Transcript Introduction to Spatial Dynamical Modelling

Gilberto Câmara, Earth System Science Center, INPE
Collective Spatial Action Models: a
Foundation for Assessing HumanEnvironment Interactions
Workshop on Cognitive and Linguistic Aspects of
Geographic Space, Las Navas, Spain, July 2010
1st Latin-American Computational Interdisciplinary
Sciences Conference, São José dos Campos, August 2010
Licence: Creative Commons ̶̶̶̶ By Attribution ̶̶̶̶ Non Commercial ̶̶̶̶ Share Alike
http://creativecommons.org/licenses/by-nc-sa/2.5/
Acknowledgments for using previous material






Martin Nowak (Harvard University, USA)
Francisco C. Santos (Université Libre de Bruxelles, Belgium)
Craig Callender (Philosophy, Univ California San Diego, USA)
Ana Aguiar (INPE, Brazil)
Tiago Carneiro (Federal University of Ouro Preto, Brazil)
Guy Brasseur (NCAR, USA)
What cooperation can achieve...
Those were the days…
http://www.youtube.com/watch?v=0HrjevD2vhk&feature=related
Collective spatial action: volunteered GI
Are Brazilians less cooperative? Less tech-savvy? Does google solve
their problems? Are they happy with their public data?
Collective spatial action: pedestrian modelling
Notting Hill Carnival (London)
Batty, “Agent-Based Pedestrian Modelling”, in: Advanced Spatial
Analysis, ESRI Press, 2003.
Collective spatial action: deforestation
CO2 emissions (PgC y-1)
Collective spatial action: global change
10
8.7
8
Fossil fuel
6
9.9 PgC
4
Land use change
2
1960
1970
1980
1990
1.2
2000
2010
12% of total
Le Quéré et al. 2009, Nature-geoscience, 2009
The fundamental question of our time
How is the Earth’s
environment changing, and
what are the consequences for
human civilization?
We need cooperation at a global level…
By the year 2050...
9 billion people: 6 billion tons
of GHG and 60 million tons
of urban pollutants.
Resource-hungry: We will
withdraw 30% of available
fresh water.
Risky living: 80% urban areas,
25% near earthquake
faults, 2% in coast lines less
than 1 m above sea level.
An explicit spatial problem in global change:
land change
“Land-change science has emerged as a foundational element of global
environment change and sustainability science” (Rindfuss et al,
“Developing a science of land change”, PNAS, 2004).
source: Global Land Project Science Plan (IGBP)
Impacts of global land change
More vulnerable communities are those most at risk
We need spatially explicit models to
understand human-environment interactions
Nature: Physical equations
Describe processes
Society: Decisions on how to
Use Earth´s resources
1973
1987
2000
Slides from LANDSAT
images: USGS
Modelling Human-Environment Interactions
How do we decide on the use of natural resources?
What are the conditions favoring success in resource mgnt?
Can we anticipate changes resulting from human decisions?
What GIScience techniques and tools are needed to model
human-environment decision making?
Clouds: statistical distributions
Clocks, clouds or ants?
Clocks: deterministic methods
Ants: emerging behaviour
Modelling collective spatial actions: the
complex systems approach
photo: Chico Albuquerque
1.
2.
3.
4.
Situated individuals (persons, groups, agents)
Interaction rules - communication
Decision rules - actions
Properties of space
Conections and flows are universal
Yeast proteins
(Barabasi and Boneabau,
SciAm, 2003)
Scientists in Silicon Valley
(Fleming and Marx, Calif Mngt
Rew, 2006)
Information flows generate cooperation
National Cancer Institute, EUA
http://visualsonline.cancer.gov
White cells attact a cancer cell (cooperative activity)
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.
Is computing also a natural science?
http://www.red3d.com/cwr/boids/
“Information processes and computation continue to be found abundantly in
the deep structures of many fields. Computing is not—in fact, never was—a
science only of the artificial.” (Peter Denning, CACM, 2007).
Computing is also a natural science
Computing studies information
flows in natural systems...
...and how to represent and
work with information flows in
artificial systems
Agent-Based Modelling: Computing approaches
to complex systems
Representations
Goal
Communication
Communication
Action
Perception
Environment
Gilbert, 2003
Four types of spatial agents
Artificial agents, artificial environment
Artificial agents, natural environment
Natural agents, artificial environment
Natural Agents, natural environment
source: Couclelis (2001)
Some caution necessary...
“Agent-based modeling meets an intuitive desire to
explicitly represent human decision making. (…)
However, by doing so, the well-known problems of
modeling a highly complex, dynamic spatial
environment are compounded by the problems of
modeling highly complex, dynamic decision-making.
(…)
The question is whether the benefits of that approach
to spatial modeling exceed the considerable costs of
the added dimensions of complexity introduced into
the modeling effort. The answer is far from clear and
in, my mind, it is in the negative. But then I am open
to being persuaded otherwise ”.
(from “Why I no longer work with agents”, 2001 LUCC
ABM Workshop)
Helen Couclelis
Some caution necessary...
“Complexity is more and more acknowledged to
be a key characteristic of the world we
live in and of the systems that cohabit our
world. It is not new for science to attempt to
understand complex systems: astronomers have
been at it for millennia, and biologists,
economists, psychologists, and others joined
them some generations ago. (…)
If, as appears to be the case, complexity (like
systems science) is too general a subject
to have much content, then particular classes of
complex systems possessing strong
properties that provide a fulcrum for theorizing
and generalizing can serve as the foci
of attention.”
(from “The Sciences of the Artificial”, 1996)
Herbert Simon (1958)
Our spatially explicit models need good social
theories to guide them
Nature: Physical equations
Describe processes
Society: Decisions on how to
Use Earth´s resources
We need social theories to understand humanenvironment interactions

