Spatial Impacts of Changes in the Population Growth Matrix

There are in fact two approaches to trace through the impacts of particular changes in the components of the population growth: (a) Examination of model stable multiregional populations (simulation approach); (b) Mathematical analysis of the impacts (analytical approach). Some mathematical impact analysis has already been performed in the paper on spatial population dynamics. It follows essentially Keyfitz's chain of derivations, but centers on the multiregional generalization of some principal formulas. In order to pursue the impact analysis further, we need some additional findings of matrix algebra. Most of the relevant ideas are collected in a recent volume on sensitivity analysis and on methods for incorporating sensitivity considerations in engineering design procedures. This paragraph deals with the analysis of the impact of changes in the growth matrix on: (a) growth rate of the stable population; (b) coefficients of the characteristic equation; (c) stable population distribution