Issues in Population Studies: Modelling Population Growth and Urbanization, Study notes of Humanities

Download Issues in Population Studies: Modelling Population Growth and Urbanization and more Study notes Humanities in PDF only on Docsity! Lecture 12: Issues in Modelling Slide 1 ISSUES IN MODELLING The major issues in population studies are as follows: • growth of population; • changes in composition of population; and • demographic processes such as nuptiality (i.e., marriage), fertility, mortality and migration. Mathematical and statistical models have been used in studies of all the above issues. Among them as compared to nuptiality more attention has been paid to modelling of fertility and mortality. PREDICTING GROWTH OF POPULATIONS AND SUBPOPULATIONS Mathematical models have been used commonly to predict the size and composition of population of a country or a geographical region. For this purpose, various functions such as linear function, geometric or exponential growth function, modified exponential function, logistic curve, Makeham curve, Gompertz curve, polynomials, hyperbolic functions and autoregressive series have been used (Misra, 1980). Among them logistic curve has found more support than any other function on empirical grounds as well as the logic that the “population increase is proportional to the absolute population size already attained and the amount still left until the maximum, where the population becomes stationary” (UN, 1973). Docsity.com Slide 2 Assuming that r is the maximum rate of increase of the population, K NK − the fraction by which the actual population (N) remains below the maximum (K), then the increase of population per unit of time is K NK rN dT dN −= The total population will then be rtbe K N −+ = 1 Figure 4.1 shows the various forms of logistic growth curve for different values of t and r (Weisstein, Eric W., 2009). In a typical logistic growth model, showing growth of population, N increases continuously from zero to a saturating level in a certain manner: initially when N is small the growth rate is also small but it continues to increase till a maximum point of growth rate is reached after which although N continues to rise but the rate of growth becomes smaller and smaller, ultimately reaching zero. Is this not a realistic assumption for population growth? Almost same thing can be said about degree of urbanization, spread of literacy and many other things in population studies. All these processes can be modelled using logistic curve. Docsity.com Slide 5 Subsequently, Brass showed that if the fertility pattern can be described by a Gompertz function of the proportion experienced by each age, then the following is a better estimate of TFR than the above (Brass, 1979). 4 3 4 2 )( P P P With improvement in data sources and development of new sources such as Sample Registration Scheme need for such models declined. Knud (1983) compared cancer mortality between sexes, cohorts and cities by using Poisson distribution for number of deaths at a particular age and the mortality rate (defined as chance of survival to age x) as follows: kx x bl = b and k are two parameters for which maximum likelihood estimates were obtained. Gompertz model has been commonly applied for studying mortality. Using an age-dependent shape parameter, Weon (2004) used a Weibull model for mortality rate µ(t), i.e., ratio of density (f(t)) and survival functions (S(t) = 1 – F(t)) for estimating maximum longevity, as follows: ))/exp()( )(tttS βα−= ] )( *)/ln( )( [*)/()( )( dt td t t t tt t βαβαµ β += Docsity.com Slide 6 He assumed that the typical human survival curves shows: a rapid decrease in survival in the first few years of life, a relatively steady decrease, and then an abrupt decrease near death. In absence of data on measures of fertility they were derived from surveys. In India demographers derived parity progression ratios from survey data and used exponential model, displaced exponential model, Poisson model and life table approach for birth intervals (Pathak, 1989; Krishnamoorthy, 1989; Pathak and Ram, 1989). PREDICTION AND ESTIMATION OF MIGRATION Studies of migration aim at estimation, prediction and explanation of migration. In this context, for the first time Ravenstein published an article in Journal of the Statistical Society in 1885 in which he showed that, as believed by William Farr and many others, migration is not without laws. He developed some well known laws of migration, such as follows, which are still difficult to refute: • The great body of migrants travel short distances. • Women outnumber men in short distance migration. • Migrants move from agricultural areas (places of dispersion) to industrial cities (places of absorption) followed by migration from centres of industrial cities to suburban areas and from remote areas to places of dispersion. • Each migration current has a counter current with similar characteristics. • The major causes of migration are economic. Docsity.com Slide 7 Four years later in 1889 Ravenstein published another article in the Journal of Royal Statistical Society. This article was based on the experience of North America and Europe (the first article was based on the experience of UK). In this article he said that people travel long distances to occupy unsettled land. Nearly 100 years later, in 1940 Samuel A. Stouffer published an article in American Sociological Review. He showed that the number of migrants from place i to place j is inversely proportional to intervening opportunities. The model was confirmed by 1n 1975 by Wadycki who found it to be quite an accurate description of migration. Zipf (1946) developed and validated a gravity model to represent that volume of migration between two cities (Mij) is directly proportion to populations of the cities (Pi and Pj) and inversely proportional to distance separating the two cities (dij) He assumed that income and unemployment are uniformly distributed over the areas. Mij = K (Pi * Pj)/D where K is a constant to be found out from the empirical data. To some sociologists the model may look funny or absurd, but Zipf found that the model fitted very well for all modes of transportation. After all, if the logic used in the model is sound that accurate data are available why would mathematical equations not produce a good fit to empirical data? Docsity.com