Results Differences in house size by region and compared to settlement size The overall Gini coefficient for all houses is 0.2385 (80% CI: 0.2355–0.2416). The Gini coefficients for each individual settlement are shown in Tables 2–4. These range between 0.1336 and 0.3189 with the mean at 0.2295. Overall, the values follow a normal distribution (Figure 3). The Gini coefficients do not appear to be related either to overall settlement size or the number of houses within each settlement (Figure 4). Fitting the log-values of settlement size to the respective Gini coefficients yields non-significant p-values for each of the three regions (p-values: 0.4129, 0.5161, 0.768). Note, however, that the largest sites tend to exhibit Gini coefficients that are close to the mean of the overall distribution. In terms of regional differences, region A has slightly lower median Gini coefficients than region B, which in turn has lower values than region C (Figure 5). However, large overlaps in the boxplots of Gini coefficients for each region suggest that the differences are not statistically significant. This is reflected in the results of Mann–Whitney U-tests of the mutual pairs A-B, A-C and B-C, none of which are significant (p-values: 0.3676, 0.6448, 0.6994). Differences in house size over time The Gini coefficients for the settlements range between 0.17 and 0.32. The greatest variability is observed in the early Trypillia phase and the start of the middle Trypillia phases until c. 4200 BC. After that, variability decreases significantly (Figure 6A & B). Before c. 4400 BC and after 3500 BC, very few data are available. In view of these uncertainties during the earliest and latest phases of the settlement sequence, our conclusions below refer exclusively to the period that is most strongly supported by the data. Looking at all the regions together (Figure 6A & B), a steady decline in the Gini coefficient from approximately 0.25 to 0.2 is noticeable in the early phase of Trypillian population aggregation, between c. 4200 and c. 3800 BC. In the subsequent late phase of aggregated settlements, Gini coefficients increase substantially to values of up to 0.25. In the following phase, between c. 3650 and c. 3500 BC, when populations dispersed away from aggregated settlements into smaller settlements this trend of increasing Gini coefficient continues, rising to more than 0.3 in some cases. In region A, early settlements such as Veselyj Kut and Chizhіvka demonstrate Gini coefficients between 0.2 and 0.25 (Figure 6C & D; Table 2). In contrast, in the following phase (c. 4000–3800 BC), settlements such as Volodymyrivka, Hlybochok and Nebelivka have much lower Gini coefficients. A reversal of this trend towards somewhat higher, though still comparatively low, Gini coefficients emerges after c. 3800 BC. This includes the mega-sites of Maidanetske and Dobrovody, and the smaller settlement of Moshuriv 1. Simultaneously, some of the emerging small settlements, such as Talne 3, show extremely low Gini coefficients. During the phase between 3650 and 3550 BC, when populations began to move away from the large aggregated Trypillia settlements, the trend towards higher Gini coefficients clearly intensifies. This is the case, for example, at Moshuriv 2 and 3, Apolyanka and Kosenivka. The pattern in region B is similar to that of region A (Figure 6C & E): in the northern sub-region, early settlements, such as Haryachkivka 7 and 8, Vil"shanka and Zabolotne, show average Gini coefficients between 0.2 and 0.3 (Table 3). The variability of house floor sizes also declines here at settlements such as Ternivka, Trostyanchyk and Bilyj Kamin". In contrast to region A, however, no large settlements are known (so far) from the phase between c. 3800 and 3700 BC. Following this hiatus, settlements with significantly higher mean Gini coefficients between 0.25 and 0.3 reappear in the northern subregion from 3750 BC onwards represented, for example, by Krynychky and Kisnycya. The pattern of house size variability in region C contrasts somewhat with the pattern in regions A and B (Figure 6C & F). Here, the Gini coefficients (Table 4) tend to increase between c. 4200 and 3900 BC; they then decrease (until at least 3800 BC) to increase again later, but the latter trend is documented only at Cunicea 3.
Conclusion We have used variability in the sizes of houses at 38 Trypillia settlements to explore changing levels of inequality across three geographical regions and two millennia using standard Gini coefficients. We interpret the results to indicate that Trypillia mega-sites successfully avoided wealth inequalities between individual households. Their communities may have achieved this through an egalitarian ideology and effective mechanisms of reconciliation of interests and intra-community redistribution of (potentially) collectively generated surplus. Our results shed new light on the nature and possible reasons for the formation and decline of these unique prehistoric communities. We contend that, by enabling members to participate actively in political decision-making processes, the social make-up of aggregated mega-sites might have had a ‘reforming’ character, which may have been decisive for attracting, for a time, large numbers of people to these communities. We therefore believe we can partially answer the frequently discussed question of why Trypillia mega-sites emerged. The mega-site concept included a levelling mechanism to prevent social inequality, with co-operative economic management and living arrangements used to minimise inequality. The Gini coefficients generated here show that this was successful for a long time. Only during the later development phase of the mega-sites, from c. 3800 BC onwards, did the tendency towards social inequality increase again. Thus, the mega-site phenomenon represents one of a series of historical examples that show that an increase in the complexity of societies is not necessarily associated with an increase in vertical social differentiation. Rather, both the emergence and the break-up of aggregated Trypillia mega-sites were primarily due to the political decisions made by the individuals and communities who lived at—and who eventually decided to leave—these vast settlements.