RESUMO
Restricted maximum likelihood estimation of genetic parameters accounting for genomic relationships has been reported to impose computational burdens which typically are many times higher than those of corresponding analyses considering pedigree based relationships only. This can be attributed to the dense nature of genomic relationship matrices and their inverses. We outline a reparameterisation of the multivariate linear mixed model to principal components and its effects on the sparsity pattern of the pertaining coefficient matrix in the mixed model equations. Using two data sets we demonstrate that this can dramatically reduce the computing time per iterate of the widely used 'average information' algorithm for restricted maximum likelihood. This is primarily due to the fact that on the principal component scale, the first derivatives of the coefficient matrix with respect to the parameters modelling genetic covariances between traits are independent of the relationship matrix between individuals, i.e. are not afflicted by a multitude of genomic relationships.
Assuntos
Cruzamento , Modelos Genéticos , Humanos , Funções Verossimilhança , Genômica/métodos , Fenótipo , Algoritmos , LinhagemRESUMO
Multivariate estimation of genetic parameters involving more than a handful of traits can be afflicted by problems arising through substantial sampling variation. We present a review of underlying causes and proposals to improve estimates, focusing on linear mixed model-based estimation via restricted maximum likelihood (REML). Both full multivariate analyses and pooling of results from overlapping subsets of traits are considered. It is suggested to impose a penalty on the likelihood designed to reduce sampling variances at the expense of a little additional bias. Simulation results are discussed which demonstrate that this can yield REML estimates that are on average closer to the population values than their unpenalized counterparts. Suitable penalties can be obtained based on assumed prior distributions of selected parameters. Necessary choices of penalty functions and of the stringency of penalization are examined. We argue that scale-free penalty functions lend themselves to a simple scheme imposing a mild, default penalty which can yield "better" estimates without being likely to incur detrimental effects.
Assuntos
Algoritmos , Biologia Computacional/métodos , Variação Genética , Modelos Genéticos , Animais , Teorema de Bayes , Funções Verossimilhança , Análise Multivariada , FenótipoRESUMO
BACKGROUND: A common measure employed to evaluate the efficacy of livestock improvement schemes is the genetic trend, which is calculated as the means of predicted breeding values for animals born in successive time periods. This implies that different cohorts refer to the same base population. For genetic evaluation schemes integrating genomic information with records for all animals, genotyped or not, this is often not the case: expected means for pedigree founders are zero whereas values for genotyped animals are expected to sum to zero at the (mean) time corresponding to the frequencies that are used to center marker allele counts when calculating genomic relationships. METHODS: The paper examines estimates of genetic trends from single-step genomic evaluations. After a review of methods which propose to align pedigree-based and genomic relationship matrices, simulation is used to illustrate the effects of alignments and choice of assumed gene frequencies on trajectories of genetic trends. RESULTS: The results show that methods available to alleviate differences between the founder populations implied by the two types of relationship matrices perform well; in particular, the meta-founder approach is advantageous. An application to data from routine genetic evaluation of Australian sheep is shown, confirming their effectiveness for practical data. CONCLUSIONS: Aligning pedigree and genomic relationship matrices for single step genetic evaluation for populations under selection is essential. Fitting meta-founders is an effective and simple method to avoid distortion of estimates of genetic trends.
Assuntos
Genômica/métodos , Técnicas de Genotipagem/veterinária , Ovinos/genética , Algoritmos , Animais , Cruzamento , Efeito Fundador , Frequência do Gene , Genética Populacional , Linhagem , Polimorfismo de Nucleotídeo Único , Seleção GenéticaRESUMO
Understanding the patterns of genetic variation and constraint for continuous reaction norms, growth trajectories, and other function-valued traits is challenging. We describe and illustrate a recent analytical method, simple basis analysis (SBA), that uses the genetic variance-covariance (G) matrix to identify "simple" directions of genetic variation and genetic constraints that have straightforward biological interpretations. We discuss the parallels between the eigenvectors (principal components) identified by principal components analysis (PCA) and the simple basis (SB) vectors identified by SBA. We apply these methods to estimated G matrices obtained from 10 studies of thermal performance curves and growth curves. Our results suggest that variation in overall size across all ages represented most of the genetic variance in growth curves. In contrast, variation in overall performance across all temperatures represented less than one-third of the genetic variance in thermal performance curves in all cases, and genetic trade-offs between performance at higher versus lower temperatures were often important. The analyses also identify potential genetic constraints on patterns of early and later growth in growth curves. We suggest that SBA can be a useful complement or alternative to PCA for identifying biologically interpretable directions of genetic variation and constraint in function-valued traits.
