A Cellular Automata Approach to Population Modeling

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A Cellular Automata Approach to Population
Modeling

• Alexa M. Silverman

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Purpose

• To use cellular automata to model population
  growth and change
• To observe the effects of various factors on the
  behavior of populations
• To determine whether a cellular-based model of
  population is valid and realistically predicts
  the behavior of individuals in a population

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Cellular Automata

• A cellular automaton is a cell on a grid which
  determines its state (live or dead) based on
  the states of neighboring cells.
• 2D cellular automata consider all eight
  neighboring cells.

2D cells with live neighbor counts
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Life

• Life notation is written s/b, where numbers on
  the right side of the slash represent neighbor
  counts needed to survive and numbers on the left
  side of the slash represent neighbor counts
  needed for cell birth.

34 Life (34/34)
Conways Game of Life (23/3)
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CA Modeling
Rumor Mill models spread of a rumor
Urban Suite Cells models growth of cities

• The field of cellular automata modeling is still
  relatively new, but several models have been
  created.

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14/3 Population Model

• For this model, the rule 14/3 was chosen because
  it causes cells to grow and move in a pattern
  resembling the spread of a species (starts
  localized and becomes more widespread).
• 14/3 automata suggest two types of individuals
  antisocial (survives with 1 neighbor) and
  social (survives with 4 neighbors).

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Code and Testing

• This program was created in NetLogo because the
  NetLogo graphics window allows for real time
  view of population growth and change. NetLogo
  code is object-based, which is ideal for a model
  where each cell must know its state, and the
  states of its eight surrounding cells.
• In test runs, the percentage and population of
  live cells are monitored. Variations occur due
  to the introduced variable of initial population
  density and the individual behavior of cells,
  which changes based on the random placement of
  cells on the grid. The nature of cellular
  modeling produces slightly different results with
  each run.

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NetLogo Interface
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Code Sample
Methods to birth and kill cells
Methods to check if a cell will survive or be
born the next turn
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Results

• High initial density causes quick decline in
  populations, isolation of groups

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Results

• Ideal initial density seems to be around 44

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Sources and Background

• http//www.kevlindev.com
• http//ccl.northwestern.edu/netlogo/
• http//psoup.math.wisc.edu/mcell/
• Individual-Based Artificial Ecosystems for Design
  and Optimization by Srinivasa Shivakar Vulli and
  Sanjeev Agarwal
• A Hybrid Agent-Cellular Space Modeling Approach
  for Fire Spread and Suprression Simulation by
  Xiolin Hu, Alexandre Muzy, Lewis Ntaimo