Figure 1.
Latifundia, malaria and their association patterns in Spain during the 1930s.
(A) Percent of land properties that were latifundia, i.e., land properties larger than 25 hectares (B) Malaria endemicity (Endemic>Intense>Minimal>Absent) (C) Correspondence analysis between malaria endemicity classes (Obtained from a partition around medoids cluster analysis, see Protocol S1 Appendix A for further details) and the percent of latifundia. Malaria categories are (End = endemic, Int = intense, Min = minimal and Abs = absent) (D) Percent of Land in Latifundia as function of malaria endemicity indices (the indices were based on the first component of a principal components analysis, PCA or Multidimensional Scaling, MDS, see legend for color and symbol explanation, see also Protocol S1 Appendix B for further details). (A) and (B) are re-drawn from Beauchamp [13].
Figure 2.
Graph of land use transition and trade between Owner i and Owner j, for a detailed explanation of the transitions see equations 1 & 2 in the methods section.
Figure 3.
At the beginning of the simulations all landowners have the same amount of land, however the state of the parcels is randomly assigned, after k iterations the model can converge to: (A) an equilibrium of equity, where all landowners have the same amount of land which is at equilibrium regarding the land use transitions, which implies (B) an uniform distribution in land ownership or (C) a Latifudium equilibrium, where all the land (in equilibrium regarding land use transitions) belongs to a single landowner, which implies (D) a skewed distribution with one (or a few) landowners accumulating land ownership. In (A) and (C) letters represent different landowners, and colors the land use, see figure legend for further details.
Figure 4.
Impact of utility combinations on the likelihood of equity as equilibrium.
In top of each panel the relations between the utilities is presented: a = forest, b = agriculture and c = empty (see equation 3 for further details). In each panel, the y axis represents the log2 of the number of parcels (m) per individual and the x axes present the log2 of the number individuals (n). Simulations were run 100 times for each combination of n and m, where the values of n and m were 2 to the power of the values in the x and y axes respectively. Contour lines give the probability of equity as equilibrium for a given parameter combination. Contour lines were obtained with a generalized additive model where the probability of latifundia formation was a smoothed function of the number of parcels and individuals in the model. In all the simulations run to draw this figure the transition rates across land use types were fixed equal to 0.5, i.e, μ = η = r = 0.5. Regarding the utilities of each land type they were always 3, 2 and 1 for any sequence of uk1>uk2>uk3, where
and
. In all panels blue corresponds to low probability of equity and green to high probability of equity.
Figure 5.
Sensitivity analysis to changes in the transition rates between land use.
In the top of each panel the degraded land recovery into forest rate (μ) is presented, the x axis represents the agricultural land degradation rate (η) and y axis deforestation rate into agricultural land (r). Simulations were run 100 times for each combination of μ, η and r. Contour lines indicate the probability of equity for a given parameter combination. Contour lines were obtained with a generalized additive model where the probability of latifundia formation was a smoothed function of the rates considered in the x and y axis. In all the simulations run to draw this figure the number of parcels per individual (m) and the number of individuals in the population were fixed to 64, a quantity that we assume to reflect the structure of rural communities in ancient Rome [19], [22] (see Figures S4, S5, S6, S7 for results with other values of m and n). Utilities were as follows: c = 3, b = 2, a = 1. In all panels blue corresponds to low probability of equity and green to high probability of equity.
Figure 6.
Ratio of initial to final landowners under disease transmission.
Panels (A) to (D) show the patterns of latifundia formation (i.e., a low ratio of initial to final landowners) under epidemic conditions (R0 = 1), panels (E) to (H) under endemic conditions (R0 = 2). In Panels (A) and (E) there is no discount rate (DR = 0, h = 1 in equation 13), in panels (B) and (F) there is 100% discount rate (DR = 100, h = 0 in eq. 14), in panels (C) and (G) there a 99.9% DR (h = 0.01 in eq. 14) and panels (D) and (H) show the results for DR<99.9. In all panels the x represents the proportion of landowners that were protected from disease transmission (0, 10, 20) and the control simulation ran under conditions that do not lead to latifundia formation (i.e., perfect equity on land ownership and use, ND in the x axis). In all simulations, parameters for land use change were set up equal to 0.5, number of landowners (n) was 64 and parcels for landowner (m) was also 64. In all the simulations run to draw this figure the transition rates across land use types were fixed equal to 0.5, i.e, μ = η = r = 0.5. Utilities were as follows: c = 3, b = 2, a = 1.