A simplified model of spatiotemporal population dynamics

This paper is an extension of the model of population growth and migration originally developed by H. Hotelling in 1921. This model consists of two ingredients, a logistic growth function and a linear spatial diffusion term. The author notes that the saturation population can be affected by the development of new technology and that improvements in transportation have increased the possibilities for migration. "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."