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Recent studies have examined the genetic correlations of single-nucleotide polymorphism (SNP) effect sizes across pairs of populations to better understand the genetic architectures of complex traits. These studies have estimated ρ g , the cross-population correlation of joint-fit effect sizes at genotyped SNPs. However, the value of ρ g depends both on the cross-population correlation of true causal effect sizes ( ρ b ) and on the similarity in linkage disequilibrium (LD) patterns in the two populations, which drive tagging effects. Here, we derive the value of the ratio ρ g / ρ b as a function of LD in each population. By applying existing methods to obtain estimates of ρ g , we can use this ratio to estimate ρ b . Our estimates of ρ b were equal to 0.55 ( SE = 0.14) between Europeans and East Asians averaged across nine traits in the Genetic Epidemiology Research on Adult Health and Aging data set, 0.54 ( SE = 0.18) between Europeans and South Asians averaged across 13 traits in the UK Biobank data set, and 0.48 ( SE = 0.06) and 0.65 ( SE = 0.09) between Europeans and East Asians in summary statistic data sets for type 2 diabetes and rheumatoid arthritis, respectively. These results implicate substantially different causal genetic architectures across continental populations.

We present a recursive construction of a 2t + 1-wise uniform set of permutations on 2n objects using a 2t+1-2n,n,i¾? combinatorial design, a t-wise uniform set of permutations on n objects and a 2t + 1-wise uniform set of permutations on n objects. Using the complete design in this procedure gives a t-wise uniform set of permutations on n objects whose size is at most t2n, the first non-trivial construction of an infinite family of t-wise uniform sets for ti¾?4. If a non-trivial design with suitable parameters is found, it will imply a corresponding improvement in the construction. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 531-540, 2015