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Background The genetic basis of phenotypic traits is highly variable and usually divided into mono-, oligo- and polygenic inheritance classes. Relatively few traits are known to be monogenic or oligogeneic. The majority of traits are considered to have a polygenic background. To what extent there are mixtures between these classes is unknown. The rapid advancement of genomic techniques makes it possible to directly map large amounts of genomic markers (GWAS) and predict unknown phenotypes (GWP). Most of the multi-marker methods for GWAS and GWP falls into one of two regularization frameworks. The first framework is based on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document}ℓ1-norm regularization (e.g. the LASSO) and is suitable for mono- and oligogenic traits, whereas the second framework regularize with the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _2$$\end{document}ℓ2-norm (e.g. ridge regression; RR) and thereby is favourable for polygenic traits. A general framework for mixed inheritance is lacking. Results We have developed a proximal operator algorithm based on the recent LAVA regularization method that jointly performs \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document}ℓ1- and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _2$$\end{document}ℓ2-norm regularization. The algorithm is built on the alternating direction method of multipliers and proximal translation mapping (LAVA ADMM). When evaluated on the simulated QTLMAS2010 data, it is shown that the LAVA ADMM together with Bayesian optimization of the regularization parameters provides an efficient approach with lower test prediction mean-squared-error (65.89) than the LASSO (66.11), Ridge regression (83.41) and Elastic net (66.11). For the real pig data the test MSE of the LAVA ADMM is 0.850 compared to the LASSO, RR and EN with 0.875, 0.853 and 0.853, respectively. Conclusions This study presents the LAVA ADMM that is capable of joint modelling of monogenic major genetic effects and polygenic minor genetic effects which can be used for both genome-wide assoiciation and prediction purposes. The statistical evaluations based on both simulated and real pig data set shows that the LAVA ADMM has better prediction properies than the LASSO, RR and EN. Julia code for the LAVA ADMM is available at: https://github.com/patwa67/LAVAADMM. Supplementary Information The online version contains supplementary material available at 10.1186/s12859-021-04436-6.

Genome-wide prediction (GWP) has become the state-of-the art method in artificial selection. Data sets often comprise number of genomic markers and individuals in ranges from a few thousands to millions. Hence, computational efficiency is important and various machine learning methods have successfully been used in GWP. Neural networks (NN) and deep learning (DL) are very flexible methods that usually show outstanding prediction properties on complex structured data, but their use in GWP is nevertheless rare and debated. This study describes a powerful NN method for genomic marker data that can easily be extended. It is shown that a one-dimensional convolutional neural network (CNN) can be used to incorporate the ordinal information between markers and, together with pooling and l (1)-norm regularization, provides a sparse and computationally efficient approach for GWP. The method, denoted CNNGWP, is implemented in the deep learning software Keras, and hyper-parameters of the NN are tuned with Bayesian optimization. Model averaged ensemble predictions further reduce prediction error. Evaluations show that CNNGWP improves prediction error by more than 25% on simulated data and around 3% on real pig data compared with results obtained with GBLUP and the LASSO. In conclusion, the CNNGWP provides a promising approach for GWP, but the magnitude of improvement depends on the genetic architecture and the heritability.

Longevity is regarded as the most important functional trait in cattle breeding with high economic value yet low heritability. In order to identify genomic regions associated with longevity, a genome wise association study was performed using data from 4887 Fleckvieh bulls and 33,556 SNPs after quality control. Single SNP regression was used for identification of important SNPs including eigenvectors as a means of correction for population structure. SNPs selected with a false discovery rate threshold of 0.05 and with local false discovery rate identified genomic regions associated with longevity which were subsequently cross checked with the National Center for Biotechnology Information (NCBI) database. This, to identify interesting genes in cattle and their homologue forms in other species. The most notable genes were SYT10 located on chromosome 5, ADAMTS3 on chromosome 6, NTRK2 on chromosome 8 and SNTG1 on chromosome 14 of the cattle genome. Several of the genes found have previously been associated with cattle fertility. Poor fertility is an important culling reason and thereby affects longevity in cattle. Several signals were located in regions sparse with described genes, which suggest that there might be several other non-identified genetic pathways for this important trait.

