Optimal transport in central place foraging, with an application to the overdispersion of heuweltjies

On the assumption of optimal transport of resources to central places, plus a simple rule for finding boundaries between the supply regions of central places and simple dynamics of central places, I show that in the case of a homogeneous environment and low mortality, the only stable equilibrium is a hexagonal array of central places of optimal size. I show that this can be applied to explain the pattern of overdispersion of heuweltjies in the southwestern Cape region of South Africa, and derive six predictions by which this explanation may be tested.