A new discrete relative-dynamics algorithm is tested using population interactions of U.S. regions. A 133-year time period is used (1850-1983) to calibrate the log-linear model's parameters using standard linear regression tests. We also report certain forecasts under different spatial disaggregation schemes of the U.S. regions, and under two different time-period steps (iterations) to the year 2050. All forecasts imply competitive exclusion for the northern regions; under certain areal disaggregations and time (iteration) steps the southern or western region also experiences conditions leading to drastic declines in their share of the U.S. population. We also report the results of certain random fluctuations on the model's parameters and their implications regarding the dynamics of the U.S. regional population structure. The outcomes seem to be robust under these fluctuations. © 1988.
Dendrinos, D. S., & Sonis, M. (1988). Nonlinear discrete relative population dynamics of the U.S. regions. Applied Mathematics and Computation, 25(4), 265–285. https://doi.org/10.1016/0096-3003(88)90124-5