Variance components models for gene-environment interaction in twin analysis.

Gene-environment interaction is likely to be a common and important source of variation for complex behavioral traits. Often conceptualized as the genetic control of sensitivity to the environment, it can be incorporated in variance components twin analyses by partitioning genetic effects into a mean part, which is independent of the environment, and a part that is a linear function of the environment. The model allows for one or more environmental moderator variables (that possibly interact with each other) that may i). be continuous or binary ii). differ between twins within a pair iii). interact with residual environmental as well as genetic effects iv) have nonlinear moderating properties v). show scalar (different magnitudes) or qualitative (different genes) interactions vi). be correlated with genetic effects acting upon the trait, to allow for a test of gene-environment interaction in the presence of gene-environment correlation. Aspects and applications of a class of models are explored by simulation, in the context of both individual differences twin analysis and, in a companion paper (Purcell & Sham, 2002) sibpair quantitative trait locus linkage analysis. As well as elucidating environmental pathways, consideration of gene-environment interaction in quantitative and molecular studies will potentially direct and enhance gene-mapping efforts.     

Estimating the parameters of the incompletely penetrant single locus model using multiple populations

A method involving the comparison of two or more populations is suggested as a means of obtaining a unique solution to the parameters of the incompletely penetrant single locus model. The proposed method allows a test of the assumptions of the model when three or more populations are compared. Equations that allow the inclusion of data on twin concordance rates and/or the proportion of affected children given neither, one or both parents affected are also given. Finally, some implications of fitting the model are discussed in terms of genetic counseling, residual environmental variance and the concept of heritability as applied to dichotomous traits.     

Estimating two-stage models for genetic influences on alcohol, tobacco or drug use initiation and dependence vulnerability in twin and family data.

Genetic research on risk of alcohol, tobacco or drug dependence must make allowance for the partial overlap of risk-factors for initiation of use, and risk-factors for dependence or other outcomes in users. Except in the extreme cases where genetic and environmental risk-factors for initiation and dependence overlap completely or are uncorrelated, there is no consensus about how best to estimate the magnitude of genetic or environmental correlations between Initiation and Dependence in twin and family data. We explore by computer simulation the biases to estimates of genetic and environmental parameters caused by model misspecification when Initiation can only be defined as a binary variable. For plausible simulated parameter values, the two-stage genetic models that we consider yield estimates of genetic and environmental variances for Dependence that, although biased, are not very discrepant from the true values. However, estimates of genetic (or environmental) correlations between Initiation and Dependence may be seriously biased, and may differ markedly under different two-stage models. Such estimates may have little credibility unless external data favor selection of one particular model. These problems can be avoided if Initiation can be assessed as a multiple-category variable (e.g. never versus early-onset versus later onset user), with at least two categories measurable in users at risk for dependence. Under these conditions, under certain distributional assumptions, recovery of simulated genetic and environmental correlations becomes possible. Illustrative application of the model to Australian twin data on smoking confirmed substantial heritability of smoking persistence (42%) with minimal overlap with genetic influences on initiation.     

Gaining New Insights into How Genetic Factors Influence Human Dental Development by Studying Twins

Many previous attempts to quantify the contribution of genetic factors to human dental variation using the classical twin design have been based on untested assumptions that lead to unreliable estimates of heritability. We have applied structural equation modelling to several different dental phenotypes in a sample of over 600 pairs of Australian twins, enabling the goodness-of-fit of the data to be tested against genetic models incorporating different components of genetic and environmental variance. Our results indicate that the contribution of additive genetic effects to phenotypic variation differs considerably between different dental traits. Heritability estimates for intercuspal distances of molar teeth and for incisal overbite and overjet are low to moderate in magnitude, whereas heritabilities for overall molar crown size and arch dimensions are moderate to high. We propose that after formation of the enamel knots during odontogenesis, the emerging pattern of molar cusps results from a cascade of local epigenetic events, rather than being under direct genetic control. Variation in molar crown size is explained best by a model incorporating additive genetic effects, as well as environmental influences that are both unique and common to co-twins. These environmental influences presumably operate in utero during the early stages of molar odontogenesis prior to crown calcification. The relatively low heritabilities noted for occlusal traits are consistent with the importance of masticatory activity and muscle function in determining the interrelationships between teeth in opposing dental arches. We believe that well-designed studies of twins, coupled with modern genome-scanning approaches, offer great potential to identify key “dental” genes and to clarify how these genes interact with the environment during development.     

