8. Modelling Settlement Rank-Size Fluctuations

This chapter proposes a model of long-term changes in human settlement pattern to identify possible generative processes behind empirically observed fluctuations in their rank-size pattern. The model assumes that per-capita fitness is a combination of the beneficial effect derived from the presence of other individuals in the same group and the finite amount of resource available locally. The former can lead to a positive frequency dependence, whereby an increase in the group size determines an increase in fitness; the latter can have detrimental effects once a group exceeds a certain size and the energetic demand becomes larger than what is available. Given that: (1) individuals have the possibility to modify their condition through group fission and fusion; and (2) the amount of resource is unlikely to be constant over space and time; we can expect fluctuations in the settlement pattern as a function of a non-linear relationship between size and fitness, as well as internally or externally induced variations in the amount of available resources. The simulation model will examine these scenarios and identify how different variables can induce different types of long-term equilibria in settlement systems.