A Simplified Model of Spatiotemporal Population Dynamics

The paper is a development of the Hotelling model of population growth and migration. In the original model, a logistic growth term is combined with linear diffusion. Since man produces his own means of subsistance and himself decides which standard of living per capita is desirable, the ‘saturation’ population cannot be regarded as a constant, and production technology and technological development are introduced. At the same time it is noted that the reach of migration has increased with developments in transportation. Basic nonlinearities are introduced by use of a production technology with increasing-decreasing returns to scale. It is demonstrated how industrial takeoffs, population transitions, and agglomerative spatial patterns can emerge by changing the model parameters.