Associations between heterozygosity and fitness traits have typically been investigated in populations characterized by low levels of inbreeding. We investigated the associations between standardized multilocus heterozygosity (stMLH) in mother trees (obtained from12 nuclear microsatellite markers) and five fitness traits measured in progenies from an inbred Scots pine population. The traits studied were proportion of sound seed, mean seed weight, germination rate, mean family height of one-year old seedlings under greenhouse conditions (GH) and mean family height of three-year old seedlings under field conditions (FH). The relatively high average inbreeding coefficient (F) in the population under study corresponds to a mixture of trees with different levels of co-ancestry, potentially resulting from a recent bottleneck. We used both frequentist and Bayesian methods of polynomial regression to investigate the presence of linear and non-linear relations between stMLH and each of the fitness traits. No significant associations were found for any of the traits except for GH, which displayed negative linear effect with stMLH. Negative HFC for GH could potentially be explained by the effect of heterosis caused by mating of two inbred mother trees (Lippman and Zamir 2006), or outbreeding depression at the most heterozygote trees and its negative impact on the fitness of the progeny, while their simultaneous action is also possible (Lynch. 1991). However,since this effect wasn't detected for FH, we cannot either rule out that the greenhouse conditions introduce artificial effects that disappear under more realistic field conditions.

Background The goal of genome-wide prediction (GWP) is to predict phenotypes based on marker genotypes, often obtained through single nucleotide polymorphism (SNP) chips. The major problem with GWP is high-dimensional data from many thousands of SNPs scored on several thousands of individuals. A large number of methods have been developed for GWP, which are mostly parametric methods that assume statistical linearity and only additive genetic effects. The Bayesian additive regression trees (BART) method was recently proposed and is based on the sum of nonparametric regression trees with the priors being used to regularize the parameters. Each regression tree is based on a recursive binary partitioning of the predictor space that approximates an unknown function, which will automatically model nonlinearities within SNPs (dominance) and interactions between SNPs (epistasis). In this study, we introduced BART and compared its predictive performance with that of the LASSO, Bayesian LASSO (BLASSO), genomic best linear unbiased prediction (GBLUP), reproducing kernel Hilbert space (RKHS) regression and random forest (RF) methods. Results Tests on the QTLMAS2010 simulated data, which are mainly based on additive genetic effects, show that cross-validated optimization of BART provides a smaller prediction error than the RF, BLASSO, GBLUP and RKHS methods, and is almost as accurate as the LASSO method. If dominance and epistasis effects are added to the QTLMAS2010 data, the accuracy of BART relative to the other methods was increased. We also showed that BART can produce importance measures on the SNPs through variable inclusion proportions. In evaluations using real data on pigs, the prediction error was smaller with BART than with the other methods. Conclusions BART was shown to be an accurate method for GWP, in which the regression trees guarantee a very sparse representation of additive and complex non-additive genetic effects. Moreover, the Markov chain Monte Carlo algorithm with Bayesian back-fitting provides a computationally efficient procedure that is suitable for high-dimensional genomic data. Electronic supplementary material The online version of this article (doi:10.1186/s12711-016-0219-8) contains supplementary material, which is available to authorized users.

Polluted soils promote rapid plant adaptation to high concentrations of trace metal elements. Biscutella laevigata is a little investigated pseudometallophyte that appears promising to study these evolutionary processes and advance understanding beyond existing model species, but its metal tolerance is insufficiently understood. We determined the zinc tolerance level and various plant responses to environmentally relevant zinc concentrations in ten metallicolous and non-metallicolous B. laevigata populations from southern Poland. In a two-phase hydroponic experiment, we scored multiple morphological and physiological traits (e.g. biomass, visible stress symptoms, element content in foliage) and assessed phenotypic variability within plant families. The structure of these quantitative traits was compared to that of neutral molecular markers to test, whether natural selection caused population differentiation in zinc tolerance. While zinc tolerance was species-wide (i.e . enhanced in all genotypes compared to a zinc sensitive reference species), we found congruent trends toward higher tolerance in metallicolous compared to non-metallicolous plants. The most indicative parameters for these differences were dry shoot biomass, dry root biomass, and particularly effective photosystem II yield. We found that enhanced zinc tolerance in metallicolous populations is driven by divergent selection in response to metal contamination. In addition, analyses of genotype x environment interaction indicated that this differentiation is heritable. These findings promote diploid accessions of B. laevigata as zinc tolerant but non-hyperaccumulating organisms to study plant adaptation to contaminated environments. Remarkably, tolerance differences between edaphic types emerged already at an environmentally relevant zinc concentration of 150 μM. This opens an unusual perspective on plant adaptation that should be tested in other non-hyperaccumulating species.

It is widely recognized that the mixed linear model is an important tool for parameter estimation in the analysis of complex pedigrees, which includes both pedigree and genomic information, and where mutually dependent genetic factors are often assumed to follow multivariate normal distributions of high dimension. We have developed a Bayesian statistical method based on the decomposition of the multivariate normal prior distribution into products of conditional univariate distributions. This procedure permits computationally demanding genetic evaluations of complex pedigrees, within the user-friendly computer package WinBUGS. To demonstrate and evaluate the flexibility of the method, we analyzed two example pedigrees: a large noninbred pedigree of Scots pine (Pinus sylvestris L.) that includes additive and dominance polygenic relationships and a simulated pedigree where genomic relationships have been calculated on the basis of a dense marker map. The analysis showed that our method was fast and provided accurate estimates and that it should therefore be a helpful tool for estimating genetic parameters of complex pedigrees quickly and reliably.

