Genetic heterogeneity of within-family variance of body weight in Atlantic salmon (Salmo salar)

BACKGROUND: Canalization is defined as the stability of a genotype against minor variations in both environment and genetics. Genetic variation in degree of canalization causes heterogeneity of within-family variance. The aims of this study are twofold: (1) quantify genetic heterogeneity of (within-family) residual variance in Atlantic salmon and (2) test whether the observed heterogeneity of (within-family) residual variance can be explained by simple scaling effects. RESULTS: Analysis of body weight in Atlantic salmon using a double hierarchical generalized linear model (DHGLM) revealed substantial heterogeneity of within-family variance. The 95% prediction interval for within-family variance ranged from ~0.4 to 1.2 kg2, implying that the within-family variance of the most extreme high families is expected to be approximately three times larger than the extreme low families. For cross-sectional data, DHGLM with an animal mean sub-model resulted in severe bias, while a corresponding sire-dam model was appropriate. Heterogeneity of variance was not sensitive to Box-Cox transformations of phenotypes, which implies that heterogeneity of variance exists beyond what would be expected from simple scaling effects. CONCLUSIONS: Substantial heterogeneity of within-family variance was found for body weight in Atlantic salmon. A tendency towards higher variance with higher means (scaling effects) was observed, but heterogeneity of within-family variance existed beyond what could be explained by simple scaling effects. For cross-sectional data, using the animal mean sub-model in the DHGLM resulted in biased estimates of variance components, which differed substantially both from a standard linear mean animal model and a sire-dam DHGLM model. Although genetic differences in canalization were observed, selection for increased canalization is difficult, because there is limited individual information for the variance sub-model, especially when based on cross-sectional data. Furthermore, potential macro-environmental changes (diet, climatic region, etc.) may make genetic heterogeneity of variance a less stable trait over time and space.

Short communication: Principal components and factor analytic models for test-day milk yield in Brazilian Holstein cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Genetic and environmental heterogeneity of residual variance of weight traits in Nellore beef cattle

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Short communication: Principal components and factor analytic models for test-day milk yield in Brazilian Holstein cattle

A total of 46,089 individual monthly test-day (TD) milk yields (10 test-days), from 7,331 complete first lactations of Holstein cattle were analyzed. A standard multivariate analysis (MV), reduced rank analyses fitting the first 2, 3, and 4 genetic principal components (PC2, PC3, PC4), and analyses that fitted a factor analytic structure considering 2, 3, and 4 factors (FAS2, FAS3, FAS4), were carried out. The models included the random animal genetic effect and fixed effects of the contemporary groups (herd-year-month of test-day), age of cow (linear and quadratic effects), and days in milk (linear effect). The residual covariance matrix was assumed to have full rank. Moreover, 2 random regression models were applied. Variance components were estimated by restricted maximum likelihood method. The heritability estimates ranged from 0.11 to 0.24. The genetic correlation estimates between TD obtained with the PC2 model were higher than those obtained with the MV model, especially on adjacent test-days at the end of lactation close to unity. The results indicate that for the data considered in this study, only 2 principal components are required to summarize the bulk of genetic variation among the 10 traits.

Longitudinal familial analysis of blood pressure involving parametric (co)variance functions

Abstract Background For analyzing longitudinal familial data we adopted a log-linear form to incorporate heterogeneity in genetic variance components over the time, and additionally a serial correlation term in the genetic effects at different levels of ages. Due to the availability of multiple measures on the same individual, we permitted environmental correlations that may change across time. Results Systolic blood pressure from family members from the first and second cohort was used in the current analysis. Measures of subjects receiving hypertension treatment were set as censored values and they were corrected. An initial check of the variance and covariance functions proposed for analyzing longitudinal familial data, using empirical semi-variogram plots, indicated that the observed trait dispersion pattern follows the assumptions adopted. Conclusion The corrections for censored phenotypes based on ordinary linear models may be an appropriate simple model to correct the data, ensuring that the original variability in the data was retained. In addition, empirical semi-variogram plots are useful for diagnosis of the (co)variance model adopted.

What are the components that contribute to variability in echocardiographic measurements in aortic stenosis?