母体遗传效应对青海细毛羊生产性能遗传参数估计的影响

为了研究母体遗传效应对青海细毛羊生长性状、产毛性状的影响,文章采用平均信息最大约束似然法应用不同混合动物模型估计青海细毛羊生产性状的遗传参数,并采用似然比检验对不同模型进行比较分析。各模型中均包括固定效应、个体直接加性遗传效应、残差效应;随机效应为:个体永久环境效应、母体遗传效应、母体永久环境效应。不同模型对随机效应作了不同考虑:模型1不考虑个体永久环境效应、母体遗传效应、母体永久环境效应;模型2考虑母体永久环境效应;模型3考虑母体遗传效应;模型4考虑母体遗传效应和母体永久环境效应;模型5考虑个体永久环境效应和母体遗传效应;模型6考虑个体永久环境效应、母体遗传效应、母体永久环境效应。各模型估计的初生重遗传力为:0.1896~0.3781;断奶重遗传力为:0.2537~0.2890;周岁重遗传力范围:0.2244~0.3225;成年羊体重遗传力范围:0.2205~0.3983;产毛量遗传力为:0.1218~0.1490;羊毛细度遗传力为:0.0983~0.4802;羊毛长度遗传力为:0.1170~0.1311。与模型1相比,模型3对于初生重、断奶重差异显著(P<0.01),对于周岁重、成年羊体重各模型与模型1的似然比检验差异不显著(P>0.05);与模型6相比,模型4、5对于羊毛细度差异显著(P<0.01),模型4对羊毛长度差异显著(P<0.05),对于产毛量各模型与模型6似然比检验差异不显著(P>0.05)。生长性状中初生重、断奶重受母体遗传效应影响显著,周岁重、成年羊体重受母体遗传效应影响不显著;产毛性状中羊毛细度、长度受母体遗传效应影响显著,产毛量受母体遗传效应影响较弱。     

母体遗传效应对青海细毛羊生产性能遗传参数估计的影响

为了研究母体遗传效应对青海细毛羊生长性状、产毛性状的影响, 文章采用平均信息最大约束似然法应用不同混合动物模型估计青海细毛羊生产性状的遗传参数, 并采用似然比检验对不同模型进行比较分析。各模型中均包括固定效应、个体直接加性遗传效应、残差效应; 随机效应为：个体永久环境效应、母体遗传效应、母体永久环境效应。不同模型对随机效应作了不同考虑：模型1不考虑个体永久环境效应、母体遗传效应、母体永久环境效应; 模型2考虑母体永久环境效应; 模型3考虑母体遗传效应; 模型4考虑母体遗传效应和母体永久环境效应; 模型5考虑个体永久环境效应和母体遗传效应; 模型6考虑个体永久环境效应、母体遗传效应、母体永久环境效应。各模型估计的初生重遗传力为：0.1896~0.3781; 断奶重遗传力为：0.2537~0.2890; 周岁重遗传力范围：0.2244~0.3225; 成年羊体重遗传力范围：0.2205~0.3983; 产毛量遗传力为：0.1218~0.1490; 羊毛细度遗传力为：0.0983~0.4802; 羊毛长度遗传力为：0.1170~0.1311。与模型1相比, 模型3对于初生重、断奶重差异显著(P<0.01), 对于周岁重、成年羊体重各模型与模型1的似然比检验差异不显著(P>0.05); 与模型6相比, 模型4、5对于羊毛细度差异显著(P<0.01), 模型4对羊毛长度差异显著(P<0.05), 对于产毛量各模型与模型6似然比检验差异不显著(P>0.05)。生长性状中初生重、断奶重受母体遗传效应影响显著, 周岁重、成年羊体重受母体遗传效应影响不显著; 产毛性状中羊毛细度、长度受母体遗传效应影响显著, 产毛量受母体遗传效应影响较弱。     

Heritability of adult body height: a comparative study of twin cohorts in eight countries.

