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1.  On estimation of genetic variance within families using genome-wide identity-by-descent sharing 
Traditionally, heritability and other genetic parameters are estimated from between-family variation. With the advent of dense genotyping, it is now possible to compute the proportion of the genome that is shared by pairs of sibs and thus undertake the estimation within families, thereby avoiding environmental covariances of family members. Formulae for the sampling variance of estimates have been derived previously for families with two sibs, which are relevant for humans, but sampling errors are large. In livestock and plants much larger families can be obtained, and simulation has shown sampling variances are then much smaller.
Based on the assumptions that realised relationship of sibs can be obtained from genomic data and that data are analyzed by restricted maximum likelihood, formulae were derived for the sampling variance of the estimates of genetic variance for arbitrary family sizes. The analysis used statistical differentiation, assuming the variance of relationships is small.
The variance of the estimate of the additive genetic variance was approximately proportional to 1/ (fn2σR2), for f families of size n and variance of relationships σR2.
Because the standard error of the estimate of heritability decreased in proportion to family size, the use of within-family information becomes increasingly efficient as the family size increases. There are however, limitations, such as near complete confounding of additive and dominance variances in full sib families.
PMCID: PMC3871764  PMID: 24007429
2.  The estimation of genetic relationships using molecular markers and their efficiency in estimating heritability in natural populations 
Molecular marker data collected from natural populations allows information on genetic relationships to be established without referencing an exact pedigree. Numerous methods have been developed to exploit the marker data. These fall into two main categories: method of moment estimators and likelihood estimators. Method of moment estimators are essentially unbiased, but utilise weighting schemes that are only optimal if the analysed pair is unrelated. Thus, they differ in their efficiency at estimating parameters for different relationship categories. Likelihood estimators show smaller mean squared errors but are much more biased. Both types of estimator have been used in variance component analysis to estimate heritability. All marker-based heritability estimators require that adequate levels of the true relationship be present in the population of interest and that adequate amounts of informative marker data are available. I review the different approaches to relationship estimation, with particular attention to optimizing the use of this relationship information in subsequent variance component estimation.
PMCID: PMC1569511  PMID: 16048788
Markov Chain Monte Carlo; allele frequency; relatedness; pedigree reconstruction; likelihood
3.  Heritability of Different Forms of Memory in the Late Onset Alzheimer’s Disease Family Study 
The study aim was to estimate the genetic contribution to individual differences in different forms of memory in a large family-based group of older adults. As part of the Late Onset Alzheimer’s Disease Family Study, 899 persons (277 with Alzheimer’s disease, 622 unaffected) from 325 families completed a battery of memory tests from which previously established composite measures of episodic memory, semantic memory, and working memory were derived. Heritability in these measures was estimated using the maximum likelihood variance component method, controlling for age, sex, and education. In analyses of unaffected family members, the adjusted heritability estimates were 0.62 for episodic memory, 0.49 for semantic memory, and 0.72 for working memory, where a heritability estimate of 1 indicates that genetic factors explain all of the phenotypic variance and a heritability of 0 indicates that genetic factors explain none. Adjustment for APOE genotype had little effect on these estimates. When analyses included affected and unaffected family members, adjusted heritability estimates were lower (0.47 for episodic memory, 0.32 for semantic memory, 0.42 for working memory). Adjusting for APOE slightly reduced the estimate for episodic memory (0.40) but had no effect on the remaining estimates. The results indicate that memory functions are under strong genetic influence in older persons with and without AD, only partly attributable to APOE. This suggests that genetic analyses of memory endophenotypes may help to identify genetic variants associated with AD.
PMCID: PMC3130303  PMID: 20930268
Alzheimer’s disease; memory; heritability; apolipoprotein E
4.  Assumptions and Properties of Limiting Pathway Models for Analysis of Epistasis in Complex Traits 
PLoS ONE  2013;8(7):e68913.
