Genetic Relationship Matrices Research Articles

DeepGBLUP: joint deep learning networks and GBLUP framework for accurate genomic prediction of complex traits in Korean native cattle

BackgroundGenomic prediction has become widespread as a valuable tool to estimate genetic merit in animal and plant breeding. Here we develop a novel genomic prediction algorithm, called deepGBLUP, which integrates deep learning networks and a genomic best linear unbiased prediction (GBLUP) framework. The deep learning networks assign marker effects using locally-connected layers and subsequently use them to estimate an initial genomic value through fully-connected layers. The GBLUP framework estimates three genomic values (additive, dominance, and epistasis) by leveraging respective genetic relationship matrices. Finally, deepGBLUP predicts a final genomic value by summing all the estimated genomic values.ResultsWe compared the proposed deepGBLUP with the conventional GBLUP and Bayesian methods. Extensive experiments demonstrate that the proposed deepGBLUP yields state-of-the-art performance on Korean native cattle data across diverse traits, marker densities, and training sizes. In addition, they show that the proposed deepGBLUP can outperform the previous methods on simulated data across various heritabilities and quantitative trait loci (QTL) effects.ConclusionsWe introduced a novel genomic prediction algorithm, deepGBLUP, which successfully integrates deep learning networks and GBLUP framework. Through comprehensive evaluations on the Korean native cattle data and simulated data, deepGBLUP consistently achieved superior performance across various traits, marker densities, training sizes, heritabilities, and QTL effects. Therefore, deepGBLUP is an efficient method to estimate an accurate genomic value. The source code and manual for deepGBLUP are available at https://github.com/gywns6287/deepGBLUP.

AGHmatrix: genetic relationship matrices in R.

The resemble between relatives computed from pedigree and genomic data is an important resource for geneticists and ecologists, who are interested in understanding how genes influence phenotypic variation, fitness adaptation, and population dynamics. The AGHmatrix software is an R-package focused on the construction of pedigree (A matrix) and/or molecular markers (G matrix), with the possibility of building a combined matrix of pedigree corrected by molecular markers (H matrix). Designed to estimate the relationships for any ploidy level, the software also includes auxiliary functions related to filtering molecular markers, compute linkage disequilibrium (LD) and check pedigree errors in large data sets. After computing the relationship matrices, results from the AGHmatrix can be used in different contexts, including on prediction of (genomic) estimated breeding values and genome-wide association studies (GWAS). AGHmatrix v2.1.0 is available under GPL-3 license in CRAN at https://cran.r-project.org/web/packages/AGHmatrix/index.html and also in GitHub at https://github.com/rramadeu/AGHmatrix. It has a comprehensive tutorial, and it follows with real data examples. Supplementary data are available at Bioinformatics online.

Single-Step Genomic Prediction of Superovulatory Response Traits in Japanese Black Donor Cows.

We assessed the performance of single-step genomic prediction of breeding values for superovulatory response traits in Japanese Black donor cows. A total of 25,332 records of the total number of embryos and oocytes (TNE) and the number of good embryos (NGE) per flush for 1874 Japanese Black donor cows were collected during 2008 and 2022. Genotype information on 36,426 autosomal single-nucleotide polymorphisms (SNPs) for 575 out of the 1,874 cows was used. Breeding values were predicted exploiting a two-trait repeatability animal model. Two genetic relationship matrices were used, one based on pedigree information (A matrix) and the other considering both pedigree and SNP marker genotype information (H matrix). Estimated heritabilities of TNE and NGE were 0.18 and 0.11, respectively, when using the H matrix, which were both slightly lower than when using the A matrix (0.26 for TNE and 0.16 for NGE). Estimated genetic correlations between the traits were 0.61 and 0.66 when using H and A matrices, respectively. When the variance components were the same in breeding value prediction, the mean reliability was greater when using the H matrix than when using the A matrix. This advantage seems more prominent for cows with low reliability when using the A matrix. The results imply that introducing single-step genomic prediction could boost the rate of genetic improvement of superovulatory response traits, but efforts should be made to maintain genetic diversity when performing selection.

