Lotka's roots under rescalings

Abstract

In the mathematical theory of stable populations, when the net maternity function is scaled by a constant divisor , changing its level without changing its shape, the rates of attrition of transient waves in the age structure of the population as it converges toward stability are altered. The attrition rates are specified by the real parts of the complex roots of Lotka 's equation. Conditions are given for the falsity of the longstanding claim that there always exists some rescaling that brings to zero the real part of the complex root governing the lowest frequency wave. A general account of scalable and unscalable roots follows for the discrete-age, Leslie formulation, elucidating and setting limits to the standard account of approach to stability.