For most complex traits, results from genome-wide association studies show that the proportion of the phenotypic variance attributable to the additive effects of individual SNPs, that is, the heritability explained by the SNPs, is substantially less than the estimate of heritability obtained by standard methods using correlations between relatives. This difference has been called the “missing heritability”. One explanation is that heritability estimates from family (including twin) studies are biased upwards. Zuk et al. revisited overestimation of narrow sense heritability from twin studies as a result of confounding with non-additive genetic variance. They propose a limiting pathway (LP) model that generates significant epistatic variation and its simple parametrization provides a convenient way to explore implications of epistasis. They conclude that over-estimation of narrow sense heritability from family data (‘phantom heritability’) may explain an important proportion of missing heritability. We show that for highly heritable quantitative traits large phantom heritability estimates from twin studies are possible only if a large contribution of common environment is assumed. The LP model is underpinned by strong assumptions that are unlikely to hold, including that all contributing pathways have the same mean and variance and are uncorrelated. Here, we relax the assumptions that underlie the LP model to be more biologically plausible. Together with theoretical, empirical, and pragmatic arguments we conclude that in outbred populations the contribution of additive genetic variance is likely to be much more important than the contribution of non-additive variance.
PMCID: PMC3728313  PMID: 23935903
5.  Multilocus estimation of selfing and its heritability 
Heredity  2012;109(3):173-179.
We describe a new method of estimating the selfing rate (S) in a mixed mating population based on a population structure approach that accounts for possible intergenerational correlation in selfing rate, giving rise to an estimate of the upper limit for heritability of selfing rate (h2). A correlation between generations in selfing rate is shown to affect one- and two-locus probabilities of identity by descent. Conventional estimates of selfing rate based on a population structure approach are positively biased by intergenerational correlation in selfing. Multilocus genotypes of individuals are used to give maximum-likelihood estimates of S and h2 in the presence of scoring artifacts. Our multilocus estimation of selfing rate and its heritability (MESH) method was tested with simulated data for a range of conditions. Selfing rate estimates from MESH have low bias and root mean squared error, whereas estimates of the heritability of selfing rate have more uncertainty. Increasing the number of individuals in a sample helps to reduce bias and root mean squared error more than increasing the number of loci of sampled individuals. Improved estimates of selfing rate, as well as estimates of its heritability, can be obtained with this method, although a large number of loci and individuals are needed to achieve best results.
PMCID: PMC3424919  PMID: 22617475
selfing; mixed mating system; descent measures; heritability; bias of selfing rate estimates
6.  Common SNPs explain a large proportion of heritability for human height 
Nature genetics  2010;42(7):565-569.
Single nucleotide polymorphisms (SNPs) discovered by genome-wide association studies (GWASs) account for only a small fraction of the genetic variation of complex traits in human populations. Where is the remaining heritability? We estimated the proportion of variance for human height explained by 294,831 SNPs genotyped on 3,925 unrelated individuals using a linear model analysis, and validated the estimation method by simulations based upon the observed genotype data. We show that 45% of variance can be explained by considering all SNPs simultaneously. Thus, most of the heritability is not missing but has not previously been detected because the individual effects are too small to pass stringent significance tests. We provide evidence that the remaining heritability is due to incomplete linkage disequilibrium (LD) between causal variants and genotyped SNPs, exacerbated by causal variants having lower minor allele frequency (MAF) than the SNPs explored to date.
PMCID: PMC3232052  PMID: 20562875
7.  Heritability of physical activity traits in Brazilian families: the Baependi Heart Study 
BMC Medical Genetics  2011;12:155.
It is commonly recognized that physical activity has familial aggregation; however, the genetic influences on physical activity phenotypes are not well characterized. This study aimed to (1) estimate the heritability of physical activity traits in Brazilian families; and (2) investigate whether genetic and environmental variance components contribute differently to the expression of these phenotypes in males and females.
The sample that constitutes the Baependi Heart Study is comprised of 1,693 individuals in 95 Brazilian families. The phenotypes were self-reported in a questionnaire based on the WHO-MONICA instrument. Variance component approaches, implemented in the SOLAR (Sequential Oligogenic Linkage Analysis Routines) computer package, were applied to estimate the heritability and to evaluate the heterogeneity of variance components by gender on the studied phenotypes.
The heritability estimates were intermediate (35%) for weekly physical activity among non-sedentary subjects (weekly PA_NS), and low (9-14%) for sedentarism, weekly physical activity (weekly PA), and level of daily physical activity (daily PA). Significant evidence for heterogeneity in variance components by gender was observed for the sedentarism and weekly PA phenotypes. No significant gender differences in genetic or environmental variance components were observed for the weekly PA_NS trait. The daily PA phenotype was predominantly influenced by environmental factors, with larger effects in males than in females.
