Edinburgh Napier University

  Early this century "S-shaped" curves, sigmoids, gained
populari ty among demographers. However, by 1940, the approach
had "fallen out of favour", being criticised for giving po,or
results and having no theoretical validity. It was also
considered that models of total population were of little
practical interest, the main forecasting procedure currently
adopted being the bottom-up "cohort-component" method.
In the light of poor forecasting performance from
component methods, a re-assessment is given in this thesis of the
use of simple trend models. A suitable means of fitting these
models to census data is developed, using a non-linear least
squares algorithm based on minimisation of a proportionately
weighted residual sum of squares. It is demonstrated that useful
models can be obtained from which, by using a top-down
methodology, component populations and vi tal components can be
derived. When these models are recast in a recursive
parameterisation, it is shown that forecasts can be obtained
which, it is argued, are superior to existing official
projections.
Regarding theoretical validity, it is argued that sigmoid
models relate closely to Malthusian theory and give a mathematical
statement of the demographic transition.
In order to judge the sui tabili ty of extrapolating from
sigmoid models, a framework using Catastrophe Theory is developed.
It is found that such a framework allows one quali tati vely to
model population changes resulting from subtle changes in
influencing variables. The use of Catastrophe Theory has
advantages over conventional demographic models as it allows a
more holistic approach to population modelling.