Emergent Pattern Detection in Vegetable Population Dynamics S. - - PDF document

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Emergent Pattern Detection in Vegetable Population Dynamics

• S. Bandini, S. Manzoni, G. Mauri, S. Redaelli
• Dept. Of Computer Science, Systems and

Communication University of Milan-Bicocca

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CAFFE (Cellular Automata For Forest Ecosystems) project

CAFFE project: interdisciplinary research involving computer scientists of University of Milano-Bicocca and biologists and ecosystem managers of Austrian Research Center.

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Studying forests

Studying interaction of forest ecosystem with other

dynamic systems (humans or other natural phenomena)

Importance of studying forests by simulation.

• Forest byorithm are very long.
• It is impracticable to do some experiments with real plants

in a real area.

One of the main goal: design a method to support

the analysis step of simulations of forests modeled according to a distributed approach.

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The CA-based forest model (1)

The model permits the simulation of the dynamics of an heterogeneous plant population:

– Different plant species can inhabit the same area and

compete for the same resources

– The CA reproduces a given territory

area, divided in cells

– Each cell can be inhabited by a tree – Each cell contains a given amount

• f resources needed by plants

to sprout, grow, survive, and reproduce themselves.

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The CA-based forest model (2)

l The resources considered in the model are:

– Water – Nitrogen – Potassium – Sunlight

l Each cell contains a given amount of each resource l At each update step of the CA the plants living in the

area need a minimum amount of resources to survive, competing with the others for them

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The CA-based forest model (3)

l The presence of a plant in a cell can also influence

surrounding area and the trees living in it

l This influence has been modeled so to keep

interactions local as follows:

– Resources flow from richer cells to poorer neighbors – Thus, a cell containing a large tree is poorer on resources,

since the tree is more “greedy”

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Example of forest simulation with “FORESTE”, a CA-based simulation tool.

During a simulation we can notice some emergent phenomena In this simulation screenshot we have two vegetal polulations represented in two different colors (light green and dark green)

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We can notice the progressive shift

• f the selected group.

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Some considerations...

l The vegetal movement is considered in a

space-time dimension through the birth/death process.

l With more plant groups emergent dynamics

are more complex and for a human operator it is very difficult to recognize all collective behaviors during a simulation.

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Detecting emergent properties

l The idea: find meaningful recurrent patterns

• f emergent phenomena

l Meaningful patterns: more definables, easyer

recognizables

l Problems:

• Patterns classification
• Patterns detection

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Using Go game patterns

l Affinity between Go and

forest systems in competition scenario.

l Using well known

spatial pattern in Go game to detect forest emergent phenomena

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Go basic rules

Concept of liberty:

free spaces around a piece, or a group of pieces.

Territory Capture

Two people play with a Go board and Go pieces, which have two colors, black and

• white. The players take

turns putting black and white pieces on the board to surround area, or territory. If I put the last surrounder piece...

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Go affinities

l With forests

– Representation of territory competition – Representation of two species – Single pieces can appear, disappear and can not move.

l With CA

– The presence of a grid that represents the territory area – The grid cells can have three states: void, black or white – The presence of local evolution rules

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Go-like patterns detected for forests ecosystems (1)

Go game Ko:

Turn over in a shared area.

Geta:

A group completely surrounded it will die.

Forests

Colored arrows represent possible directions of reproduction and free space.

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Go-like patterns detected for forests ecosystems (2)

Go game Forests Shicho:

A group shifts toward more suitable area.

Iki:

A strong group that can survive for long time.

Tsugi:

Connected groups are stronger.

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Now we have a name for the

• bserved

phenomena.

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SHICHO

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Experiments and simulations

l Goal:

– validation of Go-like patterns:

from a pattern suitable starting point to a specific final configuration (we let evolve the starting situation observing if the final state is in accordance with the expected result)

l Method:

– variation of some meaningful parameters: (pattern size,

characteristic of the involved species, species initial configurations, and others)

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Simulation experiments: example and results

An example of Geta simulation experiment: From a given starting point to an expected conclusion.

Patterns occurrence

Geta Ko Shicho Iki Tsugi

100% 0%

• ccurrence

simulations / pattern ≈ 20 In general we have a high occurrence. Patterns evolve toward the expected final configuration for the phenomenon

• ccurrence.

We have low results when it is difficult to establish a good starting situation.

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Toward an analysis automatization in CA-based simulator system

Formalization and implementation of detection algorithms to find the studied patterns in a CA system.

Simulation Step n Simulation Step n+1 Go-like patterns detection and interpretation

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An idea: the concept of group

Ni = cell i neighborhood; n ∈ Ni Definition 1 connection Given the individuals t and s we say that t is connected to s (and vice versa) if t ∈ Ns. We will indicate this with the simbol t → s. Definition 2 belonging to a group Given an individual t and a group A we say that t ∈ A if t → k where k ∈ A. trivial group definition a single isolated element i is consider a trivial group composed by only one individual. Von Neumann neighborhood

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Finding rules for pattern detection (examples)

Geta: verify if a group

is completely surrounded

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Shicho: verify if there

is the shift of the group mass centre

Tsugi: two groups

become one

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Conclusions and future works

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Suitability of Go-like patterns.

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Detecting all patterns of emergent phenomena is very difficult for a human operator. (we remark the necessity of an automatic detection method).

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We will further improve the functionalities of the proposed CA-based method for forest ecosystem representation.

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We will implement a simulator with automatic tools for pattern detection and analysis.