Evaluation of Predictive Ability of Bayesian Regularized Neural Network Using Cholesky Factorization of Genetic Relationship Matrices for Additive and Non-additive Genetic Effects

This study aimed to explore the effects of additive and non-additive genetic effects on the prediction of complex traits using Bayesian regularized artificial neural network (BRANN). The data sets were simulated for two hypothetical pedigrees with five different fractions of total genetic variance accounted by additive, additive x additive, and additive x additive x additive genetic effects. A feed forward artificial neural network (ANN) with Bayesian regularization (BR) was used to assess the performance of different nonlinear ANNs and compare their predictive ability with those from linear models under different genetic architectures of phenotypic traits. Effective number of parameters and sum of squares error (SSE) in test data sets were used to evaluate the performance of ANNs. Distribution of weights and correlation between observed and predicted values in the test data set were used to evaluate the predictive ability. There were clear and significant improvements in terms of the predictive ability of linear (equivalent Bayesian ridge regression) and nonlinear models when the proportion of additive genetic variance in total genetic variance ( ) increased. On the other hand, nonlinear models outperformed the linear models across different genetic architectures. The weights for the linear models were larger and more variable than for the nonlinear network, and presented leptokurtic distributions, indicating strong shrinkage towards 0. In conclusion, our results showed that: a) inclusion of non-additive effects did not improve the prediction ability compared to purely additive models, b) The predictive ability of BRANN architectures with nonlinear activation function were substantially larger than the linear models for the scenarios considered.

Evaluation of GENESIS, SAIGE, REGENIE and fastGWA-GLMM for genome-wide association studies of binary traits in correlated data.

Performing a genome-wide association study (GWAS) with a binary phenotype using family data is a challenging task. Using linear mixed effects models is typically unsuitable for binary traits, and numerical approximations of the likelihood function may not work well with rare genetic variants with small counts. Additionally, imbalance in the case-control ratios poses challenges as traditional statistical methods such as the Score test or Wald test perform poorly in this setting. In the last couple of years, several methods have been proposed to better approximate the likelihood function of a mixed effects logistic regression model that uses Saddle Point Approximation (SPA). SPA adjustment has recently been implemented in multiple software, including GENESIS, SAIGE, REGENIE and fastGWA-GLMM: four increasingly popular tools to perform GWAS of binary traits. We compare Score and SPA tests using real family data to evaluate computational efficiency and the agreement of the results. Additionally, we compare various ways to adjust for family relatedness, such as sparse and full genetic relationship matrices (GRM) and polygenic effect estimates. We use the New England Centenarian Study imputed genotype data and the Long Life Family Study whole-genome sequencing data and the binary phenotype of human extreme longevity to compare the agreement of the results and tools’ computational performance. The evaluation suggests that REGENIE might not be a good choice when analyzing correlated data of a small size. fastGWA-GLMM is the most computationally efficient compared to the other three tools, but it appears to be overly conservative when applied to family-based data. GENESIS, SAIGE and fastGWA-GLMM produced similar, although not identical, results, with SPA adjustment performing better than Score tests. Our evaluation also demonstrates the importance of adjusting by full GRM in highly correlated datasets when using GENESIS or SAIGE.

Estimation of direct and maternal genetic effects and annotation of potential candidate genes for weight and meat quality traits in a genotyped outdoor dual-purpose cattle breed.

