On Monotonic Convergence To Stability

The paper introduces a class of distances to stable equivalent, which monotonically decrease to zero as a population moves to stability. Kullback distance expected earlier to be a unique measure of such types turns to be a specimen of this class. It is shown that the very feature of monotonic distance is in weighing with demographic potentials of age specific deviations from stable equivalent. The paper also introduces a class of monotonic measures for convergence of different populations with common reproductive futures. Results obtained shed new light on the process of stabilization and can be used to develop different measures of age structure dynamics.