Heritability estimates for physical activity phenotypes in this sample of the Brazilian population were significant in both males and females, and varied from low to intermediate magnitude. Significant evidence for heterogeneity in variance components by gender was observed. These data add to the knowledge of the physical activity traits in the Brazilian study population, and are concordant with the notion of significant biological determination in active behavior.
PMCID: PMC3247825  PMID: 22126647
8.  Genetic and Environmental Influences on Infant Weight and Weight Change: The Fels Longitudinal Study 
Despite significant progress in understanding the mechanisms by which the prenatal/maternal environment can alter development and adult health, genetic influences on normal variation in growth are little understood. This work examines genetic and nongenetic contributions to body weight and weight change during infancy and the relationships between weight change and adult body composition. The dataset included 501 white infants in 164 nuclear and extended families in the Fels Longitudinal Study, each with 10 serial measures of weight from birth to age 3 years and 232 with body composition data in mid-adulthood. Herit-ability and covariate effects on weight and weight z-score change from birth to 2 years of age were estimated using a maximum likelihood variance decomposition method. Additive genetic effects explained a high proportion of the variance in infant weight status (h2 = 0.61–0.95), and change in weight z-score (h2 = 0.56–0.82). Covariate effects explained 27% of the phenotypic variance at 0–1 month of age and declined in effect to 6.9% of phenotypic variance by 36 months. Significant sex, gestational age, birth order, birth year, and maternal body mass index effects were also identified. For both sexes, a significant increase in weight z-score (>2 SD units) (upward centile crossing) was associated with greater adulthood stature, fat mass, and percent body fat than decrease or stability in weight z-score. Understanding genetic influences on growth rate in a well-nourished, nutritionally stable population may help us interpret the causes and consequences of centile crossing in nutritionally compromised contexts.
PMCID: PMC2801417  PMID: 17639582
9.  Quantitative genetics of cortical bone mass in healthy 10-year-old children from the Fels Longitudinal Study 
Bone  2006;40(2):464-470.
The genetic influences on bone mass likely change throughout the life span, but most genetic studies of bone mass regulation have focused on adults. There is, however, a growing awareness of the importance of genes influencing the acquisition of bone mass during childhood on lifelong bone health. The present investigation examines genetic influences on childhood bone mass by estimating the residual heritabilities of different measures of second metacarpal bone mass in a sample of 600 10-year-old participants from 144 families in the Fels Longitudinal Study. Bivariate quantitative genetic analyses were conducted to estimate genetic correlations between cortical bone mass measures, and measures of bone growth and development. Using a maximum likelihood-based variance components method for pedigree data, we found a residual heritability estimate of 0.71 for second metacarpal cortical index. Residual heritability estimates for individual measures of cortical bone (e.g., lateral cortical thickness, medial cortical thickness) ranged from 0.47 to 0.58, at this pre-pubertal childhood age. Low genetic correlations were found between cortical bone measures and both bone length and skeletal age. However, after Bonferonni adjustment for multiple testing, ρG was not significantly different from 0 for any of these pairs of traits. Results of this investigation provide evidence of significant genetic control over bone mass largely independent of maturation while bones are actively growing and before rapid accrual of bone that typically occurs during puberty.
PMCID: PMC1945206  PMID: 17056310
bone size; genetics; radiography; maturation
10.  Single-Tissue and Cross-Tissue Heritability of Gene Expression Via Identity-by-Descent in Related or Unrelated Individuals 
PLoS Genetics  2011;7(2):e1001317.
Family studies of individual tissues have shown that gene expression traits are genetically heritable. Here, we investigate cis and trans components of heritability both within and across tissues by applying variance-components methods to 722 Icelanders from family cohorts, using identity-by-descent (IBD) estimates from long-range phased genome-wide SNP data and gene expression measurements for ∼19,000 genes in blood and adipose tissue. We estimate the proportion of gene expression heritability attributable to cis regulation as 37% in blood and 24% in adipose tissue. Our results indicate that the correlation in gene expression measurements across these tissues is primarily due to heritability at cis loci, whereas there is little sharing of trans regulation across tissues. One implication of this finding is that heritability in tissues composed of heterogeneous cell types is expected to be more dominated by cis regulation than in tissues composed of more homogeneous cell types, consistent with our blood versus adipose results as well as results of previous studies in lymphoblastoid cell lines. Finally, we obtained similar estimates of the cis components of heritability using IBD between unrelated individuals, indicating that transgenerational epigenetic inheritance does not contribute substantially to the “missing heritability” of gene expression in these tissue types.