Survey
Moran, “Environmental Social Science: Human-Environment Interactions and
Sustainability” (2010)

Social simulation
Schelling, “Micromotives and macrobehavior” (1978).
Batty, “Cities and complexity” (2005).

Game theory
von Neumann and Morgenstern, “Theory of games and economic behavior” (1944)
Nash, "Equilibrium points in n-person games“ (1950).

Evolutionary dynamics
Maynard Smith, ”Evolution and the theory of games” (1982)
Axelrod, “Evolution of cooperation” (1988).
Novak, “Evolutionary dynamics: exploring the equations of life” (2005).

Institutional analysis
Ostrom, “Governing the commons” (1990).
Social Simulation: Segregation
Segregation is an outcome of individual choices
But high levels of segregation indicate mean that people
are prejudiced?
Schelling’s Model of Segregation
If people require more than 1/3 of neighbours to
be of the same kind...
...ghettos are formed!
Game Theory
GT is an analytical tool for social sciences that is used to model
strategic interactions or conflict situations.
Strategic interaction: When actions of a player influence payoffs to
other players
Game Theory
Explanation: What is the game to be played?
Prediction: What outcome will prevail?
Advice or prescription: Which strategies are likely to yield good results
in which situations?
Where can we use Game Theory?
Any situation that requires us to anticipate our rival’s response
to our action is a potential context for GT.
Economics, Political science, Biology
What is a Normal Form Game?
Players: list of players
Strategies: all actions available to all players
Payoffs: a payoff assigned to every contingency (every possible
strategy profile as the outcome of the game)
John Kennedy and Nikita Khrushchev
Modeling two-party games
Payoffs for each player depend on actions of both
Two possible strategies: A party cooperates when he performs
value-increasing promises, and defects when he breaches
Modeling choice in non-cooperative games
Player 2
Cooperate
Cooperate
Player 1
Defect
Defect
Player 1
Both cooperate cooperates,
Player 2 defects
Player 1
defects, Player
2 cooperates
Both defect
The “chicken game”
“Rebel without a cause”
Two persons drive their cars towards a cliff. They must stop or both may
die in the fall. The one that stops first will be called a "chicken," meaning a
coward.
The hawk-dove game (== chicken game)
Two individuals compete for a resource (In biological terms, its value increases in the
Darwinian fitness of the individual who obtains the resource)
Hawk
Initiate aggressive behaviour, not stopping until injured or until one's
opponent backs down.
Dove
Retreat immediately if one's opponent initiates aggressive behaviour.
Maynard Smith and Price, "The logic of animal conflict“ (Nature, 1973 )
The hawk-dove game (== chicken game)
Encyclopedia Britannica
The stag-hunt game: conflict between safety
and social cooperation
Two hunters want to kill a stag. Success is uncertain and, if it comes,
require the efforts of both. On the other hand, either hunter can forsake
his partner and catch a hare with a good chance of success.
The stag-hunt game: conflict between safety
and social cooperation
C
D
C
10,10
0,6
D
6,0
5,5
Rousseau, in A Discourse on Inequality:
“If it was a matter of hunting a deer, everyone well realized that he must
remain faithful to his post; but if a hare happened to pass within reach of
one of them, we cannot doubt that he would have gone off in pursuit of it
without scruple..."
Prisoners’ Dilemma
Two suspects are caught and put in different rooms (no
communication). They are offered the following deal:
1. If both of you confess, you will both get 3 years in prison
2. If you confesses whereas the other does not, you will get 1
year and the other gets 5 years in prison .
3. If neither of you confess, you both will get 2 years in prison.
Generalizing...
Cooperation requires at least two individuals:
A: the one providing cooperation (DONOR)
B: the one benefiting from cooperation (RECEIVER)
Donor has a cost c to cooperate
and confers a benefit b to other
player
C
D
C
b–c
-c
D
b
0
you
Payoff matrix
other
Terminology
Player 2
T = Temptation to defect
R = Reward for mutual cooperation
P = Punishment for mutual defection
S = Sucker's payoff
Generalizing...
Payoff matrix
R: mutual cooperation
other
P: mutual defection
C
