  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.