This article expands upon recent interest in Bayesian hierarchical models in quantitative genetics by developing spatial process models for inference on additive and dominance genetic variance within the context of large spatially referenced trial datasets of multiple traits of interest. Direct application of such multivariate models to large spatial datasets is often computationally infeasible because of cubic order matrix algorithms involved in estimation. The situation is even worse in Markov chain Monte Carlo (MCMC) contexts where such computations are performed for several thousand iterations. Here, we discuss approaches that help obviate these hurdles without sacrificing the richness in modeling. For genetic effects, we demonstrate how an initial spectral decomposition of the relationship matrices negates the expensive matrix inversions required in previously proposed MCMC methods. For spatial effects we discuss a multivariate predictive process that reduces the computational burden by projecting the original process onto a subspace generated by realizations of the original process at a specified set of locations (or knots). We illustrate the proposed methods using a synthetic dataset with multivariate additive and dominant genetic effects and anisotropic spatial residuals, and a large dataset from a scots pine (Pinus sylvestris L.) progeny study conducted in northern Sweden. Our approaches enable us to provide a comprehensive analysis of this large trial which amply demonstrates that, in addition to violating basic assumptions of the linear model, ignoring spatial effects can result in downwardly biased measures of heritability.

Development of selection methods that optimises selection differential subject to a constraint on the increase of inbreeding (or coancestry) in a population is an important part of breeding programmes. One such method that has received much attention in animal breeding is the optimum contribution (OC) dynamic selection method. We implemented the OC algorithm and applied it to a diallel progeny trial of Pinus sylvestris L. (Scots pine) focussing on two traits (total tree height and stem diameter). The OC method resulted in a higher increase in genetic gain (8-30%) compared to the genetic gain achieved using standard restricted selection method at the same level of coancestry constraint. Genetic merit obtained at two different levels of restriction on coancestry showed that the benefit of OC was highest when restriction was strict. At the same level of genetic merit, OC decreased coancestry with 56 and 39% for diameter and height, respectively, compared to the level of coancestry obtained using unrestricted truncation selection. Inclusion of a dominance term in the statistical model resulted in changes in contribution rank of trees with 7 and 13% for diameter and height, respectively, compared to results achieved by using a pure additive model. However, the genetic gain was higher for the pure additive model than for the model including dominance for both traits.

Aberrant expression of miRNAs, cytokines and chemokines are involved in pathogenesis of colon cancer. However, the expression of p53 mediated miRNAs, cyto- and chemokines after radiation and SN38 treatment in colon cancer remains elusive. Here, human colon cancer cells, HCT116 with wild-type, heterozygous and a functionally null p53, were treated by radiation and SN38. The expression of 384 miRNAs was determined by using the TaqMan (R) miRNA array, and the expression of cyto- and chemokines was analyzed by Meso-Scale-Discovery instrument. Up- or down-regulations of miRNAs after radiation and SN38 treatments were largely dependent on p53 status of the cells. Cytokines, IL-6, TNF-alpha, IL-1 beta, Il-4, IL-10, VEGF, and chemokines, IL-8, MIP-1 alpha were increased, and IFN-gamma expression was decreased after radiation, whereas, IL-6, IFN-gamma, TNF-alpha, IL-1 beta, Il-4, IL-10, IL-8 were decreased, and VEGF and MIP-1 alpha were increased after SN38 treatment. Bioinformatic analysis pointed out that the highly up-regulated miRNAs, let-7f-5p, miR-455-3p, miR-98, miR-155-5p and the down-regulated miRNAs, miR-1, miR-127-5p, miR-142-5p, miR-202-5p were associated with colon cancer pathways and correlated with cyto- or chemokine expression. These miRNAs have the potential for use in colon cancer therapy as they are related to p53, pro- or anti-inflammatory cyto- or chemokines after the radiation and SN38 treatment. Funding Agencies|Swedish Cancer Foundation; Swedish Research Council; Health Research Council in the South-East of Sweden

Spatial variation in resistance and virulence in the host-pathogen system Salix triandra-Melampsora amygdalinae

