Title: The migratory equations of motion.

POPLINE Document Number: 201633

Author(s):

Haag G
Weidlich W

Source citation:

In: Interregional migration: dynamic theory and comparative analysis, [edited by] W. Weidlich [and] G. Haag. Berlin, Federal Repubic of Germany, Springer-Verlag, 1988. :21-32.

Abstract:

The authors derive equations of motion for the dynamics of the population configuration. The description of the dynamics takes place on 2 levels: the stochastic and the quasideterministic level. Only the stochastic or probabilistic level is the fully consistent one for simple reasons. Since the individual decision process is described in probabilistic terms, the evolution on the macrolevel can only be a probabilistic one, too. Therefore, only the fully probabilistic treatment gives the insight into how the decision on the microlevel of individuals induce probabilistic fluctuations on the macrolevel. The mean square deviations on the macrolevel can, however, be very small because of mutual cancellations of fluctuations. The equation describing the full probabilistic evolution including the probability of deviations from the mean path is the master equation. On both the statistical and the quasideterministic level it is simple to generalize the equations so that they include migration as well as birth/death processes. It is shown how birth/death processes can be formally separated off in the mean value equation.

Keywords:

Mathematical Model
Migration
Population Dynamics
Population Theory
Birth Rate
Death Rate
Models, Theoretical
Research Methodology
Demographic Factors
Population
Demography
Social Sciences
Fertility Measurements
Fertility
Mortality