Abstract model

The empirical model is not simple and there is no basis for claiming that it generalises beyond the specific case of Ga-Selala. By abstracting from the institutional detail captured in the empirical model, we learn more about the model but not necessarily anything more general about social processes. Whether and how such abstractions can lead towards meaningful social generalisation is the subject of the companion paper (Part 1). In the present case, the abstract model provides a story about social breakdown as a consequence of HIV/AIDS or any other epidemic that is not dependent on stokvel, funeral clubs and churches in particular.

The abstract model replaced the specific social institutions of rural South Africa with an abstract set of activities in which individual agents could choose to participate. Some activities were specified as children's activities and some as adult activities. During model initialisation, individuals were assigned to activities appropriate to their age classification but otherwise at random. Participation in activities by individuals then evolved as agents joined activities in which other agents they valued (or endorsed) most highly participated. Each agent had a randomly assigned maximum number of activities in which it could engage. Religious denominations, which are important features of Ga-Selala, were left out of the abstract model but kinship was retained.

The abstract model was run over the course of a standard generation (30 years). The breaking up of the social networks over the 30 years is depicted in fig. 3. The isolated individuals are mainly at extreme ages. Babies have not had time to form friendships and amonst the oldest their friends tend to have died off. However, it is clear that the density of links is reduced in the 30-year friendship network and there are isolated clusters comprised by agents of moderate ages - neither infant nor extremely old.

Figure 3: Abstract model friendship networks

[1-year friendship network] [30-year friendship network]

For purposes of comparison, the WHO life table for France was substituted for that of South Africa. France was chosen because it has one of the longest lived populations in the world with, for example, three quarters of French women and two thirds of French men born at least 90 years ago still alive today. Hardly any South Africans live that long. The specific hypothesis to be assessed was that early deaths reduce the number of friendship links and some of those links will connect friendship clusters. The loss of those links will eventually isolate at least some friendship clusters thereby to reduce social cohesion and the possibility of replacing deceased friends. The isolation of clusters would therefore reduce the availability of social support to individuals in those clusters.

Figure 4: Abstract model: 30-year friendship network with French life table

With no change in the abstract model other than the substitution of the French for the South African life tables, the resulting social network after a 30-year simulation is that shown in fig. 4. As with the model using South African life tables, there are isolated individuals in extreme old age. The clear difference is that, using the French life tables, the social network is much more dense and, in relation to population size, less marked by isolated clusters. Moreover, the clustering coefficient for the model using the French life table is stable over time whilst the same coefficient is declining in the model using the South African life table. The clustering coefficient is the number of triads in the network - the number of cases in which two friends of an agent are themselves friends - as a proportion of the number of possible triads. The time series of clustering coefficients in the two versions of the abstract model are shown in fig. 5.

Figure 5: Abstract model cluster coefficients

[South African life table] [French life table]