Yard-Sale exchange on networks: Wealth sharing and wealth appropriation

Yard-Sale (YS) is a stochastic multiplicative wealth-exchange model with two phases: a stable one where wealth is shared, and an unstable one where wealth condenses onto one agent. YS is here studied numerically on 1d rings, 2d square lattices, and random graphs with variable average coordination, comparing its properties with those in mean field (MF). Equilibrium properties in the stable phase are almost unaffected by the introduction of a network. Measurement of decorrelation times in the stable phase allow us to determine the critical interface with very good precision, and it turns out to be the same, for all networks analyzed, as the one that can be analytically derived in MF. In the unstable phase, on the other hand, dynamical as well as asymptotic properties are strongly network-dependent. Wealth no longer condenses on a single agent, as in MF, but onto an extensive set of agents, the properties of which depend on the network. Connections with previous studies of coalescence of immobile reactants are discussed, and their analytic predictions are successfully compared with our numerical results.Comment: 10 pages, 7 figures. Submitted to JSTA

Mendelian Randomization Analysis of the Relationship Between Native American Ancestry and Gallbladder Cancer Risk

Background A strong association between the proportion of Native American ancestry and the risk of gallbladder cancer (GBC) has been reported in observational studies. Chileans show the highest incidence of GBC worldwide, and the Mapuche are the largest Native American people in Chile. We set out to investigate the causal association between Native American Mapuche ancestry and GBC risk, and the possible mediating effects of gallstone disease and body mass index (BMI) on this association. Methods Markers of Mapuche ancestry were selected based on the informativeness for assignment measure and then used as instrumental variables in two-sample mendelian randomization (MR) analyses and complementary sensitivity analyses. Result We found evidence of a causal effect of Mapuche ancestry on GBC risk (inverse variance-weighted (IVW) risk increase of 0.8% for every 1% increase in Mapuche ancestry proportion, 95% CI 0.4% to 1.2%, p = 6.6×10-5). Mapuche ancestry was also causally linked to gallstone disease (IVW risk increase of 3.6% per 1% increase in Mapuche proportion, 95% CI 3.1% to 4.0%, p = 1.0×10-59), suggesting a mediating effect of gallstones in the relationship between Mapuche ancestry and GBC. In contrast, the proportion of Mapuche ancestry showed a negative causal effect on BMI (IVW estimate -0.006 kg/m2 per 1% increase in Mapuche proportion, 95% CI -0.009 to -0.003, p = 4.4×10-5). Conclusions The results presented here may have significant implications for GBC prevention and are important for future admixture mapping studies. Given that the association between Mapuche ancestry and GBC risk previously noted in observational studies appears to be causal, primary and secondary prevention strategies that take into account the individual proportion of Mapuche ancestry could be particularly efficient