Dynamics of Two Populations with Different Birth Rates

We propose a simple model describing the dynamics of a system of two populations — more numerous natives and less numerous immigrants. The immigrants' birth rate is higher than that of the natives. Several modifications of this model taking into account changes of the birth rates due to external factors and/or possibility of contacts between the populations, are also introduced. The model is studied within two approaches — by solving a set of differential equations and through a Monte Carlo simulations. We show that the question of which population will eventually dominate depends on such factors as the probability of producing offsprings of mixed origin, assimilation of the immigrants, the ratio of the birth rates, initial numbers of the populations and the average age of an individual. In all, but two extreme cases, both populations will survive.