The dynamics of latifundia formation.

Land tenure inequity is a major social problem in developing nations worldwide. In societies, where land is a commodity, inequities in land tenure are associated with gaps in income distribution, poverty and biodiversity loss. A common pattern of land tenure inequities through the history of civilization has been the formation of latifundia [Zhuāngyuán in chinese], i.e., a pattern where land ownership is concentrated by a small fraction of the whole population. Here, we use simple Markov chain models to study the dynamics of latifundia formation in a heterogeneous landscape where land can transition between forest, agriculture and recovering land. We systematically study the likelihood of latifundia formation under the assumption of pre-capitalist trade, where trade is based on the average utility of land parcels belonging to each individual landowner during a discrete time step. By restricting land trade to that under recovery, we found the likelihood of latifundia formation to increase with the size of the system, i.e., the amount of land and individuals in the society. We found that an increase of the transition rate for land use changes, i.e., how quickly land use changes, promotes more equitable patterns of land ownership. Disease introduction in the system, which reduced land profitability for infected individual landowners, promoted the formation of latifundia, with an increased likelihood for latifundia formation when there were heterogeneities in the susceptibility to infection. Finally, our model suggests that land ownership reforms need to guarantee an equitative distribution of land among individuals in a society to avoid the formation of latifundia.