Empirical model

The model design and detail were based on interview data collected over some 10 years by the Radar Programme On the basis of this evidence and mortality tables from the World Health Organisation we made the following assumptions on initial conditions.:

• A normal household size distribution, $N(7,3)$
• Ages of household heads are normally distributed,$N(56.2,12.6)$
• An empirical discrete distribution of marital status was used of the sort represented by a histogram. The classes are married, widowed, single, divorced.
• The age difference between spouses approximates a normal distribution, N(8.43,6.5760).
• Ages of household members are gamma distributed, $\Gamma(2.4,0.086)$
• Empirical discrete distributions were used to set initial values of the number, age and gender of migrants from households in Ga-Selala

The behaviour of and social interactions amongst agents determines the social support structures that emerge during simulation runs with the models. We know from the IMAGE and published data that households in rural South African villages form savings clubs called stokvel to which all members contribute a specified amount each month and one of the households is given each month's subscriptions to buy food in bulk. The stokvel has a social function as well and is comprised by household heads who are known to and friendly with one another. From the same data sources, we know that there are funeral clubs which have many more members and act as an insurance scheme to cover the bulk of the heavy expenditures expected of households when one of their members dies. Other expenditures include lobola, which is a substantial bride price.

Household incomes in Ga-Selala derive almost entirely from state grants and pensions. The main grants are child grants paid to the household on each child less than eight years of age and pensions paid to older individuals. The grants are pooled within households.

There is also borrowing and lending of food in times of need by close family members and friends. There may also be some relatively short-term patience with stokvel members who are unable to pay their subscriptions.

Individual behaviour and social interactions are determined by declarative rulebases. The rules specify the conditions in which agents will migrate away from the village, how they will allocate limited resources among current expenditure, stokvel and funeral club subscriptions, with whom they will form friendships and sexual relations and how many of each and, in general, who they will support in time of need.

The evidence base for the implementation of the rules was IMAGE data, expertise from SEI partners, and from interviews and role playing games conducted by a joint team of modellers from the Centre for Policy Modelling and field workers from SEI-Oxford.

The rules that led to the formation of social support networks included specific rules determining the conditions in which agents would endorse other agents with desirable or undesirable labels. Some rules were straightforward and would apply only once. For example, an agent would endorse another with the label is-kin if the two agents shared grandparents or great-grandparents but not parents (were cousins but not siblings). Other rules would enable one agent to endorse another repeatedly as (say) reliable, trustworthy, capable or their pejorative opposites. In choosing its closest ``friends'', each agent ranks its acquaintances according to the goodness of the endorsements it has attached to them. The best endorsed are those it would ask for help, give help if asked and join with in the establishment and maintenance of a stokvel. The best endorsed acquaintances of each agent are also those by which it would be the most influenced. This representation of the cognitive drivers of behaviour and social interaction are taken from well established and validated principles of cognitive science and social psychology.

Figure 1: From trace to story

The results from simulations with the empirical model were checked with villagers in Ga-Selala and with officials in the municipality of Tubatse. The villagers were given stories drawn from model traces. An fragment of trace and corresponding story presented to villagers is reproduced in fig. 1.

A particular issue of policy concern is the effect of mining development on the sustainability of the village as represented by the continuing viability of its social support networks. A measure of this viability is the completeness of the social network amongst individuals where the links between nodes representing individuals indicate that at least one of the two considers the other to be a close friend. Fig. 2 shows that in a typical model run covering 25 simulated years and allowing for birth and mortality rates as given by WHO data, there are two separate friendship networks after five years but thise break up into smaller, isolated clusters after 25 years. The reason that there are two separate subnetworks in the early stages of the simulation run is that social norms in Ga-Selala do not allow friendship links (as distinct from sexual partnerships) between men and women. It seemed likely that the breaking up of friendship (and therefore social support) networks was due to early deaths in the population. This hypothesis was assessed in two ways. First, a second model was developed that abstracted from much of the specific institutional detail of the empirical model. Simulations with the abstract models would demonstrate whether the pattern of social break-up was due to the institutional fabric of the village or was more general. The second step was to substitute mortality rates from a country with a longer lived population.

Figure 2: Empirical model friendship networks

[5-year friendship network] [25-year friendship network]