Defects in crystalline solids control the properties of engineered and natural materials, and their characterization focuses our strategies to optimize performance. Electron microscopy has served as the backbone of our understanding of defect structure and their interactions, owing to beneficial spatial resolution and contrast mechanisms that enable direct imaging of defects. These defects reside in complex microstructures and chemical environments, demanding a combination of experimental approaches for full defect characterization. In this article, we describe recent progress and trends in methods for examining defects using scanning electron microscopy platforms. Several emerging approaches offer attractive benefits, for instance, in correlative microscopy across length scales and in in situ studies of defect dynamics.

The continuous uploading of polygenic additive mutational variability has been reported in several studies in laboratory species with an inbred genetic background. These studies have focused on the direct contribution of new mutations without considering the possibility of epistatic effects derived from the interaction of new mutations with pre-existing polymorphisms. In this work we focused on this main topic and analysed the statistical and biological relevance of the epistatic variance for 9 week body weight in two populations of inbred mice. We developed a new linear mixed model parameterization where founder-related additive genetic variability, additive mutational variability and the interaction terms between both sources of variation were accounted for under a Bayesian design and without requiring the inversion of a matrix of epistatic genetic covariances. The analyses focused on a six-generations data set from C57BL/6J mice (n = 3736) and a five-generations data set from C57BL/6Jhg/hg mice (n = 2843). The deviance information criterion (DIC) clearly favoured the model accounting for epistatic variability with reductions larger than 50 DIC units in both populations. Modal estimates for founder related, mutational and epistatic heritabilities were 0·068, 0·011 and 0·095 in C57BL/6J and 0·060, 0·010 and 0·113 in C57BL/6Jhg/hg , ruling out any doubt about the biological relevance of epistasis originating from new mutations in mice. These results contribute new insights on the relevance of epistasis in the genetic architecture of mammals and serve as an important component of an additional source of genetic heterogeneity for inbred strains of laboratory mice.

Imputation of moderate-density genotypes from low-density panels is of increasing interest in genomic selection, because it can dramatically reduce genotyping costs. Several imputation software packages have been developed, but they vary in imputation accuracy, and imputed genotypes may be inconsistent among methods. An AdaBoost-like approach is proposed to combine imputation results from several independent software packages, i.e. Beagle(v3.3), IMPUTE(v2.0), fastPHASE(v1.4), AlphaImpute, findhap(v2) and Fimpute(v2), with each package serving as a basic classifier in an ensemble-based system. The ensemble-based method computes weights sequentially for all classifiers, and combines results from component methods via weighted majority ‘voting’ to determine unknown genotypes. The data included 3078 registered Angus cattle, each genotyped with the Illumina BovineSNP50 BeadChip. SNP genotypes on three chromosomes (BTA1, BTA16 and BTA28) were used to compare imputation accuracy among methods, and the application involved the imputation of 50K genotypes covering 29 chromosomes based on a set of 5K genotypes. Beagle and Fimpute had the greatest accuracy among the six imputation packages, which ranged from 0·8677 to 0·9858. The proposed ensemble method was better than any of these packages, but the sequence of independent classifiers in the voting scheme affected imputation accuracy. The ensemble systems yielding the best imputation accuracies were those that had Beagle as first classifier, followed by one or two methods that utilized pedigree information. A salient feature of the proposed ensemble method is that it can solve imputation inconsistencies among different imputation methods, hence leading to a more reliable system for imputing genotypes relative to independent methods.

Bayesian regularization of artificial neural networks (BRANNs) were used to predict body mass index (BMI) in mice using single nucleotide polymorphism (SNP) markers. Data from 1896 animals with both phenotypic and genotypic (12 320 loci) information were used for the analysis. Missing genotypes were imputed based on estimated allelic frequencies, with no attempt to reconstruct haplotypes based on family information or linkage disequilibrium between markers. A feed-forward multilayer perceptron network consisting of a single output layer and one hidden layer was used. Training of the neural network was done using the Bayesian regularized backpropagation algorithm. When the number of neurons in the hidden layer was increased, the number of effective parameters, γ, increased up to a point and stabilized thereafter. A model with five neurons in the hidden layer produced a value of γ that saturated the data. In terms of predictive ability, a network with five neurons in the hidden layer attained the smallest error and highest correlation in the test data although differences among networks were negligible. Using inherent weight information of BRANN with different number of neurons in the hidden layer, it was observed that 17 SNPs had a larger impact on the network, indicating their possible relevance in prediction of BMI. It is concluded that BRANN may be at least as useful as other methods for high-dimensional genome-enabled prediction, with the advantage of its potential ability of capturing non-linear relationships, which may be useful in the study of quantitative traits under complex gene action.

Prediction of genetic values is a central problem in quantitative genetics. Over many decades, such predictions have been successfully accomplished using information on phenotypic records and family structure usually represented with a pedigree. Dense molecular markers are now available in the genome of humans, plants and animals, and this information can be used to enhance the prediction of genetic values. However, the incorporation of dense molecular marker data into models poses many statistical and computational challenges, such as how models can cope with the genetic complexity of multi-factorial traits and with the curse of dimensionality that arises when the number of markers exceeds the number of data points. Reproducing kernel Hilbert spaces regressions can be used to address some of these challenges. The methodology allows regressions on almost any type of prediction sets (covariates, graphs, strings, images, etc.) and has important computational advantages relative to many parametric approaches. Moreover, some parametric models appear as special cases. This article provides an overview of the methodology, a discussion of the problem of kernel choice with a focus on genetic applications, algorithms for kernel selection and an assessment of the proposed methods using a collection of 599 wheat lines evaluated for grain yield in four mega environments.

