title: Generalized Lotka stability.
abstract: The recently developed macroscopic approach to demography describes the age distribution of mothers and the net maternity function for a given human population entirely in terms of five parameters. Tracking of these parameters provides a number of new tools for analyzing populations and predicting their future states. Within the macroscopic approach, the new concept of generalized Lotka stability is presented in this paper, as an extension of a strong version of classic Lotka stability. The two leading parameters of the macroscopic approach, the Malthusian parameter r and the perturbation s, are computed from population data and plotted in two-dimensional parameter space. Generalized Lotka stability is then defined in terms of the movement of the (r,s)-vector over time. It may be observed in a number of human populations at specific periods of their history.
authors.affiliation: Department of Mathematics, Iowa State University, Ames, IA 50011, USA. Electronic address: jdhsmith@iastate.edu.
authors.forename: J D H
authors.initials: JD
authors.lastname: Smith
authors.affiliation: Department of Mathematics, Iowa State University, Ames, IA 50011, USA. Electronic address: czhang1@iastate.edu.
authors.forename: C
authors.initials: C
authors.lastname: Zhang
mesh_terms: D017677:Age Distribution; D003710:Demography; D005260:Female; D006801:Humans; D008962:Models, Theoretical; D009035:Mothers
keywords: Age distribution; Entropy maximization; Leslie matrix; Lotka stability; Macroscopic demography; Maternity function