Introduction

Elementary examples of the application of mathematics to population problems have been given above, for example, rates, indexes and graduation. Some formulae have also been mentioned which relate total population at one time to total population at another time, or which perform the same function in relation to separate sexes or ages. In the present chapter, some more comprehensive analyses will be discussed.

The aim of this more comprehensive form of population mathematics is to express certain aspects of demographic change in a series of comprehensive formulae. These formulae do not relate exclusively to the population situations and problems of today, to human populations or even to animate objects. The first step is to postulate a series of fundamental assumptions. The next is to develop statements and equations which derive from the assumptions; the aim is to proceed from these towards a ‘solution’, from which some new information of value about populations may be derived. In order to achieve such a development, it is usually necessary to concentrate attention upon assumptions and relationships by means of which the analysis can be completed, and population mathematics often proceeds along the paths determined by such assumptions. In this way, close contact with realistic situations may to some extent be lost. Nevertheless, some interesting and important results have been obtained, and familiarity with these results is necessary to the demographer who is to be completely equipped for the study of population.

Deterministic and stochastic processes

Vital processes occur in a series of steps or stages which follow one another in sequence and depend largely upon one another.