The Use of Mixture Models to Detect Effects of Major Genes on Quantitative Characters in a Plant Breeding Experiment

An analysis based on Elston's model of mixed major locus and polygenic inheritance is extended to include populations of progeny testing such as F(3), B(1s) and B(2s) families derived from F(2) and backcrosses in a cross between two inbred lines. Genetic hypotheses that can be validly tested by the likelihood ratio method in the analysis of a breeding experiment include homogeneity of variances due to environment and/or polygenes with transformable scale effect by Box-Cox power function, random and independent segregation of major genes, invariance of the effects of major genes with population types and additive and dominant models for polygenes. Testing hypotheses in the order suggested here can lead to a gradual simplification of the models and increases the feasibility of the subsequent analysis, but caution must be paid to the possible bias in parameter estimation and hypotheses tests. The procedure is applied to a set of data on plant height of rice with the effects of dwarf genes in crosses among three varieties. Two recessive dwarf genes are shown to be nonallelic and unlinked. One dwarf gene is shown to reduce plant height about 36-56 cm, and another 52-61 cm. The effect of polygenes, estimated as the standard deviation among possible inbred lines derived from these crosses, is about 11.7 cm. Interactions between the dwarf genes and the polygenic background are found, especially for one of the two genes. Both the polygenic effects and the interactions are much smaller than the effects of the major dwarf genes.     

Complex segregation analysis of non-myoclonic idiopathic generalized epilepsy in families ascertained from probands affected with idiopathic epilepsy with tonic-clonic seizures in Antioquia,Colombia

In an attempt to identify the possible role of major genes, multifactorial inheritance, and cohort effects in the susceptibility to idiopathic epilepsy with generalized tonic-clonic seizures of the awakening type (GTCS), complex segregation analysis was performed in 196 nuclear families ascertained through affected probands with idiopathic epilepsy with GTCS belonging to the Paisa community of Antioquia (Colombia). Models postulating no transmission, single major locus (dominant and recessive) only, and multifactorial component only, were rejected. Since the codominant single major locus model could not be rejected and models that assign no major locus to transmission, no polygenic component to transmission, and no transmission of the major effect were rejected, complex segregation analysis suggested that a major autosomal codominant allele together with a multifactorial component (mixed model) best explained clustering of idiopathic epilepsy with GTCS in families of the Paisa community. The deficit of transmission of heterozygotes (0.17) is compatible with the existence of epistasis acting on a major gene whose frequency was estimated to be 0.0211. Its transmission variance accounts for 81% of the susceptibility to idiopathic epilepsy with GTCS. The complementary variance (19%) is due to the polygenic component. Received: 19 January 1996 / Revised: 11 March 1996     

Family study and segregation analysis of Tourette syndrome: evidence for a mixed model of inheritance.

To investigate the transmission of Tourette syndrome (TS) and associated disorders within families, complex segregation analysis was performed on family study data obtained from 53 independently ascertained children and adolescents with TS and their 154 first-degree relatives. The results suggest that the susceptibility for TS is conveyed by a major locus in combination with a multifactorial background. Other models of inheritance were definitively rejected, including strictly polygenic models, all single major locus models, and mixed models with dominant and recessive major loci. The frequency of the TS susceptibility allele was estimated to be .01. The major locus accounts for over half of the phenotypic variance for TS, whereas the multifactorial background accounts for approximately 40% of phenotypic variance. Penetrance estimates suggest that all individuals homozygous for the susceptibility allele at the major locus are affected, whereas only 2.2% of males and 0.3% of females heterozygous at the major locus are affected. Of individuals affected with TS, approximately 62% are heterozygous and approximately 38% are homozygous at the major locus. While none of the families had two parents affected with TS, 19% of families had two parents affected with the broader, phenotype, which includes TS, chronic tic disorder, or obsessive-compulsive disorder.     

Platelet monoamine oxidase (MAO) activity: evidence for a single major locus.

Monoamine oxidase (MAO), a mitochondrial enzyme involved in the degradation of biogenic amines, has been associated with psychiatric morbidity. Although twin and family studies have indicated that MAO activity is familial, the exact mode of transmission is unclear. We performed segregation analysis on 154 nuclear families containing 419 individuals using the mixed model, which allows for a single major locus with a polygenic background. We were able to reject a dominant and additive locus with or without a heritable background and a recessive locus without background. The acceptable models were: (1) a codominant model without background where the mean of the heterozygote distribution was 30% of the distance from the low to the high homozygote distributions, and (2) a recessive locus with heritable background. In both cases, the gene frequency for the high-MAO allele is approximately .25--at odds with suggestions that low-MAO represents a genetic marker for a disorder such as schizophrenia with a lifetime risk of only 0.85%. To ensure that results were not artifacts from a familial, skewed distribution, the data were also analyzed after power transformation. In addition, hypotheses were tested using both the joint and conditional likelihoods to examine for possible misspecification of the model with respect to intergenerational differences. Finally, we allowed for non-Mendelian transmission probabilities to provide another class of alternatives against which to test the hypothesis of a major locus. All these approaches provided additional confirmation for the presence of a major locus segregating within these families.     