With regard to potential applications of genomic selection in small numbered breeds, we evaluated genomic models and focused on potential candidate gene annotations for weight and meat quality traits in the local Rotes Höhenvieh (RHV) breed. Traits included 6,003 birth weights (BWT), 5,719 200 d-weights (200dw), 4,594 365 d-weights (365dw), and 547 records for intramuscular fat content (IMF). A total of 581,304 SNP from 370 genotyped cattle with phenotypic records were included in genomic analyses. Model evaluations focused on single- and multiple-trait models with direct and with direct and maternal genetic effects. Genetic relationship matrices were based on pedigree (A-matrix), SNP markers (G-matrix), or both (H-matrix). Genome-wide association studies (GWASs) were carried out using linear mixed models to identify potential candidate genes for the traits of interest. De-regressed proofs (DRP) for direct and maternal genetic components were used as pseudo-phenotypes in the GWAS. Accuracies of direct breeding values were higher from models based on G or on H compared to A. Highest accuracies (> 0.89) were obtained for IMF with multiple-trait models using the G-matrix. Direct heritabilities with maternal genetic effects ranged from 0.62 to 0.66 for BWT, from 0.45 to 0.55 for 200dW, from 0.40 to 0.44 for 365dW, and from 0.48 to 0.75 for IMF. Maternal heritabilities for BWT, 200dW, and 365dW were in a narrow range from 0.21 to 0.24, 0.24 to 0.27, and 0.21 to 0.25, respectively, and from 0.25 to 0.65 for IMF. Direct genetic correlations among body weight traits were positive and favorable, and very similar from different models but showed a stronger variation with 0.31 (A), −0.13 (G), and 0.45 (H) between BWT and IMF. In gene annotations, we identified 6, 3, 1, and 6 potential candidate genes for direct genetic effect on BWT, 200dW, 365dW, and IMF traits, respectively. Regarding maternal genetic effects, four (SHROOM3, ZNF609, PECAM1, and TEX2) and two (TMEM182 and SEC11A) genes were detected as potential candidate genes for BWT and 365dW, respectively. Potential candidate genes for maternal effect on IMF were GRHL2, FGA, FGB, and CTNNA3. As the most important finding from a practical breeding perspective, a small number of genotyped RHV cattle enabled accurate breeding values for high heritability IMF.

The developmental origins of genetic factors influencing language and literacy: Associations with early-childhood vocabulary.

The heritability of language and literacy skills increases from early-childhood to adolescence. The underlying mechanisms are little understood and may involve (a) the amplification of genetic influences contributing to early language abilities, and/or (b) the emergence of novel genetic factors (innovation). Here, we investigate the developmental origins of genetic factors influencing mid-childhood/early-adolescent language and literacy. We evaluate evidence for the amplification of early-childhood genetic factors for vocabulary, in addition to genetic innovation processes. Expressive and receptive vocabulary scores at 38months, thirteen language- and literacy-related abilities and nonverbal cognition (7-13years) were assessed in unrelated children from the Avon Longitudinal Study of Parents and Children (ALSPAC, Nindividuals ≤6,092). We investigated the multivariate genetic architecture underlying early-childhood expressive and receptive vocabulary, and each of 14 mid-childhood/early-adolescent language, literacy or cognitive skills with trivariate structural equation (Cholesky) models as captured by genome-wide genetic relationship matrices. The individual path coefficients of the resulting structural models were finally meta-analysed to evaluate evidence for overarching patterns. We observed little support for the emergence of novel genetic sources for language, literacy or cognitive abilities during mid-childhood or early adolescence. Instead, genetic factors of early-childhood vocabulary, especially those unique to receptive skills, were amplified and represented the majority of genetic variance underlying many of these later complex skills (≤99%). The most predictive early genetic factor accounted for 29.4%(SE=12.9%) to 45.1%(SE=7.6%) of the phenotypic variation in verbal intelligence and literacy skills, but also for 25.7%(SE=6.4%) in performance intelligence, while explaining only a fraction of the phenotypic variation in receptive vocabulary (3.9%(SE=1.8%)). Genetic factors contributing to many complex skills during mid-childhood and early adolescence, including literacy, verbal cognition and nonverbal cognition, originate developmentally in early-childhood and are captured by receptive vocabulary. This suggests developmental genetic stability and overarching aetiological mechanisms.

Evaluation of population stratification adjustment using genome-wide or exonic variants.

Population stratification may cause an inflated type-I error and spurious association when assessing the association between genetic variations with an outcome. Many genetic association studies are now using exonic variants, which captures only 1% of the genome, however, population stratification adjustments have not been evaluated in the context of exonic variants. We compare the performance of two established approaches: principal components analysis (PCA) and mixed-effects models and assess the utility of genome-wide (GW) and exonic variants, by simulation and using a data set from the Framingham Heart Study. Our results illustrate that although the PCs and genetic relationship matrices computed by GW and exonic markers are different, the type-I error rate of association tests for common variants with additive effect appear to be properly controlled in the presence of population stratification. In addition, by considering single nucleotide variants (SNVs) that have different levels of confounding by population stratification, we also compare the power across multiple association approaches to account for population stratification such as PC-based corrections and mixed-effects models. We find that while these two methods achieve a similar power for SNVs that have a low or medium level of confounding by population stratification, mixed-effects model can reach a higher power for SNVs highly confounded by population stratification.

