Silvertown et al. (1992) [J. Ecol. 80, 527-534] introduced a cellular automaton to simulate the competitive interaction of five grass species. In this model, space is represented by a grid of sites where each site represents a small square of land that will be occupied by exactly one of K species. The dynamics are as follows:
(i) An individual of species i produces new offspring of its type at rate b(i). That is, the times between the production of offspring are independent and have an exponential distribution with mean 1/b(i).
(ii) An offspring of type i produced at x is sent to y with probability that depends on the type i and the distance from x to y.
(iii) If type i disperses to a site y is occupied by type j, a successful invasion occurs with probability p(i,j). If invasion does not occur, the site y remains unchanged.
When K=2 the system above reduces to the biased voter model so we can also call this model the multi-type biased voter model .