A major component of variation in body height is due to genetic differences, but environmental factors have a substantial contributory effect. In this study we aimed to analyse whether the genetic architecture of body height varies between affluent western societies. We analysed twin data from eight countries comprising 30,111 complete twin pairs by using the univariate genetic model of the Mx statistical package. Body height and zygosity were self-reported in seven populations and measured directly in one population. We found that there was substantial variation in mean body height between countries; body height was least in Italy (177 cm in men and 163 cm in women) and greatest in the Netherlands (184 cm and 171 cm, respectively). In men there was no corresponding variation in heritability of body height, heritability estimates ranging from 0.87 to 0.93 in populations under an additive genes/unique environment (AE) model. Among women the heritability estimates were generally lower than among men with greater variation between countries, ranging from 0.68 to 0.84 when an additive genes/shared environment/unique environment (ACE) model was used. In four populations where an AE model fit equally well or better, heritability ranged from 0.89 to 0.93. This difference between the sexes was mainly due to the effect of the shared environmental component of variance, which appears to be more important among women than among men in our study populations. Our results indicate that, in general, there are only minor differences in the genetic architecture of height between affluent Caucasian populations, especially among men.     

Genetic evaluation and selection response for growth in meat-type quail through random regression models using B-spline functions and Legendre polynomials

The objective was to estimate (co)variance functions using random regression models (RRM) with Legendre polynomials, B-spline function and multi-trait models aimed at evaluating genetic parameters of growth traits in meat-type quail. A database containing the complete pedigree information of 7000 meat-type quail was utilized. The models included the fixed effects of contemporary group and generation. Direct additive genetic and permanent environmental effects, considered as random, were modeled using B-spline functions considering quadratic and cubic polynomials for each individual segment, and Legendre polynomials for age. Residual variances were grouped in four age classes. Direct additive genetic and permanent environmental effects were modeled using 2 to 4 segments and were modeled by Legendre polynomial with orders of fit ranging from 2 to 4. The model with quadratic B-spline adjustment, using four segments for direct additive genetic and permanent environmental effects, was the most appropriate and parsimonious to describe the covariance structure of the data. The RRM using Legendre polynomials presented an underestimation of the residual variance. Lesser heritability estimates were observed for multi-trait models in comparison with RRM for the evaluated ages. In general, the genetic correlations between measures of BW from hatching to 35 days of age decreased as the range between the evaluated ages increased. Genetic trend for BW was positive and significant along the selection generations. The genetic response to selection for BW in the evaluated ages presented greater values for RRM compared with multi-trait models. In summary, RRM using B-spline functions with four residual variance classes and segments were the best fit for genetic evaluation of growth traits in meat-type quail. In conclusion, RRM should be considered in genetic evaluation of breeding programs.     

Effects of censoring on parameter estimates and power in genetic modeling.

Genetic and environmental influences on variance in phenotypic traits may be estimated with normal theory Maximum Likelihood (ML). However, when the assumption of multivariate normality is not met, this method may result in biased parameter estimates and incorrect likelihood ratio tests. We simulated multivariate normal distributed twin data under the assumption of three different genetic models. Genetic model fitting was performed in six data sets: multivariate normal data, discrete uncensored data, censored data, square root transformed censored data, normal scores of censored data, and categorical data. Estimates were obtained with normal theory ML (data sets 1-5) and with categorical data analysis (data set 6). Statistical power was examined by fitting reduced models to the data. When fitting an ACE model to censored data, an unbiased estimate of the additive genetic effect was obtained. However, the common environmental effect was underestimated and the unique environmental effect was overestimated. Transformations did not remove this bias. When fitting an ADE model, the additive genetic effect was underestimated while the dominant and unique environmental effects were overestimated. In all models, the correct parameter estimates were recovered with categorical data analysis. However, with categorical data analysis, the statistical power decreased. The analysis of L-shaped distributed data with normal theory ML results in biased parameter estimates. Unbiased parameter estimates are obtained with categorical data analysis, but the power decreases.     

