Population Turnover, Tipping Points and Markov Chains

Abstract

Invasion-succession-dominance and 'tipping points' are well-developed concepts in the human ecologist's approach to urban social structure. An attempt was made here to establish the presence, or absence, of such aggregate processes in Birmingham in the I960s. Markov-chain analysis was used to construct time paths. First, for the distribution of census areas amongst a set of states defined by the percentage of immigrant groups and, secondly, for the distribution of primary schools amongst a series of states defined by the percentages of coloured pupils. In neither instance was evidence found to support the idea of distinctive stages of population turnover. THE development of the invasion-succession-dominance concept has been central to the human ecologist's interpretation of urban growth and the distribution of population groups (Aldrich, 1975). To Burgess (1925, 1928) it provided a means of accounting for the 'wave-like' movement of immigrants through Chicago's residential space. Cressey (1938, p. 62) found it a 'common pro- cess': 'The immigrant and American groups follow rather different patterns of distribution, but behind these differences there is striking similarity in the way in which these changes take place. The common process of succession involves a cycle of invasion, conflict recession and re- organisation. These successive stages are interrelated and they recur in the movement of all groups in the city.' Undoubtedly, the invasion-succession-dominance idea is an extremely attractive one when discussed in general terms. It creates a mechanism by which population turnover can take place in urban sub-areas and permits a consideration of immigrant assimilation as a corollary of spatial dispersal through cyclic change. One may describe it intuitively, in a graphical sense, for any area in terms of an S-shaped curve. First, invasion involves the entry of a new, and sufficiently distinct, sub-group into an area, which accounts for the relatively flat lower limb of the curve. Secondly, succession takes place when the population of that area changes rapidly over time either through a substantial influx of newcomers and/or an emigration of existing groups. A sharp upturn in the curve will occur in this stage. Thirdly, and finally, dominance takes place when the incoming group becomes a substantial majority of that area's population, such that the rate of immigration slackens to give the upper limb of the S-shaped curve. Ford (195o) and Kiang (1968) both adopt this approach in their replications of the Cressey study. However, two major difficulties bedevil any reliance on such an interpretation of population turnover. There is a temptation to relate the invasion-succession-dominance sequence to all types of distinctive sub-groups. For instance, Handlin's (I959) analysis of the Negro and Puerto Rican populations in New York depended on the repeated operation of invasion-succession- dominance in a cycle of race relations. The result was an over-optimistic interpretation of the potential dispersal and assimilation of the Negro group in the light, that is, of subsequent