Several developments of techniques in the field of mathematics encouraged attempts to formulate mathematical laws of population growth.

The availability of data on population facilitated the verification of these laws. Quetelet, a Belgian astronomer, was the first to adopt a mathematical approach to the study of population growth.

The most important among the mathematical theories was the “theory of logistic” growth of population developed independently by Verhulst, and Pearl and Reed in the United States.

According to Pearl’s and Reed’s logistic law, the growth of population occurs in cycles and “within the cycle and in a specially limited area or universe, growth in the first half of the cycle starts slowly, but the absolute movement per unit of time increases steadily until the midpoint of the cycle is reached.

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After this point, the increment per unit of time becomes steadily smaller until the end of the cycle.”The total population according to this law of the logistic curve follows a S-shaped curve, as indicated in Figure 5.1.

Though the law of logistic growth of population initially attracted a great deal of attention, its usefulness for estimating and projecting future population size and as a theory of population has since been widely questioned.

This theory has been criticised mainly on socio-cultural and economic grounds. It has been pointed out that the logistic theory does not take into account the changes population growth which permits the population to exploit its resources effectively, nor does it consider the changes in the aspirations and motivations concerning various patterns of fertility behaviour.