Assuntos
Evolução Biológica , Variação Genética , Característica Quantitativa Herdável , Fatores Etários , Interação Gene-Ambiente , Crescimento/genética , Modelos Biológicos , Fenótipo , Análise de Componente Principal , TemperaturaRESUMO
Recombinant cytokines have limited anticancer efficacy mostly due to a narrow therapeutic window and systemic adverse effects. IL18 is an inflammasome-induced proinflammatory cytokine, which enhances T- and NK-cell activity and stimulates IFNγ production. The activity of IL18 is naturally blocked by a high-affinity endogenous binding protein (IL18BP). IL18BP is induced in the tumor microenvironment (TME) in response to IFNγ upregulation in a negative feedback mechanism. In this study, we found that IL18 is upregulated in the TME compared with the periphery across multiple human tumors and most of it is bound to IL18BP. Bound IL18 levels were largely above the amount required for T-cell activation in vitro, implying that releasing IL18 in the TME could lead to potent T-cell activation. To restore the activity of endogenous IL18, we generated COM503, a high-affinity anti-IL18BP that blocks the IL18BP:IL18 interaction and displaces precomplexed IL18, thereby enhancing T- and NK-cell activation. In vivo, administration of a surrogate anti-IL18BP, either alone or in combination with anti-PD-L1, resulted in significant tumor growth inhibition and increased survival across multiple mouse tumor models. Moreover, the anti-IL18BP induced pronounced TME-localized immune modulation including an increase in polyfunctional nonexhausted T- and NK-cell numbers and activation. In contrast, no increase in inflammatory cytokines and lymphocyte numbers or activation state was observed in serum and spleen. Taken together, blocking IL18BP using an Ab is a promising approach to harness cytokine biology for the treatment of cancer.
Assuntos
Interleucina-18 , Microambiente Tumoral , Animais , Humanos , Interleucina-18/metabolismo , Camundongos , Microambiente Tumoral/imunologia , Microambiente Tumoral/efeitos dos fármacos , Linhagem Celular Tumoral , Células Matadoras Naturais/imunologia , Células Matadoras Naturais/efeitos dos fármacos , Células Matadoras Naturais/metabolismo , Neoplasias/imunologia , Neoplasias/tratamento farmacológico , Ativação Linfocitária/imunologia , Ativação Linfocitária/efeitos dos fármacos , Feminino , Camundongos Endogâmicos C57BL , Peptídeos e Proteínas de Sinalização Intercelular/metabolismo , Ensaios Antitumorais Modelo de Xenoenxerto , Linfócitos T/imunologia , Linfócitos T/efeitos dos fármacos , Linfócitos T/metabolismoRESUMO
KEY MESSAGE: Here, we report on copy number variation of transposable elements and on the genome-specific proliferation in wheat. In addition, we report on revolutionary and evolutionary dynamics of transposons. Wheat is a valuable model for understanding the involvement of transposable elements (TEs) in speciation as wheat species (Triticum-Aegilops group) have diverged from a common ancestor, have undergone two events of speciation through allopolyploidy, and contain a very high fraction of TEs. However, an unbiased genome-wide examination of TE variation among these species has not been conducted. Our research utilized quantitative real time PCR to assess the relative copy numbers of 16 TE families in various Triticum and Aegilops species. We found (1) high variation and genome-specificity of TEs in wheat species, suggesting they were active throughout the evolution of wheat, (2) neither Ae. searsii nor Ae. speltoides by themselves can be the only contributors of the B genome to wheat, and (3) nonadditive changes in TE quantities in polyploid wheat. This study indicates the apparent involvement of large TEs in creating genetic variation in revolutionary and evolutionary scales following allopolyploidization events, presumably assisting in the diploidization of homeologous chromosomes.