Testing the effect–response framework: key response and effect traits determining above‐ground biomass of salt marshes

Question: How do species traits respond to environmental conditions and what is their effect on ecosystem properties? Location: Salt marshes, Northwest Germany. Methods: On 113 plots along the German mainland coast and on one island, we measured environmental parameters (soil nutrient content, inundation frequency, groundwater level and salinity), collected traits from 242 individuals (specific leaf area [SLA], whole plant C:N ratio, and dry weights of plant organs) and sampled above‐ground biomass as an ecosystem property. We constructed a path model combining environmental parameters, functional traits at community level and above‐ground biomass, which was tested against a dependence model using path analysis; model fit was evaluated by structural equation modelling (SEM). Results: The final model showed good consistency with the data and highlights the major role of groundwater level, salinity and nutrient availability as the most important factors influencing biomass allocation in salt marshes. Above‐ground living biomass was mostly determined by stem biomass, which was mediated through an allometric allocation of biomass to all other plant organs, including leaf mass. C:N ratio and SLA were the major drivers for dead biomass. Conclusion: We emphasize an indirect link between standing biomass and environmental conditions and recognize stem biomass, plant C:N ratio and SLA as keystone markers of species functioning in determining the relationship between environment and ecosystem properties.     

Estimating Modifying Effect of Age on Genetic and Environmental Variance Components in Twin Models

Twin studies have been adopted for decades to disentangle the relative genetic and environmental contributions for a wide range of traits. However, heritability estimation based on the classical twin models does not take into account dynamic behavior of the variance components over age. Varying variance of the genetic component over age can imply the existence of gene–environment (G × E) interactions that general genome-wide association studies (GWAS) fail to capture, which may lead to the inconsistency of heritability estimates between twin design and GWAS. Existing parametric G × E interaction models for twin studies are limited by assuming a linear or quadratic form of the variance curves with respect to a moderator that can, however, be overly restricted in reality. Here we propose spline-based approaches to explore the variance curves of the genetic and environmental components. We choose the additive genetic, common, and unique environmental variance components (ACE) model as the starting point. We treat the component variances as variance functions with respect to age modeled by B-splines or P-splines. We develop an empirical Bayes method to estimate the variance curves together with their confidence bands and provide an R package for public use. Our simulations demonstrate that the proposed methods accurately capture dynamic behavior of the component variances in terms of mean square errors with a data set of >10,000 twin pairs. Using the proposed methods as an alternative and major extension to the classical twin models, our analyses with a large-scale Finnish twin data set (19,510 MZ twins and 27,312 DZ same-sex twins) discover that the variances of the A, C, and E components for body mass index (BMI) change substantially across life span in different patterns and the heritability of BMI drops to ∼50% after middle age. The results further indicate that the decline of heritability is due to increasing unique environmental variance, which provides more insights into age-specific heritability of BMI and evidence of G × E interactions. These findings highlight the fundamental importance and implication of the proposed models in facilitating twin studies to investigate the heritability specific to age and other modifying factors.     

Bayesian inference of genetic parameters for ultrasound scanning traits of Kivircik lambs

Ultrasound scanning traits have been adapted in selection programs in many countries to improve carcass traits for lean meat production. As the genetic parameters of the traits interested are important for breeding programs, the estimation of these parameters was aimed at the present investigation. The estimated parameters were direct and maternal heritability as well as genetic correlations between the studied traits. The traits were backfat thickness (BFT), skin+backfat thickness (SBFT), eye muscle depth (MD) and live weights at the day of scanning (LW). The breed investigated was Kivircik, which has a high quality of meat. Six different multi-trait animal models were fitted to determine the most suitable model for the data using Bayesian approach. Based on deviance information criterion, a model that includes direct additive genetic effects, maternal additive genetic effects, direct maternal genetic covariance and maternal permanent environmental effects revealed to be the most appropriate for the data, and therefore, inferences were built on the results of that model. The direct heritability estimates for BFT, SBFT, MD and LW were 0.26, 0.26, 0.23 and 0.09, whereas the maternal heritability estimates were 0.27, 0.27, 0.24 and 0.20, respectively. Negative genetic correlations were obtained between direct and maternal effects for BFT, SBFT and MD. Both direct and maternal genetic correlations between traits were favorable, whereas BFT–MD and SBFT–MD had negligible direct genetic correlation. The highest direct and maternal genetic correlations were between BFT and SBFT (0.39) and between MD and LW (0.48), respectively. Our results, in general, indicated that maternal effects should be accounted for in estimation of genetic parameters of ultrasound scanning traits in Kivircik lambs, and SBFT can be used as a selection criterion to improve BFT.     