D
C
R(1)
S(-c)
D
T(b)
P(0)
S : sucker’s payoff
T : temptation to defect
you
Taking R = 1 and P = 0
Generalizing...
Payoff matrix
R: mutual cooperation
opponent
P: mutual defection
C
D
C
1
S
D
T
0
S : sucker’s payoff
T : temptation to defect
you
Taking R = 1 and P = 0
Different ordering -> Different tensions
greed
C D
C R S
D T P
fear
Chicken game
T >1 > S > 0
Stag-hunt game
1>T > 0 > S
Prisoner’s dilemma
T >1 > 0 > S
(Macy&Flache, PNAS 2002)
Tragedy of the Commons (Hardin, 1968)
Assume a common-property resource (exclusion is difficult and
joint use involves subtractability) with no property rights.
(Pasture open to all)
Each herdsman tries to keep as many sheep as possible on the
commons. Each tries to maximize gain.
Add those sheep!
The rational herdsman concludes that he should add another
sheep. And another…And another…And so does each herdsman
“Ruin is the destination toward which all men rush, each
pursuing his own best interest…”
Prisioner´s Dillema as a Model for the Tragedy of
the Commons
1.
Suppose the commons can support 2 sheep at no cost and that each
additional sheep put in the commons has a cost of 1/3 of its price due to
overgrazing.
2.
Assume two herdsman with one sheep on the commons each.
3.
If a herdsman puts another sheep in the commons, he receives all the
proceeds from the sale of each additional animal. His temptation is 4/3
and the sucker´s payoff for the other herdsman is -1/3.
Prisioner´s Dillema as a Model for the Tragedy of
the Commons
You are the herdsman. What are your options? Do you
cooperate or defect?
C
D
C
1
-1/3
D
4/3
1/3
you
Payoff matrix
other
Tragedy of the Commons?
Everybody’s property is nobody’s property (Hardin)
Preconditions for the tragedy of the commons
Lack of restraint on pursuits of self-interest
Consequences are externalities (I don’t have to pay)
Externalities in the global commons
Activity of one person has an impact on the well-being of another.
Positive externalities (or external benefits): Benefits realized by
those who didn’t pay for them.
Negative externalities (or external costs): Costs borne by those
who didn’t generate them. Byproducts that harm others.
SUVs in USA  Climate Change in Africa
Is the tragedy of the commons inevitable?
Experiments show that cooperation emerges if virtuous
interactions exist
source: Novak, May and Sigmund (Scientific American, 1995)
Repeated prisioner´s dillema
Four different strategies for repeated prisioner´s dillema
source: Novak, May and Sigmund (Scientific American, 1995)
Repeated prisioner´s dillema
Evolution of prisioner´s dillema comparing different strategies
source: Novak, May and Sigmund (Scientific American,
How can cooperation happen?
Nowak MA (2006). “Five rules for the evolution of cooperation” Science 314:1560-1563
(most highly cited multidisciplinary paper – ISI, 1st quarter 2010)
"I would lay down my life for two brothers or eight cousins“ (J.B.S. Haldane)
Five rules for evolution of cooperation
b = benefit for the recepient c= cost for the donor
Common pool resources (Elinor Ostrom)
The ultimate common pool resource
Governing the commons
[Ostrom, Science, 2005]
Governing the commons:
Ostrom´s conditions
1. Clearly defined boundaries
2. Congruence between appropriation and
provision rules and local conditions
3. Collective-choice arrangements:
4. Monitoring and graduated Sanctions.
5. Conflict-resolution mechanisms
6. Minimal recognition of rights to organize.
7. Organized governance activities.
Ostrom on governing the commons
“The challenge is how best to limit the use of natural resources so as to
ensure their long-term economic viability.”
“Neither the state nor the market is uniformly successful in enabling
individuals to sustain long-term, productive use of natural resource
systems.”
“Optimal equilibrium with centralized control is based on assumptions
concerning accuracy of information, monitoring capabilities,
sanctioning reliability, and zero costs of administration.”
Modelling collective spatial actions: potential
GIScience contributions
Agent
Agent
Space
Space
Benenson and Torrens, “Geographic Automata Systems”, IJGIS, 2005
(but many questions remain...)
Scientists and Engineers
Photo 51(Franklin, 1952)
Scientists build in order to study
Engineers study in order to build
Spatially-explicit land change models



