Cellular automata and many-particle systems modeling aggregation behavior among populations

A cellular automaton model is presented in order to describe mutual interactions among the individuals of a population due to social decisions. The scheme is used for getting qualitative results, comparable to field experiments carried out on a population of ants which present an aggregative behavior. We also present a second description of a biological spatially structured population of $N$ individuals by a system of stochastic differential equations of It\^o type. A ''law of large numbers'' to a continuum dynamics described by an integro-differential equation is given.