One-memory in multiperson bargaining

In Rubinstein's (1982) 2-player discounted alternating offers bargaining game, the subgame perfect equilibrium outcome is unique and equivalent to the Nash bargaining solution. However, when there are more than 2 players, every feasible partition can be sustained in subgame perfect equilibrium with a sufficiently high discount factor (Shaked 1986). We prove that when the restriction to one-memory strategies is employed in the multiplayer version of the game, the subgame perfect equilibrium is unique and equivalent to the multiplayer generalization of Rubinstein's. This also implies that the unique subgame perfect equilibrium outcome corresponds to the Nash solution in the multiplayer cooperative game

SSGAC Polygenic Scores (PGSs) in the National Longitudinal Study of Adolescent to Adult Health (Add Health)

This document describes the construction of polygenic scores (PGSs) associated with various phenotypes for respondents participating in the National Longitudinal Study of Adolescent to Adult Health (Add Health) by the Social Science Genetic Association Consortium (SSGAC). Research has shown that many outcomes of interest in the health, behavioral, and social sciences are influenced by genetics (Domingue et al. 20161; Plomin et al. 20162; Turkheimer 20003). For most human traits/behaviors, commonly referred to as phenotypes, it appears that the genetic influence on the phenotype is highly polygenic; i.e., there is no single gene that can account for the association between genetic variance and variance in the outcome. Instead, the influence of genetics on most phenotypes appears to be due to many small associations across thousands, and possibly millions, of individual single-nucleotide polymorphisms (SNPs, pronounced snips) (Chabris et al. 20154). Polygenic Scores allow researchers to avoid the methodological complexities of including thousands, or millions, of covariates in their analyses by condensing, into a single measure, the associations between individual SNPs and the phenotype of interest (Plomin, Haworth, and Davis 20095)

Polygenic Index Inventories Documentation

This guide documents the key information regarding the construction and use of polygenic indexes (PGIs) for the National Longitudinal Study of Adolescent to Adult Health (Add Health) as part of the Resource Profile and User Guide of the Polygenic Index Repository. Summary Information About PGIs Polygenic indexes (PGIs) are constructed using the same general approach (described below) and have the same substantive meaning as polygenic scores (PGSs, used more prominently in social science genomics contexts) and genetic risk scores (GRSs, used more prominently in the medical contexts). Here, we provide a brief summary of how the PGIs were constructed (please see the Methods section of Becker et al. for a more detailed description). We refer the reader to the relevant tables of Becker et al. where more information can be found

Meta-GWAS Accuracy and Power (MetaGAP) Calculator Shows that Hiding Heritability Is Partially Due to Imperfect Genetic Correlations across Studies

Large-scale genome-wide association results are typically obtained from a fixed-effects meta-analysis of GWAS summary statistics from multiple studies spanning different regions and/or time periods. This approach averages the estimated effects of genetic variants across studies. In case genetic effects are heterogeneous across studies, the statistical power of a GWAS and the predictive accuracy of polygenic scores are attenuated, contributing to the so-called ‘missing heritability’. Here, we describe the online Meta-GWAS Accuracy and Power (MetaGAP) calculator (available at www.devlaming.eu) which quantifies this attenuation based on a novel multi-study framework. By means of simulation studies, we show that under a wide range of genetic architectures, the statistical power and predictive accuracy provided by this calculator are accurate. We compare the predictions from the MetaGAP calculator with actual results obtained in the GWAS literature. Specifically, we use genomic-relatedness-matrix restricted maximum likelihood to estimate the SNP heritability and cross-study genetic correlation of height, BMI, years of education, and self-rated health in three large samples. These estimates are used as input parameters for the MetaGAP calculator. Results from the calculator suggest that cross-study heterogeneity has led to attenuation of statistical power and predictive accuracy in recent large-scale GWAS efforts on these traits (e.g., for years of education, we estimate a relative loss of 51–62% in the number of genome-wide significant loci and a relative loss in polygenic score R2of 36–38%). Hence, cross-study heterogeneity contributes to the missing heritability