Assuntos
Variações do Número de Cópias de DNA , Elementos de DNA Transponíveis , Evolução Molecular , Triticum/genética , DNA de Plantas/genética , Genoma de Planta , Poliploidia , Especificidade da Espécie , Triticum/classificaçãoRESUMO
Torture victims live with complex health conditions. It is essential for the rehabilitation of torture survivors that their traumas are recognized at an early stage. The aim of this study was to investigate (i) the prevalence of reported torture exposure, (ii) the association between demographic characteristics and exposure to torture, and (iii) the association between PTSD and exposure to torture among recently arrived refugees in Aarhus, Denmark. Data were extracted from health assessments of refugees arriving in Aarhus in the years 2017-2019, and 208 cases were included in the analysis. The prevalence of reported torture was 13.9% (29/208). Most torture victims were found among refugees arriving from Iran (17.0% (9/53)), Syria (9.3% (8/86)), and Afghanistan (25.0% (5/20)). Significant associations were found between reported torture exposure and male gender, Southeast Asian origin, and a diagnosis of PTSD. In the study, 24.5% (24/98) of males and 4.5% (5/110) of females had been subjected to torture. However, it is possible that the prevalence of female torture survivors is underestimated due to the taboos surrounding sexual assaults and fear of stigmatization. Nearly half of the torture victims in the study were diagnosed with PTSD (44.8% (13/29)). The results confirm that torture victims constitute a vulnerable group living with severe consequences, including mental illness such as PTSD. Furthermore, understanding the cultural perspectives of the distress among refugees is crucial in providing appropriate healthcare services. This study highlights the importance of addressing the mental health needs of torture survivors and tailoring interventions toward vulnerable refugee populations.
Assuntos
Refugiados , Transtornos de Estresse Pós-Traumáticos , Tortura , Masculino , Humanos , Feminino , Tortura/psicologia , Refugiados/psicologia , Estudos Transversais , Transtornos de Estresse Pós-Traumáticos/epidemiologia , Transtornos de Estresse Pós-Traumáticos/psicologia , Dinamarca/epidemiologiaRESUMO
The quantitative geneticist W. G. ('Bill') Hill, awardee of the 2018 Darwin Medal of the Royal Society and the 2019 Mendel Medal of the Genetics Society (United Kingdom), died on 17 December 2021 at the age of 81 years. Here, we pay tribute to his multiple key scientific contributions, which span population and evolutionary genetics, animal and plant breeding and human genetics. We discuss his theoretical research on the role of linkage disequilibrium (LD) and mutational variance in the response to selection, the origin of the widely used LD metric r2 in genomic association studies, the genetic architecture of complex traits, the quantification of the variation in realized relationships given a pedigree relationship and much more. We demonstrate that basic theoretical research in quantitative and statistical genetics has led to profound insights into the genetics and evolution of complex traits and made predictions that were subsequently empirically validated, often decades later.
Assuntos
Genoma , Melhoramento Vegetal , Animais , Estudo de Associação Genômica Ampla , Genômica , Humanos , Desequilíbrio de LigaçãoRESUMO
BACKGROUND: Estimation of genetic covariance matrices for multivariate problems comprising more than a few traits is inherently problematic, since sampling variation increases dramatically with the number of traits. This paper investigates the efficacy of regularized estimation of covariance components in a maximum likelihood framework, imposing a penalty on the likelihood designed to reduce sampling variation. In particular, penalties that "borrow strength" from the phenotypic covariance matrix are considered. METHODS: An extensive simulation study was carried out to investigate the reduction in average 'loss', i.e. the deviation in estimated matrices from the population values, and the accompanying bias for a range of parameter values and sample sizes. A number of penalties are examined, penalizing either the canonical eigenvalues or the genetic covariance or correlation matrices. In addition, several strategies to determine the amount of penalization to be applied, i.e. to estimate the appropriate tuning factor, are explored. RESULTS: It is shown that substantial reductions in loss for estimates of genetic covariance can be achieved for small to moderate sample sizes. While no penalty performed best overall, penalizing the variance among the estimated canonical eigenvalues on the logarithmic scale or shrinking the genetic towards the phenotypic correlation matrix appeared most advantageous. Estimating the tuning factor using cross-validation resulted in a loss reduction 10 to 15% less than that obtained if population values were known. Applying a mild penalty, chosen so that the deviation in likelihood from the maximum was non-significant, performed as well if not better than cross-validation and can be recommended as a pragmatic strategy. CONCLUSIONS: Penalized maximum likelihood estimation provides the means to 'make the most' of limited and precious data and facilitates more stable estimation for multi-dimensional analyses. It should become part of our everyday toolkit for multivariate estimation in quantitative genetics.
