Rates, intrinsic linkages, and multistate population dynamics

Demographic analyses of multistate populations are commonplace, as are situations where population stocks are known but population flows are not. Still, demographic models for multistate populations with changing rates remain at an early stage of development, limiting dynamic analyses and analytical projections. Here, a new approach, the Intrinsic Linkage-Rate Ratio (IL-RR) model, is presented and explored. The key IL parameter, w, is a simple weight for projecting populations. Using the ultimate state composition implied by the prevailing rates, the IL-RR model provides new relationships that connect multistate populations over time and allow analytical population projections. Parameter w reflects population metabolism and scales the level of the transfer rates. Compositional change is driven by the sequence of implicit stable population compositions. The IL-RR approach also provides a new method for estimating transfer rates within an interval from population numbers at the beginning and end of the interval. The new relationships developed advance the ability of demographers to model multistate populations with changing rates and to relate population stocks and flows.