Updating genetic relationship matrices and their inverses: a methodology note

Most of the calculations for genetic relationship matrices and their inverses utilized in recent (t + 1) evaluations for populations of interest can be avoided by updating these matrices at t evaluations for only new animals. This study describes and develops existing methods for updating pedigree-based and marker-based relationship matrices and their inverses. Updating some of the matrices could benefit from parallel computing.

Estimating narrow-sense heritability using family data from admixed populations.

Estimating total narrow-sense heritability in admixed populations remains an open question. In this work, we used extensive simulations to evaluate existing linear mixed-model frameworks for estimating total narrow-sense heritability in two population-based cohorts from Greenland, and compared the results with data from unadmixed individuals from Denmark. When our analysis focused on Greenlandic sib pairs, and under the assumption that shared environment among siblings has a negligible effect, the model with two relationship matrices, one capturing identity by descent and one capturing identity by state, returned heritability estimates close to the true simulated value, while using each of the two matrices alone led to downward biases. When phenotypes correlated with ancestry, heritability estimates were inflated. Based on these observations, we propose a PCA-based adjustment that recovers the true simulated heritability. We use this knowledge to estimate the heritability of ten quantitative traits from the two Greenlandic cohorts, and report differences such as lower heritability for height in Greenlanders compared with Europeans. In conclusion, narrow-sense heritability in admixed populations is best estimated when using a mixture of genetic relationship matrices on individuals with at least one first-degree relative included in the sample.

Introducing M-GCTA a Software Package to Estimate Maternal (or Paternal) Genetic Effects on Offspring Phenotypes.

There is increasing interest within the genetics community in estimating the relative contribution of parental genetic effects on offspring phenotypes. Here we describe the user-friendly M-GCTA software package used to estimate the proportion of phenotypic variance explained by maternal (or alternatively paternal) and offspring genotypes on offspring phenotypes. The tool requires large studies where genome-wide genotype data are available on mother- (or alternatively father-) offspring pairs. The software includes several options for data cleaning and quality control, including the ability to detect and automatically remove cryptically related pairs of individuals. It also allows users to construct genetic relationship matrices indexing genetic similarity across the genome between parents and offspring, enabling the estimation of variance explained by maternal (or alternatively paternal) and offspring genetic effects. We evaluated the performance of the software using a range of data simulations and estimated the computing time and memory requirements. We demonstrate the use of M-GCTA on previously analyzed birth weight data from two large population based birth cohorts, the Avon Longitudinal Study of Parents and Children (ALSPAC) and the Norwegian Mother and Child Cohort Study (MoBa). We show how genetic variation in birth weight is predominantly explained by fetal genetic rather than maternal genetic sources of variation.

Detecting the dominance component of heritability in isolated and outbred human populations

Inconsistencies between published estimates of dominance heritability between studies of human genetic isolates and human outbred populations incite investigation into whether such differences result from particular trait architectures or specific population structures. We analyse simulated datasets, characteristic of genetic isolates and of unrelated individuals, before analysing the isolate of Cilento for various commonly studied traits. We show the strengths of using genetic relationship matrices for variance decomposition over identity-by-descent based methods in a population isolate and that heritability estimates in isolates will avoid the downward biases that may occur in studies of samples of unrelated individuals; irrespective of the simulated distribution of causal variants. Yet, we also show that precise estimates of dominance in isolates are demonstrably problematic in the presence of shared environmental effects and such effects should be accounted for. Nevertheless, we demonstrate how studying isolates can help determine the existence or non-existence of dominance for complex traits, and we find strong indications of non-zero dominance for low-density lipoprotein level in Cilento. Finally, we recommend future study designs to analyse trait variance decomposition from ensemble data across multiple population isolates.

