A Cellular Automata Approach to Population Modeling Alexa M. Silverman

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

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

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) “Conway’s Game of Life” (23/3)

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.

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).

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.

NetLogo Interface

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

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

Results Ideal initial density seems to be around 44%

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