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 1 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. 2 1
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. 3 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 of resources needed by plants to sprout, grow, survive, and reproduce themselves. 4 2
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 5 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” 6 0 4 3 5 2 6 3
Example of forest simulation with “FORESTE”, a CA-based simulation tool. In this simulation screenshot we have two vegetal polulations represented in two different colors (light green and dark green) During a simulation we can notice some emergent phenomena 7 We can notice the progressive shift of the selected group. 8 4
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. 9 Detecting emergent properties l The idea : find meaningful recurrent patterns of emergent phenomena l Meaningful patterns: more definables, easyer recognizables l Problems : - Patterns classification - Patterns detection 10 5
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 11 Go basic rules Two people play with a Go board and Go pieces, which have two colors, black and Territory If I put the white . The players take last turns putting black and white surrounder pieces on the board to surround area, or territory. piece... Capture Concept of liberty : free spaces around a piece, or a group of pieces. 12 6
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 13 Go-like patterns detected for forests ecosystems (1) Go game Forests Ko: Turn over in a shared area. Geta: Colored arrows represent possible A group directions of completely reproduction and surrounded it free space. will die. 14 7
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 15 are stronger. Now we have a name for the observed phenomena. 16 8
SHICHO 17 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) 18 9
Simulation experiments: example and results Patterns occurrence simulations / pattern ≈ 20 occurrence In general we have 100% a high occurrence. An example of Geta simulation experiment: Patterns evolve toward the expected From a given starting final configuration point to an expected for the phenomenon conclusion. occurrence. We have low results 0% when it is difficult to Ko Geta Shicho Iki Tsugi establish a good starting situation. 19 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 Simulation Step n+1 Step n Go-like patterns detection and interpretation 20 10
An idea: the concept of group Ni = cell i neighborhood; n ∈ Ni Von Neumann neighborhood 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. 21 Finding rules for pattern detection (examples) Geta: verify if a group Shicho: verify if there Tsugi: two groups is completely surrounded is the shift of the group become one mass centre 8 7 6 5 4 3 2 22 1 1 2 3 4 5 6 7 8 9 11
Conclusions and future works Suitability of Go-like patterns. 1. Detecting all patterns of emergent phenomena is 2. very difficult for a human operator. (we remark the necessity of an automatic detection method). We will further improve the functionalities of the 3. proposed CA-based method for forest ecosystem representation. We will implement a simulator with automatic tools 4. for pattern detection and analysis. 23 12
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