Lattice gas model of gradual evolution

A simple dynamical model is presented for describing the gradual evolution of a variable number of species. The system is studied through Monte Carlo simulations using a lattice gas formalism. Each species is characterized by a single, scalar parameter ("adaptation") which is changed, within limits depending on the adaptation itself, at each time step. There are two independent mechanisms for removing a species from the system and one for creating a new species. We find that, regardless of the initial concentration of species, the system always reaches the same final state, characterized by the same concentration and the same average adaptation. The system is not homogeneous and contains species with different values of adaptation. The better adapted ones are found to form more symmetrical spatial patterns. Behavior similar to the one determined in the present model has been found in the evolving ecological and biological systems.