Regular pattern formation regulates population dynamics: Logistic growth in cellular automata

Regular pattern formation is common in nature, but its ecological role in population dynamics is not well understood. In this article, we present a logistic probabilistic cellular automata (LPCA) model that combines a basic logistic growth model with two-dimensional spatial dynamics to simulate regular pattern formation. For model generality, only propagation and competition were assumed to occur in LPCA, and their dynamics follow local logistic growth. Simulation outcomes show that the resource scarcity and shape of the neighborhood are the main causes of different regular patterns. We use reference data from an arid ecosystem in Shapotou to parameterize the LPCA model and find that the pattern shifts form spots, labyrinths, to gaps with decreasing resource scarcity and that anisotropic neighborhoods generate banded patterns. The influences of regular patterns on population dynamics were studied by comparing the LPCA model and its mean field approximation (MFA), which discards particular spatial configurations and makes global predictions of population dynamics. The outcomes show that regular patterns can regulate population dynamics and alter equilibrium population size. Furthermore, regular patterns work as optimized spatial configuration to balance space and resource competition.