Some general relationships in population dynamics.

This paper extends the Lotka system of stable population equations to any population. The authors present this new general system and describe its duality with the recent Preston-Coale system. They derive these results by considering the calculus of change on the surface of population density defined over age and time. They show that analysis of this Lexis surface leads to all the known fundamental relationships of the dynamics of single-region human populations, several interesting new relationships, and a duality between period and cohort life tables.