Author Summary
An important goal in biology is to understand how genotype affects gene expression. Because gene expression varies across tissues, the relationship between genotype and gene expression may be tissue-specific. In this study, we used heritability approaches to study the regulation of gene expression in two tissue types, blood and adipose tissue, as well as the regulation of gene expression that is shared across these tissues. Heritability can be partitioned into cis and trans effects by assessing identity-by-descent (IBD) at the genomic location close to the expressed gene or genome-wide, respectively, and applying variance-components methods to partition the heritability of each gene. We estimated the proportion of gene expression heritability explained by cis regulation as 37% in blood and 24% in adipose tissue. Notably, the heritability shared across tissue types was primarily due to cis regulation. Thus, the relative contribution of cis versus trans regulation is expected to increase with the number of cell types present in the tissue being assayed, just as observed in our study and in a comparison to previous work on lymphoblastoid cell lines (LCL). We specifically ruled out a substantial contribution of transgenerational epigenetic inheritance to heritability of gene expression in these cohorts by repeating our heritability analyses using segments shared IBD in distantly related Icelanders.
PMCID: PMC3044684  PMID: 21383966
11.  Genetic analyses of smoking initiation, persistence, quantity, and age-at-onset of regular cigarette use in Brazilian families: the Baependi Heart Study 
BMC Medical Genetics  2012;13:9.
The purpose of this study was to estimate the genetic influences on the initiation of cigarette smoking, the persistence, quantity and age-at-onset of regular cigarette use in Brazilian families.
The data set consisted of 1,694 individuals enrolled in the Baependi Heart Study. The heritability and the heterogeneity in genetic and environmental variance components by gender were estimated from variance components approaches, using the SOLAR (Sequential Oligogenic Linkage Analysis Routines) computer package. The mixed-effects Cox model was used for the genetic analysis of the age-at onset of regular cigarette use.
The heritability estimates were high (> 50%) for smoking initiation and were intermediate, ranging from 23.4 to 31.9%, for smoking persistence and quantity. Significant evidence for heterogeneity in variance components by gender was observed for smoking initiation and age-at-onset of regular cigarette use. Genetic factors play an important role in the interindividual variation of these phenotypes in females, while in males there is a predominant environmental component, which could be explained by greater social influences in the initiation of tobacco use.
Significant heritabilities were observed in smoking phenotypes for both males and females from the Brazilian population. These data add to the literature and are concordant with the notion of significant biological determination in smoking behavior. Samples from the Baependi Heart Study may be valuable for the mapping of genetic loci that modulate this complex biological trait.
PMCID: PMC3395823  PMID: 22289947
12.  Genetic Analysis of Serum Osteocalcin and Bone Mineral in Multigenerational Afro-Caribbean Families 
Osteocalcin (OC) is a protein constituent of bone matrix and a marker of bone formation. We characterized the heritability of serum OC measures and identified genomic regions potentially involved in the regulation of OC via high-density genome-wide linkage analysis in African ancestry individuals.
African ancestry individuals (n=459) were recruited, without regard to health status, from seven probands (mean family size = 66; 4,373 relative pairs). Residual heritability of serum OC measures was estimated and multipoint quantitative trait linkage analysis was performed using pedigree-based maximum likelihood methods.
Residual heritabilities of total OC, uncarboxylated OC, carboxylated OC and percent uncarboxylated OC were: 0.74±0.10, 0.89±0.08, 0.46±0.10 and 0.41±0.09, respectively. All OC measures were genetically correlated with whole body bone mineral content (BMC). We obtained strong evidence of bivariate linkage for percent uncarboxylated OC and whole body BMC on chromosome 17 (LOD=3.15, 99cM).
All forms of OC were highly heritable and genetically correlated with total body BMC in these African ancestry families. The identified linkage region contains several candidate genes for bone and energy metabolism including COL1A1 and TNFRSF11A. Further studies of this genomic region may reveal novel insight into the genetic regulation of OC and bone mineralization.
PMCID: PMC3768139  PMID: 21935688
osteocalcin; genome-wide linkage; African ancestry; bone mineral
13.  The Robustness of Generalized Estimating Equations for Association Tests in Extended Family Data 
Human heredity  2012;74(1):17-26.
