Elementary models for population growth and distribution analysis

A version of the Lotka-Volterra interaction model is adapted to describe population growth and migration processes in a two-region system. The regions are identified as a metropolis and its non-metropolitan hinterland. Several conditions on growth and migration regimes are imposed. The time behavior of the systems are analyzed, noting especially situations where total depopulation or population explosion eventually occur in one or both populations. Neither growth control nor migration control alone results in a condition of long-run stability in both regions. If at least a momentary condition of zero growth is achieved in both regions, it is possible to maintain finite populations if each population follows a logistic natural growth process and migration flow is proportional to the volume of interaction. It is necessary also that the natural increase limitation is strong relative to migration rates. This result holds even if one population has a net migration advantage over the other.