Multiregional Migration Projection

Multiregional migration projection extends the classic cohort-component method from a single closed population to a system of several regions that exchange migrants. Developed principally by Andrei Rogers in his 1975 Introduction to Multiregional Mathematical Demography, it replaces the ordinary Leslie matrix with a generalized growth matrix whose blocks carry not only survival and fertility within each region but also the age-specific probabilities of moving from every region to every other. Advancing a stacked population vector — population by age for each region — through repeated multiplication by this matrix projects all regions simultaneously and consistently, so that an out-migrant from one region becomes an in-migrant somewhere else and the system stays closed. The same matrix yields multistate life-table quantities such as expected lifetime spent in each region and the long-run stable spatial distribution of the population. Because the method demands smooth age-specific migration inputs, it is usually paired with Rogers-Castro model schedules, and the comparative findings of Rogers and Willekens's 1986 Migration and Settlement project established it as the standard apparatus of formal spatial demography.