OBTAINING BIRTH AND MORTALITY PATTERNS FROM STRUCTURED POPULATION TRAJECTORIES

A method is presented for unravelling the demographic equation for str uctured populations. A solution to the McKendrick-von Foerster equatio n is constructed using spline functions and this is fitted to stage-st ructured population data in such a way that the solution is smooth, po sitive, and does not imply negative death rates. The smoothness of the surface, and hence the complexity of the population model, is determi ned in a statistically optimum manner using cross validation. Time- an d age-dependent death rates can be obtained as well as time-dependent birth rates. Confidence intervals are obtained for population size and death rates that give a 95% probability that the true population dyna mics are within the intervals. Practical application of the method is demonstrated, and comparison made with three alternative methods. The method requires estimates of stage populations at a series of times an d estimates of the durations of those stages, or age ranges covered by the stages. The stage durations may vary with time.