Explain past changes, through the identification of
determining factors of land use change;
Envision which changes will happen, and their intensity,
location and time;
Assess how choices in public policy can influence change, by
building different scenarios considering different policy
options.
TerraME: Computational environment for
developing nature-society models
Cell Spaces
Support for cellular
automata and agents
Tiago Carneiro, “Nested-CA: A Foundation for Multiscale Modelling of Land Use
and Land Cover Change”, INPE, 2006.
TerraME´s components
[Carneiro, 2006]
1. Get first pair
2. Execute the ACTION
3. Timer =EVENT
1.
1:32:00
Mens. 1
2.
1:32:10
Mens. 3
3.
1:38:07
Mens. 2
4.
1:42:00
Mens.4
...
return value
true
4. timeToHappen += period
Describe spatial structure
latency
> 6 years
Describe temporal structure
Deforesting
Newly implanted
Year of
creation
Iddle
Slowing down
Deforestation =
100%
Describe rules of behaviour
Describe spatial relations
Governing the commons?
Deforestation in Amazonia
~230 scenes
Landsat/year
How could Brazil reduce
deforestation from 27.000 km2 to
7.000 km2 in 5 years?
Institutional analysis in Amazonia
Identify different agents and try to model their actions
Farms
Settlements
10 to 20 anos
Recent
Settlements
(less than 4
years)
Source: Escada, 2003
Old
Settlements
(more than
20 years)
Amazonia: multiscale analysis of land change and
beef and milk market chains with TerraME
São Felix do Xingu
INPE/PRODES 2003/2004:
Deforestation
Forest
Non-forest
Clouds/no data
Model development by Ana Paula Aguiar and Sergio Costa (INPE), using TerraME
software, built by Tiago Carneiro (UFOP) and Pedro Andrade (INPE)
Agents example: small farmers in Amazonia
Settlement/
invaded land
Sustainability path
(alternative uses, technology)
Diversify use
money surplus
Subsistence
agriculture
Create pasture/
Deforest
Manage cattle
bad land
management
Move towards
the frontier
Sustainability
path (technology)
Abandon/Sell
the property
Buy new
land
Speculator/
large/small
Agents example: large farmers in Amazonia
Diversify use
money surplus/bank loan
Buy land
from small
farmers
Create pasture/
plantation/
deforest
Manage cattle/
plantation
Buy new
land
Buy calves
from small
Speculator/
large/small
Landscape model: different rules for two main
types of agents
Beef and milk
market chain model
Land use
Change model
Small
farmers
Medium
and large
farmers
Landscape
metrics
model
Pasture
degradation
model
Several workshops in 2007 to define model rules and variables
Landscape model: different rules of behavior at different
partitions which also change in time
SÃO FÉLIX DO XINGU - 2006
FRONT
FRENTE
MIDDLE
MEIO
BACK
RETAGUARDA
Forest
River
Deforest
Not Forest
Modeling results
97 to 2006
Observed
97 to 2006
Modelling collective spatial actions: some
potential GIScience contributions
1.
2.
3.
4.
Situated individuals (persons, groups, agents): spatial
cognition, spatial analysis, scale in GIS
Interaction rules: semantics of communication, mobile
computing
Decision rules: ontology [of actions, events and processes],
spatial analysis
Properties of space: spatial analysis, spatial databases,
scale, uncertainty, vagueness
Conclusion
GlScience can make a significant contribution to global change
research, supporting spatially explicit models of humanenvironment interactions with reasoned scientific basis