Genomic analysis of diet composition finds novel loci and associations with health and lifestyle

We conducted genome-wide association study (GWAS) meta-analyses of relative caloric intake from fat, protein, carbohydrates and sugar in over 235,000 individuals. We identified 21 approximately independent lead SNPs. Relative protein intake exhibits the strongest relationships with poor health, including positive genetic associations with obesity, type 2 diabetes, and heart disease ( ≈ 0.15 − 0.5). Relative carbohydrate and sugar intake have negative genetic correlations with waist circumference, waist-hip ratio, and neighborhood poverty (|| ≈ 0.1 − 0.3). Overall, our results show that the relative intake of each macronutrient has a distinct genetic architecture and pattern of genetic correlations suggestive of health implications beyond caloric content

Selection against variants in the genome associated with educational attainment

Epidemiological and genetic association studies show that genetics play an important role in the attainment of education. Here, we investigate the effect of this genetic component on the reproductive history of 109,120 Icelanders and the consequent impact on the gene pool over time. We show that an educational attainment polygenic score, POLYEDU, constructed from results of a recent study is associated with delayed reproduction (P < 10-100) and fewer children overall. The effect is stronger for women and remains highly significant after adjusting for educational attainment. Based on 129,808 Icelanders born between 1910 and 1990, we find that the average POLYEDU has been declining at a rate of ∼0.010 standard units per decade, which is substantial on an evolutionary timescale. Most importantly, because POLYEDU only captures a fraction of the overall underlying genetic component the latter could be declining at a rate that is two to three times faster

Social competence in parents increases children’s educational attainment:Replicable genetically-mediated effects of parenting revealed by non-transmitted DNA

We recently reported an association of offspring educational attainment with polygenic risk scores (PRS) computed on parent's non-transmitted alleles for educational attainment using the second GWAS meta-analysis article on educational attainment published by the Social Science Genetic Association Consortium. Here we test the replication of these findings using a more powerful PRS from the third GWAS meta-analysis article by the Consortium. Each of the key findings of our previous paper is replicated using this improved PRS (N = 2335 adolescent twins and their genotyped parents). The association of children's attainment with their own PRS increased substantially with the standardized effect size, moving from β = 0.134, 95% CI = 0.079, 0.188 for EA2, to β = 0.223, 95% CI = 0.169, 0.278, p <.001, for EA3. Parent's PRS again predicted the socioeconomic status (SES) they provided to their offspring and increased from β = 0.201, 95% CI = 0.147, 0.256 to β = 0.286, 95% CI = 0.239, 0.333. Importantly, the PRS for alleles not transmitted to their offspring - therefore acting via the parenting environment - was increased in effect size from β = 0.058, 95% CI = 0.003, 0.114 to β = 0.067, 95% CI = 0.012, 0.122, p =.016. As previously found, this non-transmitted genetic effect was fully accounted for by parental SES. The findings reinforce the conclusion that genetic effects of parenting are substantial, explain approximately one-third the magnitude of an individual's own genetic inheritance and are mediated by parental socioeconomic competence

Polygenic prediction of educational attainment within and between families from genome-wide association analyses in 3 million individuals

We conduct a genome-wide association study (GWAS) of educational attainment (EA) in a sample of ~3 million individuals and identify 3,952 approximately uncorrelated genome-wide-significant single-nucleotide polymorphisms (SNPs). A genome-wide polygenic predictor, or polygenic index (PGI), explains 12–16% of EA variance and contributes to risk prediction for ten diseases. Direct effects (i.e., controlling for parental PGIs) explain roughly half the PGI’s magnitude of association with EA and other phenotypes. The correlation between mate-pair PGIs is far too large to be consistent with phenotypic assortment alone, implying additional assortment on PGI-associated factors. In an additional GWAS of dominance deviations from the additive model, we identify no genome-wide-significant SNPs, and a separate X-chromosome additive GWAS identifies 57