Population dynamics in variable environments. IV. Weak ergodicity in the Lotka equation.
The Hilbert projective metric is applied to the continuous-time Lotka equation in demography to establish weak ergodicity: populations with the same time-varying fecundity and mortality schedules ultimately have the same age composition. The analysis displays clearly the dynamic content of Lotka's equation and identifies a contraction operator which forces convergence of birth sequences over time. The relationship between primitivity in the discrete (Leslie) and continuous (Lotka) demographic models is made clear.
D001723:Birth Rate; D003710:Demography; D006801:Humans; D008433:Mathematics; D008954:Models, Biological