Partitioning Phenotypic Variance Due to Parent-of-Origin Effects Using Genomic Relatedness Matrices

We propose a new method, G-REMLadp, to estimate the phenotypic variance explained by parent-of-origin effects (POEs) across the genome. Our method uses restricted maximum likelihood analysis of genome-wide genetic relatedness matrices based on individuals’ phased genotypes. Genome-wide SNP data from parent child duos or trios is required to obtain relatedness matrices indexing the parental origin of offspring alleles, as well as offspring phenotype data to partition the trait variation into variance components. To calibrate the power of G-REMLadp to detect non-null POEs when they are present, we provide an analytic approximation derived from Haseman-Elston regression. We also used simulated data to quantify the power and Type I Error rates of G-REMLadp, as well as the sensitivity of its variance component estimates to violations of underlying assumptions. We subsequently applied G-REMLadp to 36 phenotypes in a sample of individuals from the Avon Longitudinal Study of Parents and Children (ALSPAC). We found that the method does not seem to be inherently biased in estimating variance due to POEs, and that substantial correlation between parental genotypes is necessary to generate biased estimates. Our empirical results, power calculations and simulations indicate that sample sizes over 10000 unrelated parent-offspring duos will be necessary to detect POEs explaining < 10% of the variance with moderate power. We conclude that POEs tagged by our genetic relationship matrices are unlikely to explain large proportions of the phenotypic variance (i.e. > 15%) for the 36 traits that we have examined.

Assessing non-additive effects in GBLUP model.

Understanding non-additive effects in the expression of quantitative traits is very important in genotype selection, especially in species where the commercial products are clones or hybrids. The use of molecular markers has allowed the study of non-additive genetic effects on a genomic level, in addition to a better understanding of its importance in quantitative traits. Thus, the purpose of this study was to evaluate the behavior of the GBLUP model in different genetic models and relationship matrices and their influence on the estimates of genetic parameters. We used real data of the circumference at breast height in Eucalyptus spp and simulated data from a population of F2. Three commonly reported kinship structures in the literature were adopted. The simulation results showed that the inclusion of epistatic kinship improved prediction estimates of genomic breeding values. However, the non-additive effects were not accurately recovered. The Fisher information matrix for real dataset showed high collinearity in estimates of additive, dominant, and epistatic variance, causing no gain in the prediction of the unobserved data and convergence problems. Estimates presented differences of genetic parameters and correlations considering the different kinship structures. Our results show that the inclusion of non-additive effects can improve the predictive ability or even the prediction of additive effects. However, the high distortions observed in the variance estimates when the Hardy-Weinberg equilibrium assumption is violated due to the presence of selection or inbreeding can converge at zero gains in models that consider epistasis in genomic kinship.

Numericware i: Identical by State Matrix Calculator.

We introduce software, Numericware i, to compute identical by state (IBS) matrix based on genotypic data. Calculating an IBS matrix with a large dataset requires large computer memory and takes lengthy processing time. Numericware i addresses these challenges with 2 algorithmic methods: multithreading and forward chopping. The multithreading allows computational routines to concurrently run on multiple central processing unit (CPU) processors. The forward chopping addresses memory limitation by dividing a dataset into appropriately sized subsets. Numericware i allows calculation of the IBS matrix for a large genotypic dataset using a laptop or a desktop computer. For comparison with different software, we calculated genetic relationship matrices using Numericware i, SPAGeDi, and TASSEL with the same genotypic dataset. Numericware i calculates IBS coefficients between 0 and 2, whereas SPAGeDi and TASSEL produce different ranges of values including negative values. The Pearson correlation coefficient between the matrices from Numericware i and TASSEL was high at .9972, whereas SPAGeDi showed low correlation with Numericware i (.0505) and TASSEL (.0587). With a high-dimensional dataset of 500 entities by 10 000 000 SNPs, Numericware i spent 382 minutes using 19 CPU threads and 64 GB memory by dividing the dataset into 3 pieces, whereas SPAGeDi and TASSEL failed with the same dataset. Numericware i is freely available for Windows and Linux under CC-BY 4.0 license at https://figshare.com/s/f100f33a8857131eb2db.