A challenge when predicting total genetic values for complex quantitative traits is that an unknown number of quantitative trait loci may affect phenotypes via cryptic interactions. If markers are available, assuming that their effects on phenotypes are additive may lead to poor predictive ability. Non-parametric radial basis function (RBF) regression, which does not assume a particular form of the genotype–phenotype relationship, was investigated here by simulation and analysis of body weight and food conversion rate data in broilers. The simulation included a toy example in which an arbitrary non-linear genotype–phenotype relationship was assumed, and five different scenarios representing different broad sense heritability levels (0·1, 0·25, 0·5, 0·75 and 0·9) were created. In addition, a whole genome simulation was carried out, in which three different gene action modes (pure additive, additive+dominance and pure epistasis) were considered. In all analyses, a training set was used to fit the model and a testing set was used to evaluate predictive performance. The latter was measured by correlation and predictive mean-squared error (PMSE) on the testing data. For comparison, a linear additive model known as Bayes A was used as benchmark. Two RBF models with single nucleotide polymorphism (SNP)-specific (RBF I) and common (RBF II) weights were examined. Results indicated that, in the presence of complex genotype–phenotype relationships (i.e. non-linearity and non-additivity), RBF outperformed Bayes A in predicting total genetic values using SNP markers. Extension of Bayes A to include all additive, dominance and epistatic effects could improve its prediction accuracy. RBF I was generally better than RBF II, and was able to identify relevant SNPs in the toy example.

The L2-Boosting algorithm is one of the most promising machine-learning techniques that has appeared in recent decades. It may be applied to high-dimensional problems such as whole-genome studies, and it is relatively simple from a computational point of view. In this study, we used this algorithm in a genomic selection context to make predictions of yet to be observed outcomes. Two data sets were used: (1) productive lifetime predicted transmitting abilities from 4702 Holstein sires genotyped for 32 611 single nucleotide polymorphisms (SNPs) derived from the Illumina® BovineSNP50 BeadChip, and (2) progeny averages of food conversion rate, pre-corrected by environmental and mate effects, in 394 broilers genotyped for 3481 SNPs. Each of these data sets was split into training and testing sets, the latter comprising dairy or broiler sires whose ancestors were in the training set. Two weak learners, ordinary least squares (OLS) and non-parametric (NP) regression were used for the L2-Boosting algorithm, to provide a stringent evaluation of the procedure. This algorithm was compared with BL [Bayesian LASSO (least absolute shrinkage and selection operator)] and BayesA regression. Learning tasks were carried out in the training set, whereas validation of the models was performed in the testing set. Pearson correlations between predicted and observed responses in the dairy cattle (broiler) data set were 0·65 (0·33), 0·53 (0·37), 0·66 (0·26) and 0·63 (0·27) for OLS-Boosting, NP-Boosting, BL and BayesA, respectively. The smallest bias and mean-squared errors (MSEs) were obtained with OLS-Boosting in both the dairy cattle (0·08 and 1·08, respectively) and broiler (−0·011 and 0·006) data sets, respectively. In the dairy cattle data set, the BL was more accurate (bias=0·10 and MSE=1·10) than BayesA (bias=1·26 and MSE=2·81), whereas no differences between these two methods were found in the broiler data set. L2-Boosting with a suitable learner was found to be a competitive alternative for genomic selection applications, providing high accuracy and low bias in genomic-assisted evaluations with a relatively short computational time.

A two-step procedure is presented for analysis of θ (FST) statistics obtained for a battery of loci, which eventually leads to a clustered structure of values. The first step uses a simple Bayesian model for drawing samples from posterior distributions of θ-parameters, but without constructing Markov chains. This step assigns a weakly informative prior to allelic frequencies and does not make any assumptions about evolutionary models. The second step regards samples from these posterior distributions as ‘data’ and fits a sequence of finite mixture models, with the aim of identifying clusters of θ-statistics. Hopefully, these would reflect different types of processes and would assist in interpreting results. Procedures are illustrated with hypothetical data, and with published allelic frequency data for type II diabetes in three human populations, and for 12 isozyme loci in 12 populations of the argan tree in Morocco.

Inferences about genetic values and prediction of phenotypes for a quantitative trait in the presence of complex forms of gene action, issues of importance in animal and plant breeding, and in evolutionary quantitative genetics, are discussed. Current methods for dealing with epistatic variability via variance component models are reviewed. Problems posed by cryptic, non-linear, forms of epistasis are identified and discussed. Alternative statistical procedures are suggested. Non-parametric definitions of additive effects (breeding values), with and without employing molecular information, are proposed, and it is shown how these can be inferred using reproducing kernel Hilbert spaces regression. Two stylized examples are presented to demonstrate the methods numerically. The first example falls in the domain of the infinitesimal model of quantitative genetics, with additive and dominance effects inferred both parametrically and non-parametrically. The second example tackles a non-linear genetic system with two loci, and the predictive ability of several models is evaluated.

This study is aimed at improving the analysis of data used in identifying marker-associated effects on quantitative traits, specifically to account for possible departures from a Gaussian distribution of the trait data and to allow for asymmetry of marker effects attributable to phenotypic divergence between parental lines. A Bayesian procedure for analysing marker effects at the whole-genome level is presented. The procedure adopts a skewed t-distribution as a prior distribution of marker effects. The model with the skewed t-process includes Gaussian prior distributions, skewed Gaussian prior distributions and symmetric t-distributions as special cases. A Markov Chain Monte Carlo algorithm for obtaining marginal posterior distributions of the unknowns is also presented. The method was applied to a dataset on three traits (live weight, carcass length and backfat depth) measured in an F2 cross between Iberian and Landrace pigs. The distribution of marker effects was clearly asymmetric for carcass length and backfat depth, whereas it was symmetric for live weight. The t-distribution seems more appropriate for describing the distribution of marker effects on backfat depth.