Genetic basis of human female pelvic morphology: a twin study

To examine the relative role of genetic and environmental factors on pelvic morphology, data on 60 pairs of female twins (30 monozygotic (MZ) and 30 dizygotic (DZ)) were analyzed. Fourteen pelvic measurements were normally distributed, and two were not. Association of twin type with the mean value of a trait was found in only 1 out of 8 traits. Heterogeneity of variance between zygosities was observed in 4 pelvic traits (50%), invalidating within-pair estimates of genetic variance for these traits. Evidence of stronger environmental covariance for MZ than DZ twins was observed for only one trait (sitting height iliocristale). A significant genetic component of variation was observed for age at menarche and in the pelvic area. In instances where inequality of variances between zygosities was demonstrated, total among-pair and within-pair mean squares were larger for dizygotic than for monozygotic twins. This is interpreted as evidence of greater environmental influence between zygosities. Environmental modification was not of the same magnitude in various pelvic traits. Bitrochanteric breadth had the highest magnitude of cultural heritability, indicating that cultural factors played an important role in determining hip breadth.     

A bivariate quantitative genetic model for a linear Gaussian trait and a survival trait

With the increasing use of survival models in animal breeding to address the genetic aspects of mainly longevity of livestock but also disease traits, the need for methods to infer genetic correlations and to do multivariate evaluations of survival traits and other types of traits has become increasingly important. In this study we derived and implemented a bivariate quantitative genetic model for a linear Gaussian and a survival trait that are genetically and environmentally correlated. For the survival trait, we considered the Weibull log-normal animal frailty model. A Bayesian approach using Gibbs sampling was adopted. Model parameters were inferred from their marginal posterior distributions. The required fully conditional posterior distributions were derived and issues on implementation are discussed. The two Weibull baseline parameters were updated jointly using a Metropolis-Hasting step. The remaining model parameters with non-normalized fully conditional distributions were updated univariately using adaptive rejection sampling. Simulation results showed that the estimated marginal posterior distributions covered well and placed high density to the true parameter values used in the simulation of data. In conclusion, the proposed method allows inferring additive genetic and environmental correlations, and doing multivariate genetic evaluation of a linear Gaussian trait and a survival trait.     

Biometrical modeling of twin and family data using standard mixed model software

Summary .   Biometrical genetic modeling of twin or other family data can be used to decompose the variance of an observed response or 'phenotype' into genetic and environmental components. Convenient parameterizations requiring few random effects are proposed, which allow such models to be estimated using widely available software for linear mixed models (continuous phenotypes) or generalized linear mixed models (categorical phenotypes). We illustrate the proposed approach by modeling family data on the continuous phenotype birth weight and twin data on the dichotomous phenotype depression. The example data sets and commands for Stata and R/S-PLUS are available at the Biometrics website.     

Estimates of correlations among yield traits and somatic cell score with different models to adjust for bovine somatotropin effects on Holstein dairy cows

Records of Holstein cows from the Dairy Records Processing Center at Raleigh, NC were edited to obtain three data sets: 65,720 first, 50,694 second, and 65,445 later lactations. Correlations among yield traits and somatic cell score were estimated with three different models: 1) bovine somatotropin (bST) administration ignored, 2) bST administration as a fixed effect and 3) administration of bST as part of the contemporary group (herd-year-month-bST). Heritability estimates ranged from 0.13 to 0.17 for milk, 0.12 to 0.20 for fat, 0.14 to 0.16 for protein yields, and 0.08 to 0.09 for somatic cell score. Estimates were less for later than first lactations. Estimates of genetic correlations among yields ranged from 0.35 to 0.85 with no important differences between estimates with the 3 models. Estimates for lactation 2 agreed with estimates for lactation 1. Estimates of genetic correlations for later lactations were generally greater than for lactations 1 and 2 except between milk and protein yields. Estimates of genetic correlations between yields and somatic cell score were mostly negative or small (-0.45 to 0.11). Estimates of environmental correlations among yield traits were similar with all models (0.77 to 0.97). Estimates of environmental correlations between yields and somatic cell score were negative (-0.22 to -0.14). Estimates of phenotypic correlations among yield traits ranged from 0.70 to 0.95. Estimates of phenotypic correlations between yields and somatic cell score were small and negative. For all three data sets and all traits, no important differences in estimates of genetic parameters were found for the two models that adjusted for bST and the model that did not.     