Assuntos
Funções Verossimilhança , Modelos Genéticos , Análise Multivariada , Algoritmos , Animais , Teorema de Bayes , Cruzamento , Simulação por Computador , Interpretação Estatística de DadosRESUMO
BACKGROUND: The dairy cattle breeding industry is a highly globalized business, which needs internationally comparable and reliable breeding values of sires. The international Bull Evaluation Service, Interbull, was established in 1983 to respond to this need. Currently, Interbull performs multiple-trait across country evaluations (MACE) for several traits and breeds in dairy cattle and provides international breeding values to its member countries. Estimating parameters for MACE is challenging since the structure of datasets and conventional use of multiple-trait models easily result in over-parameterized genetic covariance matrices. The number of parameters to be estimated can be reduced by taking into account only the leading principal components of the traits considered. For MACE, this is readily implemented in a random regression model. METHODS: This article compares two principal component approaches to estimate variance components for MACE using real datasets. The methods tested were a REML approach that directly estimates the genetic principal components (direct PC) and the so-called bottom-up REML approach (bottom-up PC), in which traits are sequentially added to the analysis and the statistically significant genetic principal components are retained. Furthermore, this article evaluates the utility of the bottom-up PC approach to determine the appropriate rank of the (co)variance matrix. RESULTS: Our study demonstrates the usefulness of both approaches and shows that they can be applied to large multi-country models considering all concerned countries simultaneously. These strategies can thus replace the current practice of estimating the covariance components required through a series of analyses involving selected subsets of traits. Our results support the importance of using the appropriate rank in the genetic (co)variance matrix. Using too low a rank resulted in biased parameter estimates, whereas too high a rank did not result in bias, but increased standard errors of the estimates and notably the computing time. CONCLUSIONS: In terms of estimation's accuracy, both principal component approaches performed equally well and permitted the use of more parsimonious models through random regression MACE. The advantage of the bottom-up PC approach is that it does not need any previous knowledge on the rank. However, with a predetermined rank, the direct PC approach needs less computing time than the bottom-up PC.
Assuntos
Cruzamento/estatística & dados numéricos , Indústria de Laticínios , Animais , Bovinos , Genótipo , Modelos Genéticos , Fenótipo , Análise de Componente Principal , Seleção GenéticaRESUMO
BACKGROUND: Interbull is a non-profit organization that provides internationally comparable breeding values for globalized dairy cattle breeding programmes. Due to different trait definitions and models for genetic evaluation between countries, each biological trait is treated as a different trait in each of the participating countries. This yields a genetic covariance matrix of dimension equal to the number of countries which typically involves high genetic correlations between countries. This gives rise to several problems such as over-parameterized models and increased sampling variances, if genetic (co)variance matrices are considered to be unstructured. METHODS: Principal component (PC) and factor analytic (FA) models allow highly parsimonious representations of the (co)variance matrix compared to the standard multi-trait model and have, therefore, attracted considerable interest for their potential to ease the burden of the estimation process for multiple-trait across country evaluation (MACE). This study evaluated the utility of PC and FA models to estimate variance components and to predict breeding values for MACE for protein yield. This was tested using a dataset comprising Holstein bull evaluations obtained in 2007 from 25 countries. RESULTS: In total, 19 principal components or nine factors were needed to explain the genetic variation in the test dataset. Estimates of the genetic parameters under the optimal fit were almost identical for the two approaches. Furthermore, the results were in a good agreement with those obtained from the full rank model and with those provided by Interbull. The estimation time was shortest for models fitting the optimal number of parameters and prolonged when under- or over-parameterized models were applied. Correlations between estimated breeding values (EBV) from the PC19 and PC25 were unity. With few exceptions, correlations between EBV obtained using FA and PC approaches under the optimal fit were ≥ 0.99. For both approaches, EBV correlations decreased when the optimal model and models fitting too few parameters were compared. CONCLUSIONS: Genetic parameters from the PC and FA approaches were very similar when the optimal number of principal components or factors was fitted. Over-fitting increased estimation time and standard errors of the estimates but did not affect the estimates of genetic correlations or the predictions of breeding values, whereas fitting too few parameters affected bull rankings in different countries.
