Genetic heterogeneity of residual variance - estimation of variance components using double hierarchical generalized linear models

Background

The sensitivity to microenvironmental changes varies among animals and may be under genetic control. It is essential to take this element into account when aiming at breeding robust farm animals. Here, linear mixed models with genetic effects in the residual variance part of the model can be used. Such models have previously been fitted using EM and MCMC algorithms.

Results

We propose the use of double hierarchical generalized linear models (DHGLM), where the squared residuals are assumed to be gamma distributed and the residual variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the variance components in the residual variance part of the model.

Conclusions

We have shown that variance components in the residual variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and residual variance parts of the model as a parameter of the DHGLM.     

Analysis of genes for alcoholism using two-disease-locus models

Using model-based two-locus methods for mapping genes, we analyzed the family data from the Collaborative Study on the Genetics of Alcoholism. Microsatellite data from 143 families ascertained through having three or more individuals affected with alcohol dependence were used for this investigation. Four regions showing evidence for linkage were identified using single-locus models from previous investigations. We investigated the genetic linkage, pattern of disease inheritance, and pair-wise genetic epistasis of these loci using the TLINKAGE program for two-disease-locus analysis.     

Detecting pleiotropy and epistasis using variance components linkage analysis in jPAP

jPAP (Java Pedigree Analysis Package) performs variance components linkage analysis of either quantitative or discrete traits. Multivariate linkage analysis of two or more traits (all quantitative, all discrete, or any combination) allows the inference of pleiotropy between the traits. The inclusion of multiple quantitative trait loci in linkage analysis allows the inference of epistasis between loci. A user-friendly graphical user interface facilitates the usage of jPAP.     

Whole-genome linkage analysis in mapping alcoholism genes using single-nucleotide polymorphisms and microsatellites

There is currently a great interest in using single-nucleotide polymorphisms (SNPs) in genetic linkage and association studies because of the abundance of SNPs as well as the availability of high-throughput genotyping technologies. In this study, we compared the performance of whole-genome scans using SNPs with microsatellites on 143 pedigrees from the Collaborative Studies on Genetics of Alcoholism provided by Genetic Analysis Workshop 14. A total of 315 microsatellites and 10,081 SNPs from Affymetrix on 22 autosomal chromosomes were used in our analyses. We found that the results from the two scans had good overall concordance. One region on chromosome 2 and two regions on chromosome 7 showed significant linkage signals (i.e., NPL >or= 2) for alcoholism from both the SNP and microsatellite scans. The different results observed between the two scans may be explained by the difference observed in information content between the SNPs and the microsatellites.     

Genetic variance components and heritability of multiallelic heterozygosity under inbreeding

The maintenance of genetic diversity in fitness-related traits remains a central topic in evolutionary biology, for example, in the context of sexual selection for genetic benefits. Among the solutions that have been proposed is directional sexual selection for heterozygosity. The importance of such selection is highly debated. However, a critical evaluation requires knowledge of the heritability of heterozygosity, a quantity that is rarely estimated in this context, and often assumed to be zero. This is at least partly the result of the lack of a general framework that allows for its quantitative prediction in small and inbred populations, which are the focus of most empirical studies. Moreover, while current predictors are applicable only to biallelic loci, fitness-relevant loci are often multiallelic, as are the neutral markers typically used to estimate genome-wide heterozygosity. To this end, we first review previous, but little-known, work showing that under most circumstances, heterozygosity at biallelic loci and in the absence of inbreeding is heritable. We then derive the heritability of heterozygosity and the underlying variances for multiple alleles and any inbreeding level. We also show that heterozygosity at multiallelic loci can be highly heritable when allele frequencies are unequal, and that this heritability is reduced by inbreeding. Our quantitative genetic framework can provide new insights into the evolutionary dynamics of heterozygosity in inbred and outbred populations.     

Pedigree analysis for quantitative traits: variance components without matrix inversion

Recent developments in the animal breeding literature facilitate estimation of the variance components in quantitative genetic models. However, computation remains intensive, and many of the procedures are restricted to specialized designs and models, unsuited to data arising from studies of natural populations. We develop algorithms that allow maximum likelihood estimation of variance components for data on arbitrary pedigree structures. The proposed methods can be implemented on microcomputers, since no intensive matrix computations or manipulations are involved. Although parts of our procedures have been previously presented, we unify these into an overall scheme whose intuitive justification clarifies the approach. Two examples are analyzed: one of data on a natural population of Salivia lyrata and the other of simulated data on an extended pedigree.     

Longitudinal variance components models for systolic blood pressure, fitted using Gibbs sampling

This paper describes an analysis of systolic blood pressure (SBP) in the Genetic Analysis Workshop 13 (GAW13) simulated data. The main aim was to assess evidence for both general and specific genetic effects on the baseline blood pressure and on the rate of change (slope) of blood pressure with time. Generalized linear mixed models were fitted using Gibbs sampling in WinBUGS, and the additive polygenic random effects estimated using these models were then used as continuous phenotypes in a variance components linkage analysis. The first-stage analysis provided evidence for general genetic effects on both the baseline and slope of blood pressure, and the linkage analysis found evidence of several genes, again for both baseline and slope.     