Heritability and Genome-Wide Association Analyses of Intracranial Carotid Artery Calcification: The Rotterdam Study.

Intracranial carotid artery calcification (ICAC) is one of the most important risk factors for stroke. Although several environmental risk factors for ICAC have been identified, its genetic background remains unclear. Between 2003 and 2006, 2034 participants from the prospective population-based Rotterdam study (mean age: 69.6±6.8 years; 51.7% female) underwent computed tomography to quantify vascular calcification in the intracranial internal carotid artery. Blood samples were drawn for genotyping. Genotypes of the participants were imputed to the 1000 Genomes reference panel to generate genetic relationship matrices for the estimation of the heritability of ICAC volume. Adjustments were made for age and sex. Subsequently, genome-wide association analyses were performed to identify specific variants. The age- and sex-adjusted heritability (h(2)) of ICAC was 47% [standard error (SE): 19%; P=0.009]. Genome-wide association analyses identified a variant on chromosome 9p21.3 (rs1537372; N=2034; P=4.75×10(-9)) and 1 variant on chromosome 11p11.2 (rs11038042, N=2034; P=3.27×10(-8)) that were significantly associated with ICAC volume. Rs1537372 replicated in an independent sample of 716 stroke patients (Pcombined=1.38×10(-10)). ICAC volume is a heritable trait, which is partly explained by common genetic variation. We identified specific genetic variants associated with ICAC, which given the importance of ICAC in stroke risk, needs replication in larger-scale studies to further elucidate its genetic basis.

Heritability and Genome-Wide Association Analyses of Human Gait Suggest Contribution of Common Variants.

Human gait is a complex neurological and musculoskeletal function, of which the genetic basis remains largely unknown. To determine the influence of common genetic variants on gait parameters, we studied 2,946 participants of the Rotterdam Study, a population-based cohort of unrelated elderly individuals. We assessed 30 gait parameters using an electronic walkway, which yielded seven independent gait domains after principal component analysis. Genotypes of participants were imputed to the 1,000 Genomes reference panel for generating genetic relationship matrices to estimate heritability of gait parameters, and for subsequent genome-wide association scans (GWASs) to identify specific variants. Gait domains with the highest age- and sex-adjusted heritability were Variability (h (2) = 61%), Rhythm (37%), and Tandem (32%). For other gait domains, heritability estimates attenuated after adjustment for height and weight. Genome-wide association scans identified a variant on 1p22.3 that was significantly associated with single support time, a variable from the Rhythm domain (rs72953990; N = 2,946; β [SE] = 0.0069 (0.0012), p = 2.30×10(-8)). This variant did not replicate in an independent sample (N = 362; p = .78). In conclusion, human gait has highly heritable components that are explained by common genetic variation, which are partly attributed to height and weight. Collaborative efforts are needed to identify robust single variant associations for the heritable parameters.

The effect of rare alleles on estimated genomic relationships from whole genome sequence data.

BackgroundRelationships between individuals and inbreeding coefficients are commonly used for breeding decisions, but may be affected by the type of data used for their estimation. The proportion of variants with low Minor Allele Frequency (MAF) is larger in whole genome sequence (WGS) data compared to Single Nucleotide Polymorphism (SNP) chips. Therefore, WGS data provide true relationships between individuals and may influence breeding decisions and prioritisation for conservation of genetic diversity in livestock. This study identifies differences between relationships and inbreeding coefficients estimated using pedigree, SNP or WGS data for 118 Holstein bulls from the 1000 Bull genomes project. To determine the impact of rare alleles on the estimates we compared three scenarios of MAF restrictions: variants with a MAF higher than 5%, variants with a MAF higher than 1% and variants with a MAF between 1% and 5%.ResultsWe observed significant differences between estimated relationships and, although less significantly, inbreeding coefficients from pedigree, SNP or WGS data, and between MAF restriction scenarios. Computed correlations between pedigree and genomic relationships, within groups with similar relationships, ranged from negative to moderate for both estimated relationships and inbreeding coefficients, but were high between estimates from SNP and WGS (0.49 to 0.99). Estimated relationships from genomic information exhibited higher variation than from pedigree. Inbreeding coefficients analysis showed that more complete pedigree records lead to higher correlation between inbreeding coefficients from pedigree and genomic data. Finally, estimates and correlations between additive genetic (A) and genomic (G) relationship matrices were lower, and variances of the relationships were larger when accounting for allele frequencies than without accounting for allele frequencies.ConclusionsUsing pedigree data or genomic information, and including or excluding variants with a MAF below 5% showed significant differences in relationship and inbreeding coefficient estimates. Estimated relationships and inbreeding coefficients are the basis for selection decisions. Therefore, it can be expected that using WGS instead of SNP can affect selection decision. Inclusion of rare variants will give access to the variation they carry, which is of interest for conservation of genetic diversity.Electronic supplementary materialThe online version of this article (doi:10.1186/s12863-015-0185-0) contains supplementary material, which is available to authorized users.