Summary: Bayesian statistical methods based on simulation techniques have recently been shown to provide powerful tools for the analysis of genetic population structure. We have previously developed a Markov chain Monte Carlo (MCMC) algorithm for characterizing genetically divergent groups based on molecular markers and geographical sampling design of the dataset. However, for large-scale datasets such algorithms may get stuck to local maxima in the parameter space. Therefore, we have modified our earlier algorithm to support multiple parallel MCMC chains, with enhanced features that enable considerably faster and more reliable estimation compared to the earlier version of the algorithm. We consider also a hierarchical tree representation, from which a Bayesian model-averaged structure estimate can be extracted. The algorithm is implemented in a computer program that features a user-friendly interface and built-in graphics. The enhanced features are illustrated by analyses of simulated data and an extensive human molecular dataset. Availability: Freely available at http://www.rni.helsinki.fi/~jic/bapspage.html

Developmental instability and fluctuating asymmetry (FA) have become important topics in evolutionary biology. For example, it has been suggested that FA could be a useful tool for identification of genetic and environmental stress factors. This study used plants from each of six populations of Scabiosa canescens and Scabiosa columbaria grown under greenhouse conditions. I tested whether there was a relationship between petal FA and allozyme heterozygosity, the heritabilities of eight traits, and population size. Flowers displayed no directional asymmetry or antisymmetry. The rare species S. canescens had significantly higher FA values than S. columbaria, but only the latter demonstrated interpopulation differentiation for the expression of FA levels. There was no evidence for an association between population-level FA and genetic variation when compared with the allozyme heterozygosity or with the heritabilities of the quantitative traits. A tendency for a negative association between FA and population size was found for both species, but it was not significant when adjusted for multiple comparison. Hence, flower FA should not be considered a reliable indicator of the amount of genetic variation in populations of S. canescens and S. columbaria.

Translational research program is intended to provide scientists with an incentive to examine research findings from the perspective of concrete applications or other uses, and to give outstanding researchers an opportunity to develop these findings into specific applications and/or economic, societal or social benefits. This program is jointly funded by the Austrian Science Fund (FWF) and the Austrian Ministry for Transport, Innovation and Technology (BMVIT). Therefore, the acknowledgments section of the paper “Evaluation of the lasso and the elastic net in genome-wide association studies” should state: “The financial support of the Austrian Ministry for Transport, Innovation and Technology (BMVIT) and the Austrian Science Fund (FWF) via the project TRP46-B19 is greatly acknowledged.”

Future adaptation to changes in the environment depends on the existence of additive genetic variances within populations. Recently, considerable attention has also been given to the non-additive component, which plays an important role in inbreeding depression and bottleneck situations. In this study, I used data from a North Carolina II crossing experiment, analysed with restricted maximum-likelihood methods, to estimate the additive and dominance genetic (co)variances for eight quantitative characters in two different-sized populations of Scabiosa canescens, a rare and threatened plant in Sweden. There was no evidence for genetic erosion in the small Hällestad population ( approximately 25 individuals) relative to the large Ahus population ( approximately 5000 individuals). In fact, slightly higher heritabilities were found in the Hällestad population. The additive genetic variance was statistically significant for all traits in both populations, but only a few additive covariances reached significance. The Hällestad population also had higher mean levels and more traits with significant dominance variance than the Ahus population. The variance attributable to maternal effects was too low to be considered significant. There was only a weak correspondence between heritabilities for each trait in the present study and previous estimates based on open-pollinated families of the same populations, but the mean heritability (over characters) was consistent between the studies.

Developmental instability and fluctuating asymmetry (FA) describe the inability of organisms to correct for random accidents under development and has become a major but controversial topic in evolutionary biology. Theoretical models predict that the level of FA should increase as a result of inbreeding, but empirical results are ambiguous. Moreover, the relationship between fitness and FA is still debated. In the current study, plants from a population of Scabiosa canescens, a locally rare species in southern Sweden, were raised under uniform growth conditions to examine the effects of one-generation of selfing and outcrossing on FA in flower morphology. The level of flower FA was significantly higher (p = 0.038) for inbred progeny than for offspring derived from outcross pollinations. Given that earlier studies of this species have found no negative relation between heterozygosity and FA, the results support the conclusion that expression of deleterious recessive alleles are responsible for the increase of FA. There was no correlation between FA and estimates of five fitness-related traits when estimated at the individual level. However, a companion study found significant inbreeding depression for all fitness traits, and a negative association between FA and fitness could therefore be asserted at the treatment level (inbred/outbred progeny). Hence, FA seems to be useful to predict inbreeding depression in S. canescens, but specific individuals with high fitness cannot be identified based on their FA levels.