Variance-component analysis (VCA), the traditional method for handling correlations within families in genetic association studies, is computationally intensive for genome-wide analyses, and the computational burden of VCA, a likelihood-based test, increases with family size and the number of genetic markers. Alternative approaches that do not require the computation of familial correlations is preferable, provided that they do not inflate type I error or decrease power. We performed a simulation study to evaluate practical alternatives to VCA that use regression with generalized estimating equations (GEE) in extended family data. We compared the properties of linear regression with GEE applied to an entire extended family structure (GEE-EXT) and GEE applied to nuclear family structures split from these extended families (GEE-SPL) to variance-components likelihood-based methods (FastAssoc). GEE-EXT was evaluated with and without robust variance estimators to estimate the standard errors. We observed similar average type I error rates from GEE-EXT and FastAssoc compared to GEE-SPL. Type I error rates for the GEE-EXT method with a robust variance estimator were marginally higher than the nominal rate when the MAF was < 0.1, but were close to nominal rate when MAF ≥ 0.2. All methods gave consistent effect estimates and had similar power. In summary, the GEE framework with the robust variance estimator, the computationally fastest and least data management intensive, appears to work well in extended families and thus provides a reasonable alternative to full variance components approaches for extended pedigrees in the GWAS setting.
PMCID: PMC3736986  PMID: 23038411
Generalized estimating equation; Variance components analysis; Family-based association study; Genome-wide scan
14.  Heritability of Susceptibility to Ionizing Radiation Induced Apoptosis of Human Lymphocyte Subpopulations 
To evaluate heritability of intrinsic radiosensitivity, induction of apoptosis in lymphocyte subpopulations was determined on samples from related individuals belonging to large kindred-families.
Methods and Materials
Quiescent lymphocytes from 334 healthy individuals were gamma-irradiated in vitro. Apoptosis was determined 18 hours post-irradiation by 8-color flow cytometry. Radiosensitivity was quantified from dose-effect curves. Intra-familial correlations and heritability were computed on 199 father-mother-offspring trios using the programs. SOLAR and SAGE. Segregation analyses were conducted using SAGE.
Marked differential susceptibility of naïve and memory T lymphocytes was demonstrated, and although age and sex were significant covariates, their effects only accounted for a minor part of the inter-individual variation. Parent-offspring and sib-sib correlations were significant for radiosensitivity of B cells, T4, T8, and of effector memory (EM) T4- and T8 subpopulations. In the T4-EM subpopulation, the phenotype showed correlations most consistent with dominant or additive genetic effects and segregation analysis was consistent with the contribution of a bi-allelic dominant locus.
Heritability was demonstrated for the susceptibility to ionizing radiation induced apoptosis of lymphocyte populations and segregation of the T4-EM radiosensitivity phenotype was consistent with a simple Mendelian transmission model involving one major gene.
PMCID: PMC1994900  PMID: 17637392
Individual radiosensitivity; radiation biology; family studies; apoptosis
15.  Genetic parameters for milk, fat and protein yields in Murrah buffaloes (Bubalus bubalis Artiodactyla, Bovidae) 
Genetics and Molecular Biology  2010;33(1):71-77.
The objective of the present study was to estimate genetic parameters for test-day milk, fat and protein yields and 305-day-yields in Murrah buffaloes. 4,757 complete lactations of Murrah buffaloes were analyzed. Co-variance components were estimated by the restricted maximum likelihood method. The models included additive direct genetic and permanent environmental effects as random effects, and the fixed effects of contemporary group, milking number and age of the cow at calving as linear and quadratic covariables. Contemporary groups were defined by herd-year-month of test for test-day yields and by herd-year-season of calving for 305-day yields. The heritability estimates obtained by two-trait analysis ranged from 0.15 to 0.24 for milk, 0.16 to 0.23 for protein and 0.13 to 0.22 for fat, yields. Genetic and phenotypic correlations were all positive. The observed population additive genetic variation indicated that selection might be an effective tool in changing population means in milk, fat and protein yields.
PMCID: PMC3036093  PMID: 21637608
test-day model; accumulated productions; heritability; genetic correlations
16.  Correlation and heritability in neuroimaging datasets: A spatial decomposition approach with application to an fMRI study of twins 
NeuroImage  2011;59(2):1132-1142.
