Models of birth trajectories with certain patterns of variations in vital rates

This article records experiments with a modified version of Lotka's stable population model. The traditional assumption of a set of unchanging net maternity rates as one of the preconditions has been replaced by allowing the rates to vary in certain ways while approaching or varying around a set of underlying constant rates. The integral equation assumes a different form but can be simplified and solved in the same old way. As a result, the birth trajectory does not necessarily attain a stable state. For certain patterns of mathematical functions the trajectory eventually becomes stable while for certain others it shows cyclical fluctuations. The variations in net maternity rates can also be postulated to follow the patterns of some measurable empirical functions which, like the mathematical functions, should be amenable to projections in the future. This information is needed for deriving the long-term solutions in additions to the information about the intrinsic rate of growth which is obtained from the traditional integral equation.