INTRODUCTION Echocardiography is the standard clinical approach for quantification of the severity of aortic stenosis (AS). A comprehensive examination of its overall reproducibility and the simultaneous estimation of its variance components by multiple operators, readers, probe applications, and beats have not been undertaken. METHOD AND RESULTS Twenty-seven subjects with AS were scanned over 7 months in the echo-department by a median of 3 different operators. From each patient and each operator multiple runs of beats from multiple probe positions were stored for later analysis by multiple readers. The coefficient of variation was 13.3%, 15.9%, 17.6%, and 20.2% for the aortic peak velocity (Vmax), and velocity time integral (VTI), and left ventricular outflow tract (LVOT) Vmax and VTI respectively. The largest individual contributors to the overall variability were the beat-to-beat variability (9.0%, 9.3%, 9.5%, 9.4% respectively) and that of inability of an individual operator to precisely apply the probe to the same position twice (8.3%, 9.4%, 12.9%, 10.7% respectively). The tracing (inter-reader) and reader (inter-reader), and operator (inter-operator) contribution were less important. CONCLUSIONS Reproducibility of measurements in AS is poorer than often reported in the literature. The source of this variability does not appear, as traditionally believed, to result from a lack of training or operator and reader specific factors. Rather the unavoidable beat-to-beat biological variability, and the inherent impossibility of applying the ultrasound probe in exactly the same position each time are the largest contributors. Consequently, guidelines suggesting greater standardisation of procedures and further training for sonographers are unlikely to result in an improvement in precision. Clinicians themselves should be wary of relying on even three-beat averages as their expected coefficient of variance is 10.3% for the peak velocity at the aortic valve.

MODIFIED TEST STATISTICS BY INTER-VOXEL VARIANCE SHRINKAGE WITH AN APPLICATION TO fMRI

Functional Magnetic Resonance Imaging (fMRI) is a non-invasive technique which is commonly used to quantify changes in blood oxygenation and flow coupled to neuronal activation. One of the primary goals of fMRI studies is to identify localized brain regions where neuronal activation levels vary between groups. Single voxel t-tests have been commonly used to determine whether activation related to the protocol differs across groups. Due to the generally limited number of subjects within each study, accurate estimation of variance at each voxel is difficult. Thus, combining information across voxels in the statistical analysis of fMRI data is desirable in order to improve efficiency. Here we construct a hierarchical model and apply an Empirical Bayes framework on the analysis of group fMRI data, employing techniques used in high throughput genomic studies. The key idea is to shrink residual variances by combining information across voxels, and subsequently to construct an improved test statistic in lieu of the classical t-statistic. This hierarchical model results in a shrinkage of voxel-wise residual sample variances towards a common value. The shrunken estimator for voxelspecific variance components on the group analyses outperforms the classical residual error estimator in terms of mean squared error. Moreover, the shrunken test-statistic decreases false positive rate when testing differences in brain contrast maps across a wide range of simulation studies. This methodology was also applied to experimental data regarding a cognitive activation task.

Latent variable models in statistical genetics

Understanding the complexities that are involved in the genetics of multifactorial diseases is still a monumental task. In addition to environmental factors that can influence the risk of disease, there is also a number of other complicating factors. Genetic variants associated with age of disease onset may be different from those variants associated with overall risk of disease, and variants may be located in positions that are not consistent with the traditional protein coding genetic paradigm. Latent Variable Models are well suited for the analysis of genetic data. A latent variable is one that we do not directly observe, but which is believed to exist or is included for computational or analytic convenience in a model. This thesis presents a mixture of methodological developments utilising latent variables, and results from case studies in genetic epidemiology and comparative genomics. Epidemiological studies have identified a number of environmental risk factors for appendicitis, but the disease aetiology of this oft thought useless vestige remains largely a mystery. The effects of smoking on other gastrointestinal disorders are well documented, and in light of this, the thesis investigates the association between smoking and appendicitis through the use of latent variables. By utilising data from a large Australian twin study questionnaire as both cohort and case-control, evidence is found for the association between tobacco smoking and appendicitis. Twin and family studies have also found evidence for the role of heredity in the risk of appendicitis. Results from previous studies are extended here to estimate the heritability of age-at-onset and account for the eect of smoking. This thesis presents a novel approach for performing a genome-wide variance components linkage analysis on transformed residuals from a Cox regression. This method finds evidence for a dierent subset of genes responsible for variation in age at onset than those associated with overall risk of appendicitis. Motivated by increasing evidence of functional activity in regions of the genome once thought of as evolutionary graveyards, this thesis develops a generalisation to the Bayesian multiple changepoint model on aligned DNA sequences for more than two species. This sensitive technique is applied to evaluating the distributions of evolutionary rates, with the finding that they are much more complex than previously apparent. We show strong evidence for at least 9 well-resolved evolutionary rate classes in an alignment of four Drosophila species and at least 7 classes in an alignment of four mammals, including human. A pattern of enrichment and depletion of genic regions in the profiled segments suggests they are functionally significant, and most likely consist of various functional classes. Furthermore, a method of incorporating alignment characteristics representative of function such as GC content and type of mutation into the segmentation model is developed within this thesis. Evidence of fine-structured segmental variation is presented.