Advances in modern neuroimaging in combination with behavioral genetics have allowed neuroscientists to investigate how genetic and environmental factors shape human brain structure and function. Estimating the heritability of brain structure and function via twin studies has become one of the major approaches in studying the genetics of the brain. In a classical twin study, heritability is estimated by computing genetic and phenotypic variation based on the similarity of monozygotic and dizygotic twins. However, heritability has traditionally been measured for univariate, scalar traits, and it is challenging to assess the heritability of a spatial process, such as a pattern of neural activity. In this work, we develop a statistical method to estimate phenotypic variance and covariance at each location in a spatial process, which in turn can be used to estimate the heritability of a spatial dataset. The method is based on a dimensionally-reduced model of spatial variation in paired images, in which adjusted least squares estimates can be used to estimate the key model parameters. The advantage of the proposed method compared to conventional methods such as a voxelwise or mean-ROI approaches is demonstrated in both a simulation study and a real data study assessing genetic influence on patterns of brain activity in the visual and motor cortices in response to a simple visuomotor task.
PMCID: PMC3219840  PMID: 21763433
Heritability; Intraclass Correlation; Twin Study; Spatial Analysis; Genetics
17.  Estimating Heritabilities and Genetic Correlations: Comparing the ‘Animal Model’ with Parent-Offspring Regression Using Data from a Natural Population 
PLoS ONE  2008;3(3):e1739.
Quantitative genetic parameters are nowadays more frequently estimated with restricted maximum likelihood using the ‘animal model’ than with traditional methods such as parent-offspring regressions. These methods have however rarely been evaluated using equivalent data sets. We compare heritabilities and genetic correlations from animal model and parent-offspring analyses, respectively, using data on eight morphological traits in the great reed warbler (Acrocephalus arundinaceus). Animal models were run using either mean trait values or individual repeated measurements to be able to separate between effects of including more extended pedigree information and effects of replicated sampling from the same individuals. We show that the inclusion of more pedigree information by the use of mean traits animal models had limited effect on the standard error and magnitude of heritabilities. In contrast, the use of repeated measures animal model generally had a positive effect on the sampling accuracy and resulted in lower heritabilities; the latter due to lower additive variance and higher phenotypic variance. For most trait combinations, both animal model methods gave genetic correlations that were lower than the parent-offspring estimates, whereas the standard errors were lower only for the mean traits animal model. We conclude that differences in heritabilities between the animal model and parent-offspring regressions were mostly due to the inclusion of individual replicates to the animal model rather than the inclusion of more extended pedigree information. Genetic correlations were, on the other hand, primarily affected by the inclusion of more pedigree information. This study is to our knowledge the most comprehensive empirical evaluation of the performance of the animal model in relation to parent-offspring regressions in a wild population. Our conclusions should be valuable for reconciliation of data obtained in earlier studies as well as for future meta-analyses utilizing estimates from both traditional methods and the animal model.
PMCID: PMC2254494  PMID: 18320057
18.  The influence of animals from embryo transfer on the genetic evaluation of growth in Simmental beef cattle by using multi-trait models 
Genetics and Molecular Biology  2013;36(1):43-49.
The weight records from Simmental beef cattle were used in a genetic evaluation of growth with or without the inclusion of animals obtained by embryo transfer. A multi-trait model in which embryo transfer individuals were excluded (MTM1) contained 29,510 records from 10,659 animals, while another model without exclusion of these animals (MTM2) contained 62,895 weight records from 23,160 animals. The weight records were adjusted for ages of 100, 205, 365, 450, 550 and 730 days. The (co)variance components and genetic parameters were estimated by the restricted maximum likelihood method. The (co)variance components were similar in both models, except for maternal permanent environment variance. Direct heritabilities (h2d) in MTM1 were 0.04, 0.11, 0.20, 0.27, 0.31 and 0.42, while in MTM2 they were 0.11, 0.11, 0.17, 0.21, 0.22 and 0.26 for 100, 205, 365, 450, 550 and 730 days of age, respectively. Estimates of h2d in MTM1 were higher than in MTM2 for the weight at 365 days of age. Genetic correlations between weights in both models ranged from moderate to high, suggesting that these traits may be determined mainly by the same genes. Animals from embryo transfer may be included in the genetic evaluation of Simmental beef cattle in Brazil; this inclusion may provide potential gains in accuracy and genetic gains by reducing the interval between generations.
PMCID: PMC3615524  PMID: 23569407
body weight; (co)variance components; heritability
19.  Patterns of methylation heritability in a genome-wide analysis of four brain regions 
Nucleic Acids Research  2013;41(4):2095-2104.