Genetic variability in milking speed of dairy goats

The present investigation deals with the genetic variability of milking speed, measured as the volume of milk collected during the first minute of milking (MD1), and its association with dairy traits. Data originated from 2589 lactations of 1421 Alpine goats, sired by 93 bucks, measured between 1985 and 1997 at the Moissac Goat Experimental Station (Lozère, France). Two genetic analyses were carried out. Firstly, a polygenic model was used to estimate genetic and phenotypic parameters among milking speed and dairy traits using a multiple-trait animal model. Secondly, segregation analysis was used to test the hypothesis of mixed model inheritance (polygenes + major gene) for MF1. Heritability and repeatability of MF1 under the polygenic model were high (0.65 and 0.82, respectively). Estimated genetic and phenotypic correlations between milking speed and dairy traits were low, positive for yields and negative for contents. Segregation analysis yielded a highly significant likelihood ratio, confirming the segregation of a major gene with two alleles with partial dominance. The difference between the mean values of the two homozygotes was around 2.3 phenotypic standard deviation units of the trait. The major gene explained more than 60% of the estimated total genetic variance. The estimate of the 'residual' heritability, after taking into account the effect of the major locus, was 0.30.     

Conditional likelihood score functions for mixed models in linkage analysis

In this paper, we develop a general strategy for linkage analysis, applicable for arbitrary pedigree structures and genetic models with one major gene, polygenes and shared environmental effects. Extending work of Whittemore (1996), McPeek (1999) and Hossjer (2003d), the efficient score statistic is computed from a conditional likelihood of marker data given phenotypes. The resulting semiparametric linkage analysis is very similar to nonparametric linkage based on affected individuals. The efficient score S depends not only on identical-by-descent sharing and phenotypes, but also on a few parameters chosen by the user. We focus on (1) weak penetrance models, where the major gene has a small effect and (2) rare disease models, where the major gene has a possibly strong effect but the disease causing allele is rare. We illustrate our results for a large class of genetic models with a multivariate Gaussian liability. This class incorporates one major gene, polygenes and shared environmental effects in the liability, and allows e.g. binary, Gaussian, Poisson distributed and life-length phenotypes. A detailed simulation study is conducted for Gaussian phenotypes. The performance of the two optimal score functions S(wpairs) and S(normdom) are investigated. The conclusion is that (i) inclusion of polygenic effects into the score function increases overall performance for a wide range of genetic models and (ii) score functions based on the rare disease assumption are slightly more powerful.     

A genome scan for eye color in 502 twin families: most variation is due to a QTL on chromosome 15q.

We have rated eye color on a 3-point scale (1 = blue/grey, 2 = hazel/green, 3 = brown) in 502 twin families and carried out a 5-10 cM genome scan (400-757 markers). We analyzed eye color as a threshold trait and performed multipoint sib pair linkage analysis using variance components analysis in Mx. A lod of 19.2 was found at the marker D15S1002, less than 1 cM from OCA2, which has been previously implicated in eye color variation. We estimate that 74% of variance in eye color liability is due to this QTL and a further 18% due to polygenic effects. However, a large shoulder on this peak suggests that other loci affecting eye color may be telomeric of OCA2 and inflating the QTL estimate. No other peaks reached genome-wide significance, although lods > 2 were seen on 5p and 14q and lods >1 were additionally seen on chromosomes 2, 3, 6, 7, 8, 9, 17 and 18. Most of these secondary peaks were reduced or eliminated when we repeated the scan as a two locus analysis with the 15q linkage included, although this does not necessarily exclude them as false positives. We also estimated the interaction between the 15q QTL and the other marker locus but there was only minor evidence for additive x additive epistasis. Elaborating the analysis to the full two-locus model including non-additive main effects and interactions did not strengthen the evidence for epistasis. We conclude that most variation in eye color in Europeans is due to polymorphism in OCA2 but that there may be modifiers at several other loci.     

Evidence of a major gene from Bayesian segregation analyses of liability to osteochondral diseases in pigs

Bayesian segregation analyses were used to investigate the mode of inheritance of osteochondral lesions (osteochondrosis, OC) in pigs. Data consisted of 1163 animals with OC and their pedigrees included 2891 animals. Mixed-inheritance threshold models (MITM) and several variants of MITM, in conjunction with Markov chain Monte Carlo methods, were developed for the analysis of these (categorical) data. Results showed major genes with significant and substantially higher variances (range 1.384-37.81), compared to the polygenic variance (sigmau2). Consequently, heritabilities for a mixed inheritance (range 0.65-0.90) were much higher than the heritabilities from the polygenes. Disease allele frequencies range was 0.38-0.88. Additional analyses estimating the transmission probabilities of the major gene showed clear evidence for Mendelian segregation of a major gene affecting osteochondrosis. The variants, MITM with informative prior on sigmau2, showed significant improvement in marginal distributions and accuracy of parameters. MITM with a "reduced polygenic model" for parameterization of polygenic effects avoided convergence problems and poor mixing encountered in an "individual polygenic model." In all cases, "shrinkage estimators" for fixed effects avoided unidentifiability for these parameters. The mixed-inheritance linear model (MILM) was also applied to all OC lesions and compared with the MITM. This is the first study to report evidence of major genes for osteochondral lesions in pigs; these results may also form a basis for underpinning the genetic inheritance of this disease in other animals as well as in humans.     