Comparison of three-dimensional profiles over time

In this paper, we describe an analysis for data collected on a three-dimensional spatial lattice with treatments applied at the horizontal lattice points. Spatial correlation is accounted for using a conditional autoregressive model. Observations are defined as neighbours only if they are at the same depth. This allows the corresponding variance components to vary by depth. We use the Markov chain Monte Carlo method with block updating, together with Krylov subspace methods, for efficient estimation of the model. The method is applicable to both regular and irregular horizontal lattices and hence to data collected at any set of horizontal sites for a set of depths or heights, for example, water column or soil profile data. The model for the three-dimensional data is applied to agricultural trial data for five separate days taken roughly six months apart in order to determine possible relationships over time. The purpose of the trial is to determine a form of cropping that leads to less moist soils in the root zone and beyond.We estimate moisture for each date, depth and treatment accounting for spatial correlation and determine relationships of these and other parameters over time.

A Bayesian analysis of an agricultural field trial with three spatial dimensions

Modern technology now has the ability to generate large datasets over space and time. Such data typically exhibit high autocorrelations over all dimensions. The field trial data motivating the methods of this paper were collected to examine the behaviour of traditional cropping and to determine a cropping system which could maximise water use for grain production while minimising leakage below the crop root zone. They consist of moisture measurements made at 15 depths across 3 rows and 18 columns, in the lattice framework of an agricultural field. Bayesian conditional autoregressive (CAR) models are used to account for local site correlations. Conditional autoregressive models have not been widely used in analyses of agricultural data. This paper serves to illustrate the usefulness of these models in this field, along with the ease of implementation in WinBUGS, a freely available software package. The innovation is the fitting of separate conditional autoregressive models for each depth layer, the ‘layered CAR model’, while simultaneously estimating depth profile functions for each site treatment. Modelling interest also lay in how best to model the treatment effect depth profiles, and in the choice of neighbourhood structure for the spatial autocorrelation model. The favoured model fitted the treatment effects as splines over depth, and treated depth, the basis for the regression model, as measured with error, while fitting CAR neighbourhood models by depth layer. It is hierarchical, with separate onditional autoregressive spatial variance components at each depth, and the fixed terms which involve an errors-in-measurement model treat depth errors as interval-censored measurement error. The Bayesian framework permits transparent specification and easy comparison of the various complex models compared.

Mapping quantitative trait loci in a wild population using linkage and linkage disequilibrium analyses

Historical information can be used, in addition to pedigree, traits and genotypes, to map quantitative trait locus (QTL) in general populations via maximum likelihood estimation of variance components. This analysis is known as linkage disequilibrium (LD) and linkage mapping, because it exploits both linkage in families and LD at the population level. The search for QTL in the wild population of Soay sheep on St. Kilda is a proof of principle. We analysed the data from a previous study and confirmed some of the QTLs reported. The most striking result was the confirmation of a QTL affecting birth weight that had been reported using association tests but not when using linkage-based analyses. Copyright © Cambridge University Press 2010.

Linkage mapping of CVD risk traits in the isolated Norfolk Island population

To understand the underlying genetic architecture of cardiovascular disease (CVD) risk traits, we undertook a genome-wide linkage scan to identify CVD quantitative trait loci (QTLs) in 377 individuals from the Norfolk Island population. The central aim of this research focused on the utilization of a genetically and geographically isolated population of individuals from Norfolk Island for the purposes of variance component linkage analysis to identify QTLs involved in CVD risk traits. Substantial evidence supports the involvement of traits such as systolic and diastolic blood pressures, high-density lipoprotein-cholesterol, low-density lipoprotein-cholesterol, body mass index and triglycerides as important risk factors for CVD pathogenesis. In addition to the environmental inXuences of poor diet, reduced physical activity, increasing age, cigarette smoking and alcohol consumption, many studies have illustrated a strong involvement of genetic components in the CVD phenotype through family and twin studies. We undertook a genome scan using 400 markers spaced approximately 10 cM in 600 individuals from Norfolk Island. Genotype data was analyzed using the variance components methods of SOLAR. Our results gave a peak LOD score of 2.01 localizing to chromosome 1p36 for systolic blood pressure and replicated previously implicated loci for other CVD relevant QTLs.

Susceptibility to ankylosing spondylitis in twins: The role of genes, HLA, and the environment

Objective To determine the relative effects of genetic and environmental factors in susceptibility to ankylosing spondylitis (AS). Methods Twins with AS were identified from the Royal National Hospital for Rheumatic Diseases database. Clinical and radiographic examinations were performed to establish diagnoses, and disease severity was assessed using a combination of validated scoring systems. HLA typing for HLA-B27, HLA-B60, and HLA-DR1 was performed by polymerase chain reaction with sequence- specific primers, and zygosity was assessed using microsatellite markers. Genetic and environmental variance components were assessed with the program Mx, using data from this and previous studies of twins with AS. Results Six of 8 monozygotic (MZ) twin pairs were disease concordant, compared with 4 of 15 B27-positive dizygotic (DZ) twin pairs (27%) and 4 of 32 DZ twin pairs overall (12.5%). Nonsignificant increases in similarity with regard to age at disease onset and all of the disease severity scores assessed were noted in disease-concordant MZ twins compared with concordant DZ twins. HLA-B27 and B60 were associated with the disease in probands, and the rate of disease concordance was significantly increased among DZ twin pairs in which the co- twin was positive for both B27 and DR1. Additive genetic effects were estimated to contribute 97% of the population variance. Conclusion Susceptibility to AS is largely genetically determined, and the environmental trigger for the disease is probably ubiquitous. HLA-B27 accounts for a minority of the overall genetic susceptibility to AS.