DNA methylation has been implicated in a number of diseases and other phenotypes. It is, therefore, of interest to identify and understand the genetic determinants of methylation and epigenomic variation. We investigated the extent to which genetic variation in cis-DNA sequence explains variation in CpG dinucleotide methylation in publicly available data for four brain regions from unrelated individuals, finding that 3–4% of CpG loci assayed were heritable, with a mean estimated narrow-sense heritability of 30% over the heritable loci. Over all loci, the mean estimated heritability was 3%, as compared with a recent twin-based study reporting 18%. Heritable loci were enriched for open chromatin regions and binding sites of CTCF, an influential regulator of transcription and chromatin architecture. Additionally, heritable loci were proximal to genes enriched in several known pathways, suggesting a possible functional role for these loci. Our estimates of heritability are conservative, and we suspect that the number of identified heritable loci will increase as the methylome is assayed across a broader range of cell types and the density of the tested loci is increased. Finally, we show that the number of heritable loci depends on the window size parameter commonly used to identify candidate cis-acting single-nucleotide polymorphism variants.
PMCID: PMC3575819  PMID: 23303775
20.  Modelling the growth curve of Maine-Anjou beef cattle using heteroskedastic random coefficients models 
A heteroskedastic random coefficients model was described for analyzing weight performances between the 100th and the 650th days of age of Maine-Anjou beef cattle. This model contained both fixed effects, random linear regression and heterogeneous variance components. The objective of this study was to analyze the difference of growth curves between animals born as twin and single bull calves. The method was based on log-linear models for residual and individual variances expressed as functions of explanatory variables. An expectation-maximization (EM) algorithm was proposed for calculating restricted maximum likelihood (REML) estimates of the residual and individual components of variances and covariances. Likelihood ratio tests were used to assess hypotheses about parameters of this model. Growth of Maine-Anjou cattle was described by a third order regression on age for a mean growth curve, two correlated random effects for the individual variability and independent errors. Three sources of heterogeneity of residual variances were detected. The difference of weight performance between bulls born as single and twin bull calves was estimated to be equal to about 15 kg for the growth period considered.
PMCID: PMC2705454  PMID: 12270103
heteroskedastic random coefficient model; EM-REML; robust estimators; growth curve; Maine-Anjou breed
21.  Genetic and Environmental Contributions to Carotid Intima-Media Thickness and Obesity Phenotypes in the Northern Manhattan Family Study 
Background and Purpose
Both carotid intima-media thickness (IMT) and obesity are independent determinants of stroke and cardiovascular disease. The prevalence of obesity is higher in Hispanics. The genetic basis of IMT and obesity has not been well-characterized in Caribbean Hispanics. The purpose of this study was to examine the genetic and environmental contributions to IMT and obesity in this population.
The data included 440 subjects from 77 Caribbean Hispanic families. Mean IMT and maximum IMT were measured in the internal carotid artery, common carotid artery, and carotid bifurcation. The total IMT was calculated as the mean value of IMT at all segments. Obesity phenotypes included body mass index (BMI), waist circumference, waist-to-hip ratio (WHR), and skin-fold thickness. Variance component methods were used to estimate age-adjusted and sex-adjusted heritability. Bivariate analyses were conducted to test for genetic and environmental correlations between IMT and obesity.
Heritabilities for IMT ranged from 9% to 40%, with the highest for total maximum IMT and lowest for internal carotid artery maximum IMT. Heritabilities for BMI, waist circumference, WHR, and skin-fold thickness were 44%, 47%, 5%, and 36%, respectively. There were significant genetic, but not environmental, correlations between IMT and BMI, waist circumference, and skin-fold thickness. There were no genetic or environmental correlations between IMT and WHR.
We found a substantial genetic contribution to IMT, BMI, waist circumference, and skin-fold thickness. Obesity and IMT may share common genetic factors. Future gene mapping studies are warranted to identify genes predisposing to IMT and obesity in this population.