In the current study, we used bootstrap analyses and the common principal component (CPC) method of Flury (1988) to estimate and compare the G-matrix of Scabiosa columbaria and S. canescens populations. We found three major patterns in the G-matrices: (i) the magnitude of the (co)variances was more variable among characters than among populations, (ii) different populations showed high (co)variance for different characters, and (iii) there was a tendency for S. canescens to have higher genetic (co)variances than S. columbaria. The hypothesis of equal G-matrices was rejected in all comparisons and there was no evidence that the matrices differed by a proportional constant in any of the analyses. The two 'species matrices' were found to be unrelated, both for raw data and data standardized over populations, and there was significant between-population variation in the G-matrix in both species. Populations of S. canescens showed conservation of structure (principal components) in their G-matrices, contrasting with the lack of common structure among the S. columbaria matrices. Given these observations and the results from previous studies, we propose that selection may be responsible for some of the variation between the G-matrices, at least in S. columbaria and at the between-species level. (Less)

Studies of fluctuating asymmetry (FA), a measure of developmental instability (DI), may provide insights into the importance of genetic factors in the long-term survival of small and isolated populations. In the present study of the rare, endemic plant Silene diclinis, I tested how moderate inbreeding within populations (full-sib crosses) and hybridization between populations influenced levels of developmental instability of petals and leaves, using plants derived from controlled crosses and raised under uniform growth conditions. The area and length of petals and leaves were digitized and measured with an image analysis system, but only bifid petals could be tested for true fluctuating asymmetry (normally distributed left-minus-right values with a mean of zero). Based on a bootstrap procedure, I found little evidence for directional asymmetry and antisymmetry in the area and length of the two lobes of the petals. Only the length measurements showed a significant leptokurtic distribution, which may reflect limited resolution (too few classes) in the image analysis system. Randomization tests were performed to test for differences between crossing treatments. Levels of FA of petal area and petal length were significantly higher for both the inbred and the interpopulation hybrid progenies relative to offspring from crosses between unrelated plants from the same population (control). There was no significant treatment effect on DI of leaves. Comparison of plants in the control group revealed that DI of leaf area was significantly higher than FA of petal area, and that these parameters were uncorrelated. This study demonstrates that FA of petals in Silene diclinis is sensitive to moderate levels of inbreeding and outbreeding, and therefore might serve as an indicator of genetic stress.

Comparison of quantitative genetic variation and allozyme diversity within and between populations of Scabiosa canescens and S. columbaria

The goal of genome-wide association studies (GWAS) is to identify the best subset of single-nucleotide polymorphisms (SNPs) that strongly influence a certain trait. State of the art GWAS comprise several thousand or even millions of SNPs, scored on a substantially lower number of individuals. Hence, the number of variables greatly exceeds the number of observations, which also is known as the p≫n problem. This problem has been tackled by using Bayesian variable selection methods, for example stochastic search variable selection (SSVS) and Bayesian penalized regression methods (Bayesian lasso; BLA and Bayesian ridge regression; BRR). Even though the above mentioned approaches are capable of dealing with situations where p≫n, it is also known that these methods experience problems when the predictor variables are correlated. The potential problem that linkage disequilibrium (LD) between SNPs can introduce is often ignored. The main contribution of this study is to assess the performance of SSVS, BLA, BRR and a recently introduced method denoted hybrid correlation based search (hCBS) with respect to their ability to identify quantitative trait loci, where SNPs are partially highly correlated. Furthermore, each method’s capability to predict phenotypes based on the selected SNPs and their computational demands are studied. Comparison is based upon three simulated datasets where the simulated phenotypes are assumed to be normally distributed. Results indicate that all methods perform reasonably well with respect to true positive detections but often detect too many false positives on all datasets. As the heritability decreases, the Bayesian penalized regression methods are no longer able to detect any predictors because of shrinkage. Overall, BLA slightly outperformed the other methods and provided superior results in terms of highest true positive/ false positive ratio, but SSVS achieved the best properties on the real LD data.

Background and Aims: The adaptive plastic reactions of plant populations to changing climatic factors, such as winter temperatures and photoperiod, have changed during range shifts after the last glaciation. Timing of flowering is an adaptive trait regulated by environmental cues. Its genetics has been intensively studied in annual plants, but in perennials it is currently not well characterized. This study examined the genetic basis of differentiation in flowering time, morphology, and their plastic responses to vernalization in two locally adapted populations of the perennial Arabidopsis lyrata: (1) to determine whether the two populations differ in their vernalization responses for flowering phenology and morphology; and (2) to determine the genomic areas governing differentiation and vernalization responses. Methods: Two A. lyrata populations, from central Europe and Scandinavia, were grown in growth-chamber conditions with and without cold treatment. A QTL analysis was performed to find genomic regions that interact with vernalization. Key Results: The population from central Europe flowered more rapidly and invested more in inflorescence growth than the population from alpine Scandinavia, especially after vernalization. The alpine population had consistently a low number of inflorescences and few flowers, suggesting strong constraints due to a short growing season, but instead had longer leaves and higher leaf rosettes. QTL mapping in the F2 population revealed genomic regions governing differentiation in flowering time and morphology and, in some cases, the allelic effects from the two populations on a trait were influenced by vernalization (QTL × vernalization interactions). Conclusions: The results indicate that many potentially adaptive genetic changes have occurred during colonization; the two populations have diverged in their plastic responses to vernalization in traits closely connected to fitness through changes in many genomic areas.