Assuntos
Bovinos/genética , Análise Fatorial , Modelos Genéticos , Análise de Componente Principal , Algoritmos , Animais , Cruzamento , Feminino , Testes Genéticos , Masculino , Análise de RegressãoRESUMO
The existence of buffering mechanisms is an emerging property of biological networks, and this results in the buildup of robustness through evolution. So far, there are no explicit methods to find loci implied in buffering mechanisms. However, buffering can be seen as interaction with genetic background. Here we develop this idea into a tractable model for quantitative genetics, in which the buffering effect of one locus with many other loci is condensed into a single statistical effect, multiplicative on the total additive genetic effect. This allows easier interpretation of the results and simplifies the problem of detecting epistasis from quadratic to linear in the number of loci. Using this formulation, we construct a linear model for genome-wide association studies that estimates and declares the significance of multiplicative epistatic effects at single loci. The model has the form of a variance components, norm reaction model and likelihood ratio tests are used for significance. This model is a generalization and explanation of previous ones. We test our model using bovine data: Brahman and Tropical Composite animals, phenotyped for body weight at yearling and genotyped at high density. After association analysis, we find a number of loci with buffering action in one, the other, or both breeds; these loci do not have a significant statistical additive effect. Most of these loci have been reported in previous studies, either with an additive effect or as footprints of selection. We identify buffering epistatic SNPs present in or near genes reported in the context of signatures of selection in multi-breed cattle population studies. Prominent among these genes are those associated with fertility (INHBA, TSHR, ESRRG, PRLR, and PPARG), growth (MSTN, GHR), coat characteristics (KIT, MITF, PRLR), and heat resistance (HSPA6 and HSPA1A). In these populations, we found loci that have a nonsignificant statistical additive effect but a significant epistatic effect. We argue that the discovery and study of loci associated with buffering effects allow attacking the difficult problems, among others, of the release of maintenance variance in artificial and natural selection, of quick adaptation to the environment, and of opposite signs of marker effects in different backgrounds. We conclude that our method and our results generate promising new perspectives for research in evolutionary and quantitative genetics based on the study of loci that buffer effect of other loci.
Assuntos
Bovinos/genética , Epistasia Genética , Fertilidade/genética , Loci Gênicos/genética , Estudo de Associação Genômica Ampla/veterinária , Animais , Peso Corporal , Cruzamento , Feminino , Genótipo , Masculino , Modelos Genéticos , Fenótipo , Polimorfismo de Nucleotídeo Único/genética , Seleção GenéticaRESUMO
Eigenvalues and eigenvectors of covariance matrices are important statistics for multivariate problems in many applications, including quantitative genetics. Estimates of these quantities are subject to different types of bias. This article reviews and extends the existing theory on these biases, considering a balanced one-way classification and restricted maximum-likelihood estimation. Biases are due to the spread of sample roots and arise from ignoring selected principal components when imposing constraints on the parameter space, to ensure positive semidefinite estimates or to estimate covariance matrices of chosen, reduced rank. In addition, it is shown that reduced-rank estimators that consider only the leading eigenvalues and -vectors of the "between-group" covariance matrix may be biased due to selecting the wrong subset of principal components. In a genetic context, with groups representing families, this bias is inverse proportional to the degree of genetic relationship among family members, but is independent of sample size. Theoretical results are supplemented by a simulation study, demonstrating close agreement between predicted and observed bias for large samples. It is emphasized that the rank of the genetic covariance matrix should be chosen sufficiently large to accommodate all important genetic principal components, even though, paradoxically, this may require including a number of components with negligible eigenvalues. A strategy for rank selection in practical analyses is outlined.
Assuntos
Variação Genética , Análise de Variância , Viés , Simulação por Computador , Modelos Genéticos , Tamanho da AmostraRESUMO
BACKGROUND: Analysis of data on genotypes with different expression in different environments is a classic problem in quantitative genetics. A review of models for data with genotype x environment interactions and related problems is given, linking early, analysis of variance based formulations to their modern, mixed model counterparts. RESULTS: It is shown that models developed for the analysis of multi-environment trials in plant breeding are directly applicable in animal breeding. In particular, the 'additive main effect, multiplicative interaction' models accommodate heterogeneity of variance and are characterised by a factor-analytic covariance structure. While this can be implemented in mixed models by imposing such structure on the genetic covariance matrix in a standard, multi-trait model, an equivalent model is obtained by fitting the common and specific factors genetic separately. Properties of the mixed model equations for alternative implementations of factor-analytic models are discussed, and extensions to structured modelling of covariance matrices for multi-trait, multi-environment scenarios are described. CONCLUSION: Factor analytic models provide a natural framework for modelling genotype x environment interaction type problems. Mixed model analyses fitting such models are likely to see increasing use due to the parsimonious description of covariance structures available, the scope for direct interpretation of factors as well as computational advantages.
