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Mixed models can correct for population structure for genomic regions under selection

Nature Reviews Genetics volume 14, page 300 (2013)Cite this article

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An article in this journal by Price et al. (New approaches to population stratification in genome-wide association studies. Nature Reviews Genetics 11, 459–463 (2010))1 showed by simulations that mixed models2 may be susceptible to spurious associations on markers with unusual allele frequency differences between populations, such as markers in regions under selection. They stated that the reason for the spurious associations or inflation of test statistics is because mixed models model population structure as a random effect, although it is a fixed effect.

After investigating this problem further, we found that modelling population structure as a random effect is not the cause of inflation and that it is a kinship matrix that determines the performance of mixed models. The kinship matrix defines pairwise genetic relatedness among individuals and is usually estimated by using all genotyped markers. Because most markers in the simulations carried out by Price et al.1 have small allele frequency differences between two populations, a kinship matrix estimated from all markers does not effectively capture the population structure. However, when a kinship matrix is computed from the first principal component or from only the unusually differentiated markers (UDMs), we find that mixed models achieve almost the same performance as EIGENSTRAT3, which is a method that incorporates population structure as a fixed effect (Table 1). A kinship matrix that captures the same information as the first principal component vector can be obtained by computing the outer product of the vector: wwT, where w is the first principal component vector. Use of this matrix in mixed models is closely related to including the first principal component as a covariate in EIGENSTRAT. As for the kinship matrix generated from UDMs, because UDMs are not known in advance, one may try to detect these using methods to identify markers under selection, one of which was developed by our group. This method, which is called spatial ancestry analysis (SPA)4, correctly identifies UDMs in the simulations, and mixed models with kinship estimated from those markers detected by SPA have almost the same inflation as kinship from the true UDMs.

Table 1 Genomic control inflation factor of mixed models with various kinship matrices
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References

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Acknowledgements

J.H.S. and E.E. are supported by US National Science Foundation grants 0513612, 0731455, 0729049, 0916676 and 1065276, and US National Institutes of Health grants K25-HL080079, U01-DA024417, P01-HL30568 and P01-HL28481.

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  1. Jae Hoon Sul is at the Computer Science Department, University of California, Los Angeles, California 90095, USA.,

    Jae Hoon Sul

  2. Eleazar Eskin is at the Department of Human Genetics, University of California, Los Angeles, California 90095, USA.,

    Eleazar Eskin

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  1. Jae Hoon Sul
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  2. Eleazar Eskin
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Correspondence to Eleazar Eskin.

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Sul, J., Eskin, E. Mixed models can correct for population structure for genomic regions under selection. Nat Rev Genet 14, 300 (2013). https://doi.org/10.1038/nrg2813-c1

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