A novel hierarchical quantitative trait locus (QTL) mapping method using a polynomial growth function and a multiple-QTL model (with no dependence in time) in a multitrait framework is presented. The method considers a population-based sample where individuals have been phenotyped (over time) with respect to some dynamic trait and genotyped at a given set of loci. A specific feature of the proposed approach is that, instead of an average functional curve, each individual has its own functional curve. Moreover, each QTL can modify the dynamic characteristics of the trait value of an individual through its influence on one or more growth curve parameters. Apparent advantages of the approach include: (1) assumption of time-independent QTL and environmental effects, (2) alleviating the necessity for an autoregressive covariance structure for residuals and (3) the flexibility to use variable selection methods. As a by-product of the method, heritabilities and genetic correlations can also be estimated for individual growth curve parameters, which are considered as latent traits. For selecting trait-associated loci in the model, we use a modified version of the well-known Bayesian adaptive shrinkage technique. We illustrate our approach by analysing a sub sample of 500 individuals from the simulated QTLMAS 2009 data set, as well as simulation replicates and a real Scots pine (Pinus sylvestris) data set, using temporal measurements of height as dynamic trait of interest.

Summary This article expands upon recent interest in Bayesian hierarchical models in quantitative genetics by developing spatial process models for inference on additive and dominance genetic variance within the context of large spatially referenced trial datasets. Direct application of such models to large spatial datasets are, however, computationally infeasible because of cubic-order matrix algorithms involved in estimation. The situation is even worse in Markov chain Monte Carlo (MCMC) contexts where such computations are performed for several iterations. Here, we discuss approaches that help obviate these hurdles without sacrificing the richness in modeling. For genetic effects, we demonstrate how an initial spectral decomposition of the relationship matrices negate the expensive matrix inversions required in previously proposed MCMC methods. For spatial effects, we outline two approaches for circumventing the prohibitively expensive matrix decompositions: the first leverages analytical results from Ornstein–Uhlenbeck processes that yield computationally efficient tridiagonal structures, whereas the second derives a modified predictive process model from the original model by projecting its realizations to a lower-dimensional subspace, thereby reducing the computational burden. We illustrate the proposed methods using a synthetic dataset with additive, dominance, genetic effects and anisotropic spatial residuals, and a large dataset from a Scots pine (Pinus sylvestris L.) progeny study conducted in northern Sweden. Our approaches enable us to provide a comprehensive analysis of this large trial, which amply demonstrates that, in addition to violating basic assumptions of the linear model, ignoring spatial effects can result in downwardly biased measures of heritability.

Background The combination of optimized contribution dynamic selection and various mating schemes was investigated over seven generations for a typical tree breeding scenario. The allocation of mates was optimized using a simulated annealing algorithm for various object functions including random mating (RM), positive assortative mating (PAM) and minimization of pair-wise coancestry between mates (MCM) all combined with minimization of variance in family size and coancestry. The present study considered two levels of heritability (0.05 and 0.25), two restrictions on relatedness (group coancestry; 1 and 2%) and two maximum permissible numbers of crosses in each generation (100 and 400). The infinitesimal genetic model was used to simulate the genetic architecture of the trait that was the subject of selection. A framework of the long term genetic contribution of ancestors was used to examine the impacts of the mating schemes on population parameters. Results MCM schemes produced on average, an increased rate of genetic gain in the breeding population, although the difference between schemes was small but significant after seven generations (up to 7.1% more than obtained with RM). In addition, MCM reduced the level of inbreeding by as much as 37% compared with RM, although the rate of inbreeding was similar after three generations of selection. PAM schemes yielded levels of genetic gain similar to those produced by RM, but the increase in the level of inbreeding was substantial (up to 43%). Conclusion The main reason why MCM schemes yielded higher genetic gains was the improvement in managing the long term genetic contribution of founders in the population; this was achieved by connecting unrelated families. In addition, the accumulation of inbreeding was reduced by MCM schemes since the variance in long term genetic contributions of founders was smaller than in the other schemes. Consequently, by combining an MCM scheme with an algorithm that optimizes contributions of the selected individuals, a higher long term response is obtained while reducing the risk within the breeding program.