Assuntos
Meio Ambiente , Modelos Genéticos , Animais , Animais Domésticos/genética , Cruzamento , Cruzamentos Genéticos , Genótipo , Modelos Estatísticos , Plantas/genéticaRESUMO
WOMBAT is a software package for quantitative genetic analyses of continuous traits, fitting a linear, mixed model; estimates of covariance components and the resulting genetic parameters are obtained by restricted maximum likelihood. A wide range of models, comprising numerous traits, multiple fixed and random effects, selected genetic covariance structures, random regression models and reduced rank estimation are accommodated. WOMBAT employs up-to-date numerical and computational methods. Together with the use of efficient compilers, this generates fast executable programs, suitable for large scale analyses. Use of WOMBAT is illustrated for a bivariate analysis. The package consists of the executable program, available for LINUX and WINDOWS environments, manual and a set of worked example, and can be downloaded free of charge from (http://agbu. une.edu.au/~kmeyer/wombat.html).
Assuntos
Funções Verossimilhança , Modelos Genéticos , Software , Animais , CamundongosRESUMO
Hematopoietic stem cells (HSCs) are rare cells that generate all the various types of blood and immune cells. High-quality transcriptome data have enabled the identification of significant genes for HSCs. However, most genes are expressed in various forms by alternative splicing (AS), extending transcriptome complexity. Here, we delineate AS to determine which isoforms are expressed in mouse HSCs. Our analysis of microarray and RNA-sequencing data includes differential expression of splicing factors that may regulate AS, and a complete map of splicing isoforms. Multiple types of isoforms for known HSC genes and unannotated splicing that may alter gene function are presented. Transcriptome-wide identification of genes and their respective isoforms in mouse HSCs will open another dimension for adult stem cells.
Assuntos
Processamento Alternativo , Células-Tronco Hematopoéticas/metabolismo , Transcriptoma , Animais , Análise por Conglomerados , Biologia Computacional/métodos , Proteínas de Ligação a DNA/genética , Éxons , Perfilação da Expressão Gênica , Ontologia Genética , Células-Tronco Hematopoéticas/citologia , Proteínas de Homeodomínio/genética , Íntrons , Camundongos , Fenótipo , Fatores de Transcrição/genética , NavegadorRESUMO
Multivariate estimates of genetic parameters are subject to substantial sampling variation, especially for smaller data sets and more than a few traits. A simple modification of standard, maximum-likelihood procedures for multivariate analyses to estimate genetic covariances is described, which can improve estimates by substantially reducing their sampling variances. This is achieved by maximizing the likelihood subject to a penalty. Borrowing from Bayesian principles, we propose a mild, default penalty-derived assuming a Beta distribution of scale-free functions of the covariance components to be estimated-rather than laboriously attempting to determine the stringency of penalization from the data. An extensive simulation study is presented, demonstrating that such penalties can yield very worthwhile reductions in loss, i.e., the difference from population values, for a wide range of scenarios and without distorting estimates of phenotypic covariances. Moreover, mild default penalties tend not to increase loss in difficult cases and, on average, achieve reductions in loss of similar magnitude to computationally demanding schemes to optimize the degree of penalization. Pertinent details required for the adaptation of standard algorithms to locate the maximum of the likelihood function are outlined.
Assuntos
Variação Genética/genética , Funções Verossimilhança , Modelos Genéticos , Análise Multivariada , Algoritmos , Teorema de Bayes , Simulação por Computador , Fenótipo , Tamanho da AmostraRESUMO
Estimating the genetic and environmental variances for multivariate and function-valued phenotypes poses problems for estimation and interpretation. Even when the phenotype of interest has a large number of dimensions, most variation is typically associated with a small number of principal components (eigen-vectors or eigenfunctions). We propose an approach that directly estimates these leading principal components; these then give estimates for the covariance matrices (or functions). Direct estimation of the principal components reduces the number of parameters to be estimated, uses the data efficiently, and provides the basis for new estimation algorithms. We develop these concepts for both multivariate and function-valued phenotypes and illustrate their application in the restricted maximum-likelihood framework.