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Updated: Feb 28, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete
J Ricardo G Mendonça1, Yeva Gevorgyan2
1Escola de Artes, Ciências e Humanidades, Universidade de São Paulo Rua Arlindo Bettio 1000, Ermelino Matarazzo, 03828-000 São Paulo, SP, Brazil.
Abstract:
We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with nonoverlapping generations. Beginning with a general six-parameter model, we find constraints on the transition probabilities of the PCA that guarantee that the ensuing approximations make sense in terms of population dynamics and classify the valid combinations thereof. Several possible models display a negative cubic term that can be interpreted as a weak Allee factor. We also investigate the conditions under which a one-parameter PCA derived from the more general six-parameter model can generate valid population growth dynamics. Numerical simulations illustrate the behavior of some of the PCA found.
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