Figure 1.

Rationale for the proposed test of association. (a) A graphical model describing population structure and its effects on a trait of interest. Population structure is captured by a common latent variable z among a set of loci x_i (i =1,2, …, m), via the allele frequencies π_i(z). When one locus has a causal effect on the trait, this induces spurious associations with other loci affected by population structure. At the same time, population structure may be correlated with lifestyle and environment as these are all possibly related to ancestry and geography. (b) Accounting for confounding due to latent population structure. Left panel: A test for association between the i^th SNP x_i and trait y without taking into account z will produce a spurious association due to the fact that both x_i and y are confounded with z. Right panel: A test for association between x_i|π_i(z) and y will be an unbiased because conditioning on π_i(z) breaks the relationship between z and x_i.