Genetic analysis of plasma sitosterol, apoprotein B, and lipoproteins in a large Amish pedigree with sitosterolemia.

We previously reported the finding of phytosterolemia, xanthomatosis, and hyperapobetalipoproteinemia (hyperapoB) in five siblings in a large Amish pedigree ascertained through a 13-year-old boy who died suddenly from advanced coronary atherosclerosis. Here, we present further analyses of the plasma levels of the plant sterol, sitosterol, of low density (beta) lipoprotein (LDL) sterol, and of LDL B protein. Of 254 relatives and spouses of the proband, 90.5% were examined. A series of genetic models were explored using a pedigree analysis where parameters reflecting frequency, transmission, and penetrance of putative genotypes were examined simultaneously using a maximum likelihood approach. Segregation analysis of the sitosterol levels showed that the phenotype of sitosterolemia was controlled by a rare autosomal recessive gene. There was also significant familial correlation in plasma sitosterol levels that was attributed to a polygenic component under a mixed model but could also be due to shared environments such as diets. The recessive model was supported by our finding that the plasma sitosterol levels in the parents and in six children born to three of the five sitosterolemics were less than 1 mg/dl, well within the normal range. The phenotype of hyperapoB is based on an elevated level of LDL B protein in the presence of a normal LDL cholesterol level (low LDL sterol to LDL B ratio). For both LDL sterol and LDL B, a polygenic model showed a slightly greater improvement in ln likelihood than did the Mendelian single locus model when both were compared to a sporadic model. Similar results were obtained for sterol levels of high density (alpha) lipoprotein (HDL) sterol. When segregation analysis was performed using the ratio of LDL sterol to LDL B, the Mendelian single locus model gave a slightly better fit to the data than did the polygenic model. While the analyses presented here provided unequivocal evidence for the recessive phenotype of phytosterolemia, we also identified a possible single gene factor that could account for the major portion of the strong familial aggregation in the ratio of LDL sterol to LDL B, and to a lesser extent LDL B. However, there is clear evidence of familial aggregation for these traits in this pedigree beyond that due to Mendelian components.     

An analysis of the genetics of schizophrenia

Abstract

Data on the inheritance of schizophrenia indicate that both genetics and environment contribute importantly to the manifestation of the disease. However, heterogeneity of the data makes an accurate analysis very difficult. In this paper, a crude analysis of a threshold model, using a polygenic or a single gene hypothesis, shows that both are in approximate agreement with the data. Though argument about genetic models seems futile when virtually any model can account for the data, the single gene hypothesis is unavoidably more attractive at this stage. If a single gene is involved, the allele predisposing toward schizophrenia should be considered as essentially, though not entirely, recessive; all genotypes would be strongly affected by unknown environmental factors; and even some genetically normal individuals would manifest the disorder.     

Major gene detection for fusiform rust resistance using Bayesian complex segregation analysis in loblolly pine

The presence of major genes affecting rust resistance of loblolly pine was investigated in a progeny population that was generated with a half-diallel mating of six parents. A Bayesian complex segregation analysis was used to make inference about a mixed inheritance model (MIM) that included polygenic effects and a single major gene effect. Marginalizations were achieved by using Gibbs sampler. A parent block sampling by which genotypes of a parent and its offspring were sampled jointly was implemented to improve mixing. The MIM was compared with a pure polygenic model (PM) using Bayes factor. Results showed that the MIM was a better model to explain the inheritance of rust resistance than the pure PM in the diallel population. A large major gene variance component estimate (> 50% of total variance), indicated the existence of major genes for rust resistance in the studied loblolly pine population. Based on estimations of parental genotypes, it appears that there may be two or more major genes affecting disease phenotypes in this diallel population.     

A method to optimize selection on multiple identified quantitative trait loci

A mathematical approach was developed to model and optimize selection on multiple known quantitative trait loci (QTL) and polygenic estimated breeding values in order to maximize a weighted sum of responses to selection over multiple generations. The model allows for linkage between QTL with multiple alleles and arbitrary genetic effects, including dominance, epistasis, and gametic imprinting. Gametic phase disequilibrium between the QTL and between the QTL and polygenes is modeled but polygenic variance is assumed constant. Breeding programs with discrete generations, differential selection of males and females and random mating of selected parents are modeled. Polygenic EBV obtained from best linear unbiased prediction models can be accommodated. The problem was formulated as a multiple-stage optimal control problem and an iterative approach was developed for its solution. The method can be used to develop and evaluate optimal strategies for selection on multiple QTL for a wide range of situations and genetic models.     

Maximum Likelihood Analysis of Rare Binary Traits under Different Modes of Inheritance

Maximum likelihood methodology was applied to determine the mode of inheritance of rare binary traits with data structures typical for swine populations. The genetic models considered included a monogenic, a digenic, a polygenic, and three mixed polygenic and major gene models. The main emphasis was on the detection of major genes acting on a polygenic background. