The mixed linear model has been widely used in genome-wide association studies (GWAS), but its application to multi-locus GWAS analysis has not been explored and assessed. Here, we implemented a fast multi-locus random-SNP-effect EMMA (FASTmrEMMA) model for GWAS. The model is built on random single nucleotide polymorphism (SNP) effects and a new algorithm. This algorithm whitens the covariance matrix of the polygenic matrix K and environmental noise, and specifies the number of nonzero eigenvalues as one. The model first chooses all putative quantitative trait nucleotides (QTNs) with ≤ 0.005 P-values and then includes them in a multi-locus model for true QTN detection. Owing to the multi-locus feature, the Bonferroni correction is replaced by a less stringent selection criterion. Results from analyses of both simulated and real data showed that FASTmrEMMA is more powerful in QTN detection and model fit, has less bias in QTN effect estimation and requires a less running time than existing single- and multi-locus methods, such as empirical Bayes, settlement of mixed linear model under progressively exclusive relationship (SUPER), efficient mixed model association (EMMA), compressed MLM (CMLM) and enriched CMLM (ECMLM). FASTmrEMMA provides an alternative for multi-locus GWAS.

Unlike a character measured at a finite set of landmark points, function-valued traits are those that change as a function of some independent and continuous variable. These traits, also called infinite-dimensional characters, can be described as the character process and include a number of biologically, economically, or biomedically important features, such as growth trajectories, allometric scalings, and norms of reaction. Here we present a new statistical infrastructure for mapping quantitative trait loci (QTL) underlying the character process. This strategy, termed functional mapping, integrates mathematical relationships of different traits or variables within the genetic mapping framework. Logistic mapping proposed in this article can be viewed as an example of functional mapping. Logistic mapping is based on a universal biological law that for each and every living organism growth over time follows an exponential growth curve (e.g., logistic or S-shaped). A maximum-likelihood approach based on a logistic-mixture model, implemented with the EM algorithm, is developed to provide the estimates of QTL positions, QTL effects, and other model parameters responsible for growth trajectories. Logistic mapping displays a tremendous potential to increase the power of QTL detection, the precision of parameter estimation, and the resolution of QTL localization due to the small number of parameters to be estimated, the pleiotropic effect of a QTL on growth, and/or residual correlations of growth at different ages. More importantly, logistic mapping allows for testing numerous biologically important hypotheses concerning the genetic basis of quantitative variation, thus gaining an insight into the critical role of development in shaping plant and animal evolution and domestication. The power of logistic mapping is demonstrated by an example of a forest tree, in which one QTL affecting stem growth processes is detected on a linkage group using our method, whereas it cannot be detected using current methods. The advantages of functional mapping are also discussed.

This article is concerned with feature screening and variable selection for varying coefficient models with ultrahigh-dimensional covariates. We propose a new feature screening procedure for these models based on conditional correlation coefficient. We systematically study the theoretical properties of the proposed procedure, and establish their sure screening property and the ranking consistency. To enhance the finite sample performance of the proposed procedure, we further develop an iterative feature screening procedure. Monte Carlo simulation studies were conducted to examine the performance of the proposed procedures. In practice, we advocate a two-stage approach for varying coefficient models. The two-stage approach consists of (a) reducing the ultrahigh dimensionality by using the proposed procedure and (b) applying regularization methods for dimension-reduced varying coefficient models to make statistical inferences on the coefficient functions. We illustrate the proposed two-stage approach by a real data example. Supplementary materials for this article are available online.

Summary: Grafting has been widely used to improve horticultural traits. It has also served increasingly as a tool to investigate the long‐distance transport of molecules that is an essential part for key biological processes. Many studies have revealed the molecular mechanisms of graft‐induced phenotypic variation in anatomy, morphology and production. Here, we review the phenomena and their underlying mechanisms by which macromolecules, including RNA, protein, and even DNA, are transported between scions and rootstocks via vascular tissues. We further propose a conceptual framework that characterizes and quantifies the driving mechanisms of scion–rootstock interactions toward vascular reconnection and regeneration.