SummaryNorway spruce is a boreal forest tree species of significant ecological and economic importance. Hence there is a strong imperative to dissect the genetics underlying important wood quality traits in the species. We performed a functional genome‐wide association study (GWAS) of 17 wood traits in Norway spruce using 178 101 single nucleotide polymorphisms (SNPs) generated from exome genotyping of 517 mother trees. The wood traits were defined using functional modelling of wood properties across annual growth rings. We applied a Least Absolute Shrinkage and Selection Operator (LASSO‐based) association mapping method using a functional multilocus mapping approach that utilizes latent traits, with a stability selection probability method as the hypothesis testing approach to determine a significant quantitative trait locus. The analysis provided 52 significant SNPs from 39 candidate genes, including genes previously implicated in wood formation and tree growth in spruce and other species. Our study represents a multilocus GWAS for complex wood traits in Norway spruce. The results advance our understanding of the genetics influencing wood traits and identifies candidate genes for future functional studies.

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We introduce a Bayesian method for estimating hidden population substructure using multilocus molecular markers and geographical information provided by the sampling design. The joint posterior distribution of the substructure and allele frequencies of the respective populations is available in an analytical form when the number of populations is small, whereas an approximation based on a Markov chain Monte Carlo simulation approach can be obtained for a moderate or large number of populations. Using the joint posterior distribution, posteriors can also be derived for any evolutionary population parameters, such as the traditional fixation indices. A major advantage compared to most earlier methods is that the number of populations is treated here as an unknown parameter. What is traditionally considered as two genetically distinct populations, either recently founded or connected by considerable gene flow, is here considered as one panmictic population with a certain probability based on marker data and prior information. Analyses of previously published data on the Moroccan argan tree (Argania spinosa) and of simulated data sets suggest that our method is capable of estimating a population substructure, while not artificially enforcing a substructure when it does not exist. The software (BAPS) used for the computations is freely available from http://www.rni.helsinki.fi/~mjs.

Twin studies have been adopted for decades to disentangle the relative genetic and environmental contributions for a wide range of traits. However, heritability estimation based on the classical twin models does not take into account dynamic behavior of the variance components over age. Varying variance of the genetic component over age can imply the existence of geneenvironment (G 3 E) interactions that general genome-wide association studies (GWAS) fail to capture, which may lead to the inconsistency of heritability estimates between twin design and GWAS. Existing parametric G 3 E interaction models for twin studies are limited by assuming a linear or quadratic form of the variance curves with respect to a moderator that can, however, be overly restricted in reality. Here we propose spline-based approaches to explore the variance curves of the genetic and environmental components. We choose the additive genetic, common, and unique environmental variance components (ACE) model as the starting point. We treat the component variances as variance functions with respect to age modeled by B-splines or P-splines. We develop an empirical Bayes method to estimate the variance curves together with their confidence bands and provide an R package for public use. Our simulations demonstrate that the proposed methods accurately capture dynamic behavior of the component variances in terms of mean square errors with a data set of .10,000 twin pairs. Using the proposed methods as an alternative and major extension to the classical twin models, our analyses with a large-scale Finnish twin data set (19,510 MZ twins and 27,312 DZ same-sex twins) discover that the variances of the A, C, and E components for body mass index (BMI) change substantially across life span in different patterns and the heritability of BMI drops to $50% after middle age. The results further indicate that the decline of heritability is due to increasing unique environmental variance, which provides more insights into age-specific heritability of BMI and evidence of G 3 E interactions. These findings highlight the fundamental importance and implication of the proposed models in facilitating twin studies to investigate the heritability specific to age and other modifying factors.KEYWORDS twin models; penalized B-splines; age-specific heritability; empirical Bayes predictor; body mass index T WIN studies have been broadly used as a tool to investigate heritability for decades. A recent comprehensive meta-analysis reported 17,804 heritability estimates for various traits based on twin studies (Polderman et al. 2015).Estimation methods and software such as structural equation modeling (SEM) based on the classical twin models consisting of additive genetic, common, and unshared environmental effects have been well established and extensively adopted (Rijsdijk and Sham 2002). Extensions for longitudinal data or time-to-event phenotypes based on the classical twin models have been proposed (Boomsma et al. 1989;Pitkäniemi et al. 2007). Nevertheless, one of...