Gene-driven predator–prey dynamics in cellular automata with energy constraints and spatial adaptation

We propose a spatially explicit, gene-driven cellular automaton model to investigate predator–prey eco-evolutionary dynamics under periodic environmental forcing. Producers and consumers interact on a two-dimensional lattice through localized rules incorporating energy metabolism and heritable foraging strategies. Simulations across multiple stochastic realizations demonstrate persistent coexistence, bounded non-equilibrium oscillations, and adaptive spatial pattern formation. Quantitative analyses reveal low extinction frequencies, characteristic oscillation statistics, and convergence of consumer strategies toward intermediate values. Comparative experiments with fixed strategies and without environmental periodicity confirm that coupled genetic adaptation and energy constraints are essential for long-term system stability.