Stochastic Lanczos estimation of genomic variance components for linear mixed-effects models

BackgroundLinear mixed-effects models (LMM) are a leading method in conducting genome-wide association studies (GWAS) but require residual maximum likelihood (REML) estimation of variance components, which is computationally demanding. Previous work has reduced the computational burden of variance component estimation by replacing direct matrix operations with iterative and stochastic methods and by employing loose tolerances to limit the number of iterations in the REML optimization procedure. Here, we introduce two novel algorithms,stochastic Lanczos derivative-free REML(SLDF_REML) andLanczos first-order Monte Carlo REML(L_FOMC_REML), that exploit problem structure via the principle of Krylov subspace shift-invariance to speed computation beyond existing methods. Both novel algorithms only require a single round of computation involving iterative matrix operations, after which their respective objectives can be repeatedly evaluated using vector operations. Further, in contrast to existing stochastic methods,SLDF_REMLcan exploit precomputed genomic relatedness matrices (GRMs), when available, to further speed computation.ResultsResults of numerical experiments are congruent with theory and demonstrate that interpreted-language implementations of both algorithms match or exceed existing compiled-language software packages in speed, accuracy, and flexibility.ConclusionsBoth theSLDF_REMLandL_FOMC_REMLalgorithms outperform existing methods for REML estimation of variance components for LMM and are suitable for incorporation into existing GWAS LMM software implementations.Full list of author information is available at the end of the article

About the heritability influence to the growth performance in Scots pine (Pinus sylvestris L.) progeny trials

Pärilikkuse mõjust hariliku männi (Pinus sylvestrisL.) kasvuomadustele järglaskatsetesThe progeny trials of the Scots pine founded in Järvselja Training and Experimental Forest District in 1966 and 1967 by E. Pihelgas were analysed to estimate the heritability of height and diameter characteristics, and also the dependence of progeny properties on the plus tree and single tree phenotype. The data set consists of 513 height and 3707 breast height diameter measurements of 39-and 40-years-old progenies of 40 mother trees. The analysis was carried out with the SAS package, Release 9.1, mainly with ANOVA tools implemented SAS/MIXED procedure. Heritability h2was calculated from the mother tree and residual variance components assuming a limited number of father trees for each progeny. Using the REML estimation procedures, the heritability of the stem height was found approximately equal to 1 and it was 0.19 for the DBH. Considering the mother tree characteristics, the age was significantly correlated with the progeny height.