Refining genetically inferred relationships using treelet covariance smoothing

Recent technological advances coupled with large sample sets have uncovered many factors underlying the genetic basis of traits and the predisposition to complex disease, but much is left to discover. A common thread to most genetic investigations is familial relationships. Close relatives can be identified from family records, and more distant relatives can be inferred from large panels of genetic markers. Unfortunately these empirical estimates can be noisy, especially regarding distant relatives. We propose a new method for denoising genetically-inferred relationship matrices by exploiting the underlying structure due to hierarchical groupings of correlated individuals. The approach, which we call Treelet Covariance Smoothing, employs a multiscale decomposition of covariance matrices to improve estimates of pairwise relationships. On both simulated and real data, we show that smoothing leads to better estimates of the relatedness amongst distantly related individuals. We illustrate our method with a large genome-wide association study and estimate the "heritability" of body mass index quite accurately. Traditionally heritability, defined as the fraction of the total trait variance attributable to additive genetic effects, is estimated from samples of closely related individuals using random effects models. We show that by using smoothed relationship matrices we can estimate heritability using population-based samples. Finally, while our methods have been developed for refining genetic relationship matrices and improving estimates of heritability, they have much broader potential application in statistics. Most notably, for error-in-variables random effects models and settings that require regularization of matrices with block or hierarchical structure.

Detecting genes for variation in parasite burden and immunological traits in a wild population: testing the candidate gene approach

Identifying the genes underlying phenotypic variation in natural populations can provide novel insight into the evolutionary process. The candidate gene approach has been applied to studies of a number of traits in various species, in an attempt to elucidate their genetic basis. Here, we test the application of the candidate gene approach to identify the loci involved in variation in gastrointestinal parasite burden, a complex trait likely to be controlled by many loci, in a wild population of Soay sheep. A comprehensive literature review, Gene Ontology databases, and comparative genomics resources between cattle and sheep were used to generate a list of candidate genes. In a pilot study, these candidates, along with 50 random genes, were then sequenced in two pools of Soay sheep; one with low gastrointestinal nematode burden and the other high, using a NimbleGen sequence capture experiment. Further candidates were identified from single nucleotide polymorphisms (SNPs) that were highly differentiated between high- and low-resistance sheep breeds. A panel of 192 candidate and control SNPs were then typed in 960 individual Soay sheep to examine whether they individually explained variation in parasite burden, as measured as faecal egg count, as well as two immune measures (Teladorsagia circumcincta-specific antibodies and antinuclear antibodies). The cumulative effect of the candidate and control SNPs were estimated by fitting genetic relationship matrices (GRMs) as random effects in animal models of the three traits. No more significant SNPs were identified in the pilot sequencing experiment and association study than expected by chance. Furthermore, no significant difference was found between the proportions of candidate or control SNPs that were found to be significantly associated with parasite burden/immune measures. No significant effect of the candidate or control gene GRMs was found. There is thus little support for the candidate gene approach to the identification of loci explaining variation in parasitological and immunological traits in this population. However, a number of SNPs explained significant variation in multiple traits and significant correlations were found between the proportions of variance explained by individual SNPs across multiple traits. The significant SNPs identified in this study may still, therefore, merit further investigation.