Two Models for Multiregional Population Dynamics

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Abstract
A general linear demographic model is derived which subsumes a wide variety of previously proposed population models. The general model includes in particular the linear model of interregional population growth and distribution developed by Rogers and others. One feature of this model is criticized, the allocation of outmigrants from any region in constant proportions among possible destination regions. Insofar as persons migrate to economic opportunities, outmigrants will distribute themselves among regions in proportion to these opportunities. Insofar as the economy of a region services its population, opportunities will vary directly with population. This suggests the introduction of a new model which allows for the variable allocation of outmigrants from each region according to the distribution of population among possible destination regions. Such a model is proposed, and it turns out to be nonlinear. The linear and nonlinear models are compared by applying them to the analysis of migration between three regions of the United States during 1955–1960. In the course of developing the new model, a set of interregional migration statistics is defined which eliminates the imperfect duality between interregional in- and out-migration rates.

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