high levels of segregation indicate mean that people are prejudiced?

Schelling Model for Segregation Start with a CA with “white” and “black” cells (random) The new cell state is the state of the majority of the cell’s Moore neighbours White cells change to black if there are X or more black neighbours Black cells change to white if there are X or more white neighbours How long will it take for a stable state to occur?

Schelling’s Model of Segregation Schelling (1971) demonstrates a theory to explain the persistence of racial segregation in an environment of growing tolerance If individuals will tolerate racial diversity, but will not tolerate being in a minority in their locality, segregation will still be the equilibrium situation

Schelling’s Model of Segregation < 1/3 Micro-level rules of the game Stay if at least a third of neighbors are “kin” Move to random location otherwise

Tolerance values above 30%: formation of ghettos Schelling’s Model of Segregation

The Modified Majority Model for Segregation Include random individual variation Some individuals are more susceptible to their neighbours than others In general, white cells with five neighbours change to black, but: – Some “white” cells change to black if there are only four “black” neighbours – Some “white” cells change to black only if there are six “black” neighbours Variation of individual difference What happens in this case after 50 iterations and 500 iterations?

Zhang: Residential segregation in an all- integrationist world Some studies show that most people prefer to live in a non-segregated society. Why there is so much segregation?

References  J. Zhang. Residential segregation in an all- integrationist world. Journal of Economic Behaviour & Organization, v. 54 pp  T. C. Shelling. Micromotives and Macrobehavior. Norton, New York. 1978

Some photos from Diógenes Alves ( Land use change in Amazonia

~230 scenes Landsat/year Yearly detailed estimates of clear-cut areas LANDSAT-class data (wall-to-wall) INPE: Clear-cut deforestation mapping of Amazonia since 1988

Is this sound science? Scenarios for Amazônia in 2020 Otimistic scenario: 28% of deforestation Pessimistic scenario: 42% of deforestation “We generated two models with realistic but differing assumptions--termed the "optimistic" and "nonoptimistic" scenarios-- for the future of the Brazilian Amazon. The models predict the spatial distribution of deforested or heavily degraded land, as well as moderately degraded, lightly degraded, and pristine forests”. W. Laurance et al, “The Future of the Brazilian Amazon?”, Science, 2001

The Future of Brazilian Amazonia? Optimistic scenario: 28% of deforestation (1 million km 2 ) by 2020 Complete degradation up to 20 km from roads (existing and projected) Moderate degradation up to 50 km from roads Reduced degradation up to 100 km from roads

Smallest yearly increase since the 1970s Yearly rates of deforestation:

Laurance et al., 2001 Optimistic scenario(2020) Savannas and deforestation Moderate degradation Degradação leve Floresta intocada Doomsday scenario and actual data... Data from INPE (Prodes, 2008) Savannas, non-forested areas, deforested or heavely degrated Deforestation Forest

Laurance et al., 2001 Optimistic scenario(2020) Doomsday scenario and actual data... Data from INPE (Prodes, 2008) About 1 million km2 deforested in 2020 For Laurance´s optimistic scenario to occur, there should be km2 of deforestation yearly from 2010 to 2020! About km2 deforested in 2010

Brazilian scientists write to Science Amazon Deforestation Models: Challenging the Only-Roads Approach “Deforestation predictions presented by Laurance et al. are based on the assumption that the governmental road infrastructure is the prime factor driving deforestation. Simplistic models such as Laurance et al. may deviate attention from real deforestation causes, being potentially misleading in terms of deforestation control.”

Improving deforestation prediction using agent- based models Decision MODEL Parameters

São Felix do Xingu study: multiscale analysis of the coevolution of land use dynamics and beef and milk market chains São Felix do Xingu Deforestation Forest Non-forest Clouds/no data INPE/PRODES 2003/2004:

Forest Not Forest Deforest River Change : deforestation and cattle

Create pasture/ Deforest Speculator/ large/small bad land management money surplus Subsistence agriculture Diversify use Manage cattle Move towards the frontier Abandon/Sell the property Buy new land Settlement/ invaded land Sustainability path (alternative uses, technology) Sustainability path (technology) Agents example: small farmers in Amazonia

Create pasture/ plantation/ deforest Speculator/ large/small money surplus/bank loan Diversify use Buy new land Manage cattle/ plantation Buy calves from small Buy land from small farmers Agents example: large farmers in Amazonia

Forest Not Forest Deforest River Observed deforestation from 1997 to 2006

Local scale Regional scale CATTLE CHAIN MODEL Flows: goods, information, etc.. Connections: Agents LANDSCAPE DYNAMICS MODEL - Front - Medium - Rear INDIVIDUAL AGENTS Large and small farmers Local farmers Frontier Region SCENARIOS

Land use Change model Beef and milk market chain model Small farmers agents Medium and large farmers agents Land use Change model Small farmers agents Medium and large farmers agents Landscape metrics model Pasture degradation model Several workshops in 2007 to define model rules and variables Landscape model: different rules for two main types of actors

Landscape model: different rules of behavior at different partitions Forest Not Forest Deforest River FRONT MIDDLE BACK SÃO FÉLIX DO XINGU

Landscape model: different rules of behavior at different partitions which also change in time FRENTE MEIO RETAGUARDA Forest Not Forest Deforest River FRONT MIDDLE BACK SÃO FÉLIX DO XINGU

Modeling results 97 to 2006 Observed 97 to 2006