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We investigate one-dimensional elementary probabilistic cellular automata(PCA) whose dynamics in first-order mean-field approximation yields discretelogisticlike growth models for a single-species unstructured population withnonoverlapping generations. Beginning with a general six-parameter model, wefind constraints on the transition probabilities of the PCA that guarantee thatthe ensuing approximations make sense in terms of population dynamics andclassify the valid combinations thereof. Several possible models display anegative cubic term that can be interpreted as a weak Allee factor. We alsoinvestigate the conditions under which a one-parameter PCA derived from themore general six-parameter model can generate valid population growth dynamics.Numerical simulations illustrate the behavior of some of the PCA found.

physical review. e

Approximate probabilistic cellular automata for the dynamics of  single-species populations under discrete logisticlike growth with and  without weak Allee effects