A short review of cellular automata models in ecology is given. Introduction of a spatial dimension into a discrete-time Markov chain leads to a class of cellular automata called spatio-temporal Markov chains (STMC). The behaviour of the model is determined by its temporal and spatial orders. It has been proven that STMC models have ergodic distributions in certain cases for spatial order 0. Simulations suggest that STMC models of higher spatial order also have ergodic distributions. The model of Dytham (1995) is demonstrated to be an STMC. Modelling population dynamics of three plant species on a lawn, two STMC models of different order are compared. The model validation shows a good agreement for Glechoma hederacea, but large deviations for Lolium perenne and Trifolium repens. The species-dependent performance of the models can be explained by selective grazing. Modifications of the transition matrices are used to examine possible causes of the deviations. ; This is the author's final draft of the paper published as Ecological Modelling, 1998, 107 (2-3), pp. 113-125. The final version is available from http://www.sciencedirect.com. Doi: 10.1016/S0304-3800(97)00202-0