There has been a tremendous advancement of Bayesian methodology in quantitative genetics and evolutionary biology. Still, there are relatively few publications that apply this methodology, probably because the availability of multipurpose and user-friendly software is somewhat limited. It is here described how only a few rows of code of the well-developed and very flexible Bayesian software WinBUGS (Lunn et al. 2000) can be used for inference of the additive polygenic variance and heritabilty in pedigrees of general design. The presented code is illustrated by application to an earlier published dataset of Scots pine.

Accurate and fast computation of quantitative genetic variance parameters is of great importance in both natural and breeding populations. For experimental designs with complex relationship structures it can be important to include both additive and dominance variance components in the statistical model. In this study, we introduce a Bayesian Gibbs sampling approach for estimation of additive and dominance genetic variances in the traditional infinitesimal model. The method can handle general pedigrees without inbreeding. To optimize between computational time and good mixing of the Markov chain Monte Carlo (MCMC) chains, we used a hybrid Gibbs sampler that combines a single site and a blocked Gibbs sampler. The speed of the hybrid sampler and the mixing of the single-site sampler were further improved by the use of pretransformed variables. Two traits (height and trunk diameter) from a previously published diallel progeny test of Scots pine (Pinus sylvestris L.) and two large simulated data sets with different levels of dominance variance were analyzed. We also performed Bayesian model comparison on the basis of the posterior predictive loss approach. Results showed that models with both additive and dominance components had the best fit for both height and diameter and for the simulated data with high dominance. For the simulated data with low dominance, we needed an informative prior to avoid the dominance variance component becoming overestimated. The narrow-sense heritability estimates in the Scots pine data were lower compared to the earlier results, which is not surprising because the level of dominance variance was rather high, especially for diameter. In general, the hybrid sampler was considerably faster than the blocked sampler and displayed better mixing properties than the single-site sampler.

Additive genetic variance might usually be expected to decrease in a finite population because of genetic drift. However, both theoretical and empirical studies have shown that the additive genetic variance of a population could, in some cases, actually increase owing to the action of genetic drift in presence of non-additive effects. We used Monte–Carlo simulations to address a less-well-studied issue: the effects of directional truncation selection on a trait affected by non-additive genetic variation. We investigated the effects on genetic variance and the response to selection. We compared two different genetic models, representing various numbers of loci. We found that the additive genetic variance could also increase in the case of truncation selection, when dominance and epistasis was present. Additive-by-additive epistatic effects generally gave a higher increase in additive variance compared to dominance. However, the magnitude of the increase differed depending on the particular model and on the number of loci.

Multi-trait (co)variance estimation is an important topic in plant and animal breeding. In this study we compare estimates obtained with restricted maximum likelihood (REML) and Bayesian Gibbs sampling of simulated data and of three traits (diameter, height and branch angle) from a 26-year-old partial diallel progeny test of Scots pine (Pinus sylvestris L.). Based on the results from the simulated data we can conclude that the REML estimates are accurate but the mode of posterior distributions from the Gibbs sampling can be overestimated depending on the level of the heritability. The mean and median of the posteriors were considerably higher than the expected values of the heritabilities. The confidence intervals calculated with the delta method were biased downwardly. The highest probability density (HPD) interval provides a better interval estimate, but could be slightly biased at the lower level. Similar differences between REML and Gibbs sampling estimates were found for the Scots pine data. We conclude that further simulation studies are needed in order to evaluate the effect of different priors on (co)variance components in the genetic individual model.

Comparison of the level of differentiation at neutral molecular markers (estimated as F(ST) or G(ST)) with the level of differentiation at quantitative traits (estimated as Q(ST)) has become a standard tool for inferring that there is differential selection between populations. We estimated Q(ST) of timing of bud set from a latitudinal cline of Pinus sylvestris with a Bayesian hierarchical variance component method utilizing the information on the pre-estimated population structure from neutral molecular markers. Unfortunately, the between-family variances differed substantially between populations that resulted in a bimodal posterior of Q(ST) that could not be compared in any sensible way with the unimodal posterior of the microsatellite F(ST). In order to avoid publishing studies with flawed Q(ST) estimates, we recommend that future studies should present heritability estimates for each trait and population. Moreover, to detect variance heterogeneity in frequentist methods (ANOVA and REML), it is of essential importance to check also that the residuals are normally distributed and do not follow any systematically deviating trends.

Plants from a population of Scabiosa canescens, a locally rare species with a narrow ecological amplitude, were raised under uniform growth conditions to examine the phenotypic effects of one generation selfing and outcrossing. Particular attention was given to direct components of fitness (seedling biomass, rosette leaf number, head number, flower number per head), but two morphological characters (plant height, flower size) were also considered. Estimates of inbreeding depression (delta), adjusted for maternal effects and lack of balance, were compared and tested for significance using randomization and bootstrap procedures. Inbreeding significantly depressed several characters during both early and late stages of the life cycle, with delta ranging from 0.14 (flower size) to 0.37 (seedling biomass). Based on these and other results, we propose that S. canescens is susceptible to inbreeding and that the genetic basis of inbreeding depression varies across life stages.