Is disease severity in ankylosing spondylitis genetically determined?

Objective. To assess the role of genes and the environment in determining the severity of ankylosing spondylitis. Methods: One hundred seventy-three families with >1 case of ankylosing spondylitis were recruited (120 affected sibling pairs, 26 affected parent-child pairs, 20 families with both first- and second-degree relatives affected, and 7 families with only second-degree relatives affected), comprising a total of 384 affected individuals. Disease severity was assessed by the Bath Ankylosing Spondylitis Disease Activity Index (BASDAI) and functional impairment was determined using the Bath Ankylosing Spondylitis Functional Index (BASFI). Disease duration and age at onset were also studied. Variance-components modeling was used to determine the genetic and environmental components Contributing to familiality of the traits examined, and complex segregation analysis was performed to assess different disease models. Results. Both the disease activity and functional capacity as assessed by the BASDAI and the BASFI, respectively, were found to be highly familial (BASDAI familiality 0.51 [P = 10-4], BASFI familiality 0,68 [P = 3 × 10-7]). No significant shared environmental component was demonstrated to be associated with either the BASDAI or the BASFI. Including age at disease onset and duration of disease as covariates made no difference in the heritability assessments. A strong correlation was noted between the BASDAI and the BASFI (genetic correlation 0.9), suggesting the presence of shared determinants of these 2 measures. However, there was significant residual heritability for each measure independent of the other (BASFI residual heritability 0.48, BASDAI 0,36), perhaps indicating that not all genes influencing disease activity influence chronicity. No significant heritability of age at disease onset was found (heritability 0.18; P = 0.2). Segregation studies suggested the presence of a single major gene influencing the BASDAI and the BASFI. Conclusion. This study demonstrates a major genetic contribution to disease severity in ankylosing spondylitis. As with susceptibility to ankylosing spondylitis, shared environmental factors play little role in determining the disease severity.

Suggestive linkage of the parathyroid receptor type 1 to osteoporosis

We have investigated the role of 23 candidate genes in the control of bone mineral density (BMD) by linkage studies in families of probands with osteoporosis (lumbar spine [LS] or femoral neck [FN] BMD T score < -2.5) and low BMD relative to an age- and gender-matched cohort (Z score < -2.0). One hundred and fifteen probands (35 male, 80 female) and 499 of their first- or second-degree relatives (223 males and 276 females) were recruited for the study. BMD was measured at the LS and FN using dual-energy X-ray absorptiometry and expressed as age- and gender-matched Z scores corrected for body mass index. The candidate genes studied were the androgen receptor, type I collagen A1 (COLIA1), COLIA2, COLIIA1, vitamin D receptor (VDR), colony-stimulating factor 1, calcium-sensing receptor, epidermal growth factor (EGF), estrogen receptor 1 (ESR1), fibrillin type 1, insulin-like growth factor 1, interleukin-1 alpha (IL-1α), interleukin-4 (IL-4), interleukin-6 (IL-6), interleukin-11 (IL-11), osteopontin, parathyroid hormone (PTH), PTH-related peptide, PTH receptor type 1 (PTHR1), transforming growth factor-beta 1, and tumor necrosis factors alpha and beta. Sixty-four microsatellites lying close to or within these genes were investigated for linkage with BMD. Using the program MapMaker/Sibs there was suggestive evidence of linkage between BMD and PTHR1 (maximum LOD score obtained [MLS] 2.7-3.5). Moderate evidence of linkage was also observed with EGF (MLS 1.8), COLIA1 (MLS 1.7), COLIIA1/VDR (MLS 1.7), ESR1 (MLS 1.4), IL-1α (MLS 1.4), IL-4 (MLS 1.2), and IL-6 (MLS 1.2). Variance components analysis using the program ACT, correcting for proband-wise ascertainment, also showed evidence of linkage (p ≤0.05) at markers close to or within the candidate genes IL- 1α, PTHR1, IL-6, and COLIIA1/VDR. Further studies will be required to confirm these findings, to refine the location of gene responsible for the observed linkage, and to screen the candidate genes targeted at these loci for mutations.