PMCID: PMC1325223  PMID: 15331789
carotid arteries; genetics; obesity; stroke
22.  Finding the missing heritability in pediatric obesity: the contribution of genome-wide complex trait analysis 
Known single-nucleotide polymorphisms (SNPs) explain <2% of the variation in body mass index (BMI) despite the evidence of >50% heritability from twin and family studies, a phenomenon termed ‘missing heritability'. Using DNA alone for unrelated individuals, a novel method (in a software package called Genome-wide Complex Trait Analysis, GCTA) estimates the total additive genetic influence due to common SNPs on whole-genome arrays. GCTA has made major inroads into explaining the ‘missing heritability' of BMI in adults. This study provides the first GCTA estimate of genetic influence on adiposity in children. Participants were from the Twins Early Development Study (TEDS), a British twin birth cohort. BMI s.d. scores (BMI-SDS) were obtained from validated parent-reported anthropometric measures when children were about 10 years old (mean=9.9; s.d.=0.84). Selecting one child per family (n=2269), GCTA results from 1.7 million DNA markers were used to quantify the additive genetic influence of common SNPs. For direct comparison, a standard twin analysis in the same families estimated the additive genetic influence as 82% (95% CI: 0.74–0.88, P<0.001). GCTA explained 30% of the variance in BMI-SDS (95% CI: 0.02–0.59; P=0.02). These results indicate that 37% of the twin-estimated heritability (30/82%) can be explained by additive effects of multiple common SNPs, and provide compelling evidence for strong genetic influence on adiposity in childhood.
PMCID: PMC3826033  PMID: 23528754
Genome-wide Complex Trait Analysis (GCTA); missing heritability; children; twins; genetics
23.  Quantitative genetic analysis of responses to larval food limitation in a polyphenic butterfly indicates environment- and trait-specific effects 
Ecology and Evolution  2013;3(10):3576-3589.
Different components of heritability, including genetic variance (VG), are influenced by environmental conditions. Here, we assessed phenotypic responses of life-history traits to two different developmental conditions, temperature and food limitation. The former represents an environment that defines seasonal polyphenism in our study organism, the tropical butterfly Bicyclus anynana, whereas the latter represents a more unpredictable environment. We quantified heritabilities using restricted maximum likelihood (REML) procedures within an “Information Theoretical” framework in a full-sib design. Whereas development time, pupal mass, and resting metabolic rate showed no genotype-by-environment interaction for genetic variation, for thorax ratio and fat percentage the heritability increased under the cool temperature, dry season environment. Additionally, for fat percentage heritability estimates increased under food limitation. Hence, the traits most intimately related to polyphenism in B. anynana show the most environmental-specific heritabilities as well as some indication of cross-environmental genetic correlations. This may reflect a footprint of natural selection and our future research is aimed to uncover the genes and processes involved in this through studying season and condition-dependent gene expression.
PMCID: PMC3797501  PMID: 24223292
Environment; heritability; life history; reaction norm; stress
24.  Family-based genome-wide association study for simulated data of Framingham Heart Study 
BMC Proceedings  2009;3(Suppl 7):S124.
Genome-wide association studies (GWAS) have quickly become the norm in dissecting the genetic basis of complex diseases. Family-based association approaches have the advantages of being robust to possible hidden population structure in samples. Most of these methods were developed with limited markers. Their applicability and performance for GWAS need to be examined. In this report, we evaluated the properties of the family-based association method implemented by ASSOC in the S.A.G.E package using the simulated data sets for the Framingham Heart Study, and found that ASSOC is a highly useful tool for GWAS.
PMCID: PMC2795897  PMID: 20017990
25.  Correcting for bias in estimation of quantitative trait loci effects 
Estimates of quantitative trait loci (QTL) effects derived from complete genome scans are biased, if no assumptions are made about the distribution of QTL effects. Bias should be reduced if estimates are derived by maximum likelihood, with the QTL effects sampled from a known distribution. The parameters of the distributions of QTL effects for nine economic traits in dairy cattle were estimated from a daughter design analysis of the Israeli Holstein population including 490 marker-by-sire contrasts. A separate gamma distribution was derived for each trait. Estimates for both the α and β parameters and their SE decreased as a function of heritability. The maximum likelihood estimates derived for the individual QTL effects using the gamma distributions for each trait were regressed relative to the least squares estimates, but the regression factor decreased as a function of the least squares estimate. On simulated data, the mean of least squares estimates for effects with nominal 1% significance was more than twice the simulated values, while the mean of the maximum likelihood estimates was slightly lower than the mean of the simulated values. The coefficient of determination for the maximum likelihood estimates was five-fold the corresponding value for the least squares estimates.
PMCID: PMC2697222  PMID: 16093012
genetic markers; quantitative trait loci; genome scans; maximum likelihood; dairy cattle

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