The concept of developmental instability (DI) is frequently used in evolutionary biology, and a range of definitions has been proposed. Moreover, numerous different statistical methods have been used for estimation of DI. The common basis for all methods is that measures need to be obtained from repeated structures within organisms. In the case of fluctuating asymmetry, mirror images could be interpreted as the repeats of each other. All repeats of a trait on one organism should, from a quantitative perspective, have the same genetic foundation. Most previous methods have not accounted for the genetics of the underlying trait. It is here shown how a statistical method from quantitative genetics (the repeated records animal model) can be used for assessment of DI, based on estimation of the variance due to the permanent environment. Moreover, Gibbs sampling is used for inference of the parameters, which provides a Bayesian framework where posterior distributions easily can be calculated from any functions of the variance components. The method is applied to a real dataset from two populations of the plant Scabiosa canescens, and results shows that it works well under realistic situations.

This study shows how a Gibbs sampling approach can be used for Bayesian inference of inbreeding depression. The method presented is mainly concerned with organisms that can be both selfed and outcrossed. Tests performed on simulated data with unequal variances and missing observations show that the method works well. Real data from the plant Scabiosa canescens is also analyzed.

Made available in DSpace on 2018-12-11T17:22:15Z (GMT). No. of bitstreams: 0 Previous issue date: 2018-08-22 Background: Runs of homozygosity (ROH) islands are stretches of homozygous sequence in the genome of a large proportion of individuals in a population. Algorithms for the detection of ROH depend on the similarity of haplotypes. Coverage gaps and copy number variants (CNV) may result in incorrect identification of such similarity, leading to the detection of ROH islands where none exists. Misidentified hemizygous regions will also appear as homozygous based on sequence variation alone. Our aim was to identify ROH islands influenced by marker coverage gaps or CNV, using Illumina BovineHD BeadChip (777 K) single nucleotide polymorphism (SNP) data for Austrian Brown Swiss, Tyrol Grey and Pinzgauer cattle. Methods: ROH were detected using clustering, and ROH islands were determined from population inbreeding levels for each marker. CNV were detected using a multivariate copy number analysis method and a hidden Markov model. SNP coverage gaps were defined as genomic regions with intermarker distances on average longer than 9.24 kb. ROH islands that overlapped CNV regions (CNVR) or SNP coverage gaps were considered as potential artefacts. Permutation tests were used to determine if overlaps between CNVR with copy losses and ROH islands were due to chance. Diversity of the haplotypes in the ROH islands was assessed by haplotype analyses. Results: In Brown Swiss, Tyrol Grey and Pinzgauer, we identified 13, 22, and 24 ROH islands covering 26.6, 389.0 and 35.8 Mb, respectively, and we detected 30, 50 and 71 CNVR derived from CNV by using both algorithms, respectively. Overlaps between ROH islands, CNVR or coverage gaps occurred for 7, 14 and 16 ROH islands, respectively. About 37, 44 and 52% of the ROH islands coverage in Brown Swiss, Tyrol Grey and Pinzgauer, respectively, were affected by copy loss. Intersections between ROH islands and CNVR were small, but significantly larger compared to ROH islands at random locations across the genome, implying an association between ROH islands and CNVR. Haplotype diversity for reliable ROH islands was lower than for ROH islands that intersected with copy loss CNVR. Conclusions: Our findings show that a significant proportion of the ROH islands in the bovine genome are artefacts due to CNV or SNP coverage gaps. Division of Livestock Sciences (NUWI) University of Natural Resources and Life Sciences, Gregor-Mendel Strasse 33 Lilongwe University of Agriculture and Natural Resources, P. O. Box 219 School of Agricultural and Veterinarian Sciences Jaboticabal Department of Preventive Veterinary Medicine and Animal Reproduction São Paulo State University (UNESP) National Livestock Resources Research Institute, P.O Box 96 Department of Animal Breeding and Genetics Swedish University of Agricultural Sciences, Box 7023 Department of Animal Science Faculty of Agriculture University of Zagreb, Svetošimunska cesta 25 School of Veterinary Medicine Araçatuba Department of Support Production and Animal Health São Paulo State University (UNESP) Animal Genomics and Improvement Laboratory School of Agricultural and Veterinarian Sciences Jaboticabal Department of Preventive Veterinary Medicine and Animal Reproduction São Paulo State University (UNESP) School of Veterinary Medicine Araçatuba Department of Support Production and Animal Health São Paulo State University (UNESP)