Multiple testing correction in linear mixed models

BACKGROUND: Multiple hypothesis testing is a major issue in genome-wide association studies (GWAS), which often analyze millions of markers. The permutation test is considered to be the gold standard in multiple testing correction as it accurately takes into account the correlation structure of the genome. Recently, the linear mixed model (LMM) has become the standard practice in GWAS, addressing issues of population structure and insufficient power. However, none of the current multiple testing approaches are applicable to LMM. RESULTS: We were able to estimate per-marker thresholds as accurately as the gold standard approach in real and simulated datasets, while reducing the time required from months to hours. We applied our approach to mouse, yeast, and human datasets to demonstrate the accuracy and efficiency of our approach. CONCLUSIONS: We provide an efficient and accurate multiple testing correction approach for linear mixed models. We further provide an intuition about the relationships between per-marker threshold, genetic relatedness, and heritability, based on our observations in real data. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13059-016-0903-6) contains supplementary material, which is available to authorized users

The life and work of Zbyněk Šidák (1933–1999)

summary:Zbyněk Šidák, the chief editor of the Applications of Mathematics, an outstanding Czech statistician and probabilist, died on November 12, 1999, aged 66 years. This article is devoted to memory of him and outlines his life and scientific work

Mating patterns and genetic diversity in the wild Daffodil Narcissus longispathus (Amaryllidaceae)

Despite the importance of Narcissus to ornamental horticulture, there have been no population genetic studies of wild species, many of which have narrow distributions. Here, we measure selfing rates and levels of genetic diversity at allozyme loci in six populations of Narcissus longispathus, a self-compatible daffodil endemic to a few mountain ranges in southeastern Spain. The populations were distributed among four distinct river valleys encompassing two main watersheds in the Sierra de Cazorla mountains. Selfing rates averaged 0.37 (range 0.23–0.46), resulting in significant inbreeding coefficients for the progeny (f=0.324). In contrast, estimates of inbreeding in parental genotypes were not significantly different from zero (f=0.001), indicating that few selfed offspring survive to maturity because of inbreeding depression. Species-wide estimates of genetic diversity for the six populations were Ps=0.38, Hes=0.119 and As=1.27 with significant genetic differentiation among populations theta=0.15. The observed patterns of genetic differentiation among populations are likely influenced by the mating system, and a combination of local topography, watershed affinities and gene flow.Peer reviewe