Maximum-likelihood variance components analysis of heritabilities of cranial nonmetric traits

Nonmetric traits of the cranium are often used to support hypotheses of the history and divergence of human populations. These studies rely on the assumption that nonmetric traits are heritable, yet few skeletal series exist with associated pedigree information that allow for the calculation of additive genetic variance, or heritability. In addition, traits for which heritabilities have been published represent dichotomous present/absent forms instead of the range of expression that can be observed for many nonmetric characters. In the present study I use a maximum-likelihood variance components analysis to calculate univariate narrow-sense heritability estimates on the skeletal series from Hallstatt, Austria, for 9 sutural bones, 27 multilevel traits, and dichotomized present/absent forms for 19 of these multilevel characters. Most of the trait heritabilities do not differ significantly from a model of h2 = 0, and they have large standard errors. In a heuristic comparison of multilevel versus dichotomous trait forms, most of the nonmetric characters showed no differences in heritability between the two methods used for parsing the phenotypic variation, although where differences were noted, the presence-absence version had higher heritabilities. These results have implications not only for the use of particular nonmetric traits in population studies but also for the practice of character dichotomization in data collection.     

Exact multipoint quantitative-trait linkage analysis in pedigrees by variance components

Methods based on variance components are powerful tools for linkage analysis of quantitative traits, because they allow simultaneous consideration of all pedigree members. The central idea is to identify loci making a significant contribution to the population variance of a trait, by use of allele-sharing probabilities derived from genotyped marker loci. The technique is only as powerful as the methods used to infer these probabilities, but, to date, no implementation has made full use of the inheritance information in mapping data. Here we present a new implementation that uses an exact multipoint algorithm to extract the full probability distribution of allele sharing at every point in a mapped region. At each locus in the region, the program fits a model that partitions total phenotypic variance into components due to environmental factors, a major gene at the locus, and other unlinked genes. Numerical methods are used to derive maximum-likelihood estimates of the variance components, under the assumption of multivariate normality. A likelihood-ratio test is then applied to detect any significant effect of the hypothesized major gene. Simulations show the method to have greater power than does traditional sib-pair analysis. The method is freely available in a new release of the software package GENEHUNTER.     

Genetic association analysis using sibship data: a multilevel model approach

Family based association study (FBAS) has the advantages of controlling for population stratification and testing for linkage and association simultaneously. We propose a retrospective multilevel model (rMLM) approach to analyze sibship data by using genotypic information as the dependent variable. Simulated data sets were generated using the simulation of linkage and association (SIMLA) program. We compared rMLM to sib transmission/disequilibrium test (S-TDT), sibling disequilibrium test (SDT), conditional logistic regression (CLR) and generalized estimation equations (GEE) on the measures of power, type I error, estimation bias and standard error. The results indicated that rMLM was a valid test of association in the presence of linkage using sibship data. The advantages of rMLM became more evident when the data contained concordant sibships. Compared to GEE, rMLM had less underestimated odds ratio (OR). Our results support the application of rMLM to detect gene-disease associations using sibship data. However, the risk of increasing type I error rate should be cautioned when there is association without linkage between the disease locus and the genotyped marker.     

Genetic analysis of gliadin components in winter wheat using two-dimensional polyacrylamide gel electrophoresis

Summary Blocks of gliadin components found both in a number of varieties and in single F₂ grains of winter wheat intervarietal hybrids have been studied by two-dimensional electrophoresis combining electrophoresis in acidic aluminium-lactate buffer (pH3.1) and SDS-electrophoresis. Gliadin components (spots) have been shown to be inherited as linked groups (blocks), codominantly and in accordance with a gene dosage in triploid endosperm. Blocks include components differing in their electrophoretic mobility and molecular weight. Some allelic variants of blocks differ only in presence of few additional components or in the electrophoretic mobility of components with similar molecular weights; other variants may contain no similar components. Apparently, in the course of evolution, mutations in individual genes of gliadin-coding loci and processes changing the number of expressing genes and the sizes of their structural part occurred.     

SNP allele frequency estimation in DNA pools and variance components analysis

The estimation of single nucleotide polymorphism (SNP) allele frequency in pooled DNA samples has been proposed as a cost-effective approach to whole genome association studies. However, the key issue is the allele frequency window in which a genotyping method operates and provides a statistically reliable answer. We assessed the homogeneous mass extend assay and estimated the variance associated with each experimental stage. We report that a relationship between estimated allele frequency and variance might exist, suggesting that high statistical power can be retained at low, as well as high, allele frequencies. Assuming this relationship, the formation of subpools consisting of 100 samples retains an effective sample size greater than 70% of the true sample size, with a savings of 11-fold the cost of an individual genotyping study, regardless of allele frequency.     

TLINKAGE-IMPRINT: a model-based approach to performing two-locus genetic imprinting analysis

OBJECTIVES: Imprinting refers to the expression of only one copy of a gene pair, which is determined by the parental origin of the copy. Imprinted genes play a role in the development of several complex diseases, including cancers and mental disorders. In certain situations, two-trait-loci models are shown to be more powerful than one-trait-locus models. However, no current methods use pedigree structure efficiently and perform two-locus imprinting analyses. In this paper, we apply the Elston-Stewart algorithm to the parametric two-trait-loci imprinting model used by Strauch et al. [2000] to obtain a method for qualitative trait linkage analyses that explicitly models imprinting and can be applied to large pedigrees. METHODS: We considered a parametric approach based on 4 x 4 penetrance matrix to account for imprinting and modified TLINKAGE software to implement this approach. We performed simulation studies using a small and a large pedigree under dominant and imprinted and dominant or imprinted scenarios. Furthermore, we developed a likelihood ratio-based test for imprinting that compares the logarithm of odds (LOD) score obtained using the two-locus imprinting model with that obtained using the standard two-locus model that does not allow for imprinting. RESULTS: In simulation studies of three scenarios where the true mode of inheritance included imprinting, accurate modeling through the proposed approach yielded higher LOD scores and better recombination fraction estimates than the traditional two-locus model that does not allow for imprinting. CONCLUSIONS: This imprinting model will be useful in identifying the genes responsible for several complex disorders that are potentially caused by a combination of imprinted and non-imprinted genes.