Semiparametric maximum likelihood methods for analyzing genetic and environmental effects with case-control mother-child pair data

Summary Case-control mother-child pair design represents a unique advantage for dissecting genetic susceptibility of complex traits because it allows the assessment of both maternal and offspring genetic compositions. This design has been widely adopted in studies of obstetric complications and neonatal outcomes. In this work, we developed an efficient statistical method for evaluating joint genetic and environmental effects on a binary phenotype. Using a logistic regression model to describe the relationship between the phenotype and maternal and offspring genetic and environmental risk factors, we developed a semiparametric maximum likelihood method for the estimation of odds ratio association parameters. Our method is novel because it exploits two unique features of the study data for the parameter estimation. First, the correlation between maternal and offspring SNP genotypes can be specified under the assumptions of random mating, Hardy-Weinberg equilibrium, and Mendelian inheritance. Second, environmental exposures are often not affected by offspring genes conditional on maternal genes. Our method yields more efficient estimates compared with the standard prospective method for fitting logistic regression models to case-control data. We demonstrated the performance of our method through extensive simulation studies and the analysis of data from the Jerusalem Perinatal Study.     

Allelic penetrance approach as a tool to model two-locus interaction in complex binary traits

Many binary phenotypes do not follow a classical Mendelian inheritance pattern. Interaction between genetic and environmental factors is thought to contribute to the incomplete penetrance phenomena often observed in these complex binary traits. Several two-locus models for penetrance have been proposed to aid the genetic dissection of binary traits. Such models assume linear genetic effects of both loci in different mathematical scales of penetrance, resembling the analytical framework of quantitative traits. However, changes in phenotypic scale are difficult to envisage in binary traits and limited genetic interpretation is extractable from current modeling of penetrance. To overcome this limitation, we derived an allelic penetrance approach that attributes incomplete penetrance to the stochastic expression of the alleles controlling the phenotype, the genetic background and environmental factors. We applied this approach to formulate dominance and recessiveness in a single diallelic locus and to model different genetic mechanisms for the joint action of two diallelic loci. We fit the models to data on the genetic susceptibility of mice following infections with Listeria monocytogenes and Plasmodium berghei. These models gain in genetic interpretation, because they specify the alleles that are responsible for the genetic (inter)action and their genetic nature (dominant or recessive), and predict genotypic combinations determining the phenotype. Further, we show via computer simulations that the proposed models produce penetrance patterns not captured by traditional two-locus models. This approach provides a new analysis framework for dissecting mechanisms of interlocus joint action in binary traits using genetic crosses.     

(Co)Variance components and genetic parameter estimates for growth traits in Moghani sheep

Genetic parameters were estimated for birth weight (BW), weaning weight (WW), yearling weight (YW), average daily gain from birth to weaning (ADG1) and average daily gain from weaning to yearling (ADG2) in Moghani sheep. Maximum number of data was 4237 at birth, but only 1389 records at yearling were investigated. The data was collected from 1995 to 2007 at the Breeding Station of Moghani sheep in Jafarabad, Moghan, Iran. (Co)Variance components and genetic parameters were estimated with different models which including direct effects, with and without maternal additive genetic effects as well as maternal permanent environmental effects using restricted maximum likelihood (REML) method. The most appropriate model for each trait was determined based on likelihood ratio tests and Akaike's Information Criterion (AIC). Maternal effects were important only for pre-weaning traits. Direct heritability estimates for BW, ADG1, WW, ADG2 and YW were 0.07, 0.08, 0.09, 0.09 and 0.17, respectively. Fractions of variance due to maternal permanent environmental effects on phenotypic variance were 0.08 for ADG1. Maternal heritability estimates for BW and WW were 0.18 and 0.06, respectively. Multivariate analysis was performed using the most appropriate models obtained in univariate analysis. Direct genetic correlations among studied traits were positive and ranged from 0.37 for BW–ADG2 to 0.85 for ADG1–YW. Maternal genetic correlation estimate between BW and WW was 0.33. Phenotypic and environmental correlation estimates were generally lower than those of genetic correlation. Low direct heritability estimates imply that mass selection for these traits results in slow genetic gain.