The concept of demographic potential and its applications

The paper contents the review of development of the concepts of reproductive value and growth potential earlier introduced by R. Fisher and by P. Vincent for the asymptotically stable population. On the ground of axiomatic approach these concepts are developed for the population with arbitrary time-dependent reproduction regime. Both continuous and discrete models of the close population are considered in the classical form given by A. Lotka and P. Leslie respectively. The possibility of developing the concept for arbitrary population model is illustrated on the case of the age-parity dependent fertility model. Properties of the demographic potential are concerned as well as its applications to estimation of demographic parameters, to comparative study of populations, to modeling the demographic transition, and to aggregate population modeling. Models presented are verified on test examples and on empirical data from the population of the world and different countries. The population history and prospects of Russia are examined using the models introduced. The population model incorporating the migration flows is also developed and approved on the US historical data. Using the demographic potential concept a general result is derived on the ergodic property for arbitrary linear population model. Results of Schoen, Kim, Rubinov, and Chystakova on monotonic convergence to stability are also sufficiently improved. Results presented can be used in studying the population dynamics, in demographic projecting, and in building and examining the economic-demographic models.