The evolution of living beings with continuous and consistent progress toward adaptation and ways to model evolution along principles as close as possible to Darwin’s are important areas of focus in Artificial Life. Though genetic algorithms and evolutionary strategies are good methods for modeling selection, crossover, and mutation, biological systems are undeniably spatially distributed processes in which living organisms interact with locally available individuals rather than with the entire population at once. This work presents a model for the survival of organisms during a change in the environment to a less favorable one, putting them at risk of extinction, such as many organisms experience today under climate change or local habitat loss or fragmentation. Local spatial structure of resources and environmental quality also impacts the capacity of an evolving population to adapt. The problem is considered on a probabilistic cellular automaton with update rules based on the principles of genetic algorithms. To carry out simulations according to the described model, the Darwinian cellular automata are introduced, and the software has been designed with the code available open source. An experimental evaluation of the behavioral characteristics of the model was carried out, completed by a critical evaluation of the results obtained, parametrically describing conditions and thresholds under which extinction or survival of the population may occur.