Multiregional Demography
Also known as: Multiregional Population Analysis, Multiregional Life Table, Rogers Multiregional Model
Multiregional demography extends the classical tools of mathematical demography — the life table, the Leslie matrix, and stable-population theory — from a single closed population to a system of interconnected regions linked by migration. Developed by Andrei Rogers, it tracks people not only by age but by region of residence, modeling birth, death, and interregional movement simultaneously. The result is a unified matrix framework that yields multiregional life tables, projections, and stable regional population shares, making it the foundation for analyzing how migration shapes the size and distribution of populations across space.
Key highlights
- Models fertility, mortality, and interregional migration in one internally consistent matrix framework.
- Produces multiregional life tables giving expected years lived in each region by region of origin.
- Yields the system's intrinsic growth rate and stable joint age-region distribution from an eigen-analysis.
- Avoids the inconsistencies of applying net migration separately to each region by using directional flows.
Intuition
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How it works
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When to use it
Use multiregional demography when migration between regions materially shapes population dynamics and you need internally consistent projections, life tables, or stable structures for a system of regions rather than each in isolation. It is the rigorous alternative to applying net-migration rates region by region. Assumptions: age- and region-specific rates of fertility, mortality, and origin-destination migration are available and roughly constant over the projection (or are themselves projected), and migration is well measured as directional flows. Do NOT use full multiregional models when only crude net migration is known (the directional flow data the method requires are missing), when the number of regions makes the matrices unwieldy relative to the data quality, or when a single-region cohort-component projection with net migration suffices for the question at hand.
Strengths & limitations
- Models fertility, mortality, and interregional migration in one internally consistent matrix framework.
- Produces multiregional life tables giving expected years lived in each region by region of origin.
- Yields the system's intrinsic growth rate and stable joint age-region distribution from an eigen-analysis.
- Avoids the inconsistencies of applying net migration separately to each region by using directional flows.
- Requires detailed origin-destination migration data by age, which are often unavailable or unreliable.
- The matrices grow large as the number of regions increases, straining data and computation.
- Assumes migration rates depend only on current age and region (a Markov assumption), ignoring duration and history of residence.
- Constant-rate stable analysis is a long-run idealization rarely realized when migration regimes shift.
Common pitfalls
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Applications
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Frequently asked
How does multiregional demography relate to the multistate life table?
They are mathematically the same framework. In multiregional demography the discrete states are geographic regions and transitions are migrations; in the general multistate (increment-decrement) life table the states can be any discrete categories such as employment, marital, or health status. Rogers's multiregional methods are the spatial instance of multistate demography.
Why not just use net migration in a single-region projection?
Net migration is the difference between inflows and outflows and is not a rate of any well-defined population, so applying it region by region can produce inconsistent or even negative populations and ignores where migrants come from and go. The multiregional model uses directional origin-destination flows, which keeps the regional system internally consistent and lets the destinations of out-migrants be tracked explicitly.
What is a multiregional stable population?
It is the long-run joint distribution of population by age and region that emerges if the current age-, region-, and migration-specific rates are held constant indefinitely. It is given by the dominant eigenvector of the multiregional growth matrix, and the associated eigenvalue gives the system's single intrinsic growth rate shared by all regions in the long run.
Sources
- 1.Rogers, A. (1975). Introduction to Multiregional Mathematical Demography. John Wiley & Sons, New York.ISBN 9780471730354
- 2.Preston, S. H., Heuveline, P., & Guillot, M. (2001). Demography: Measuring and Modeling Population Processes. Blackwell.ISBN 9781557864512
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ScholarGate. (2026, June 22). Multiregional Demography. ScholarGate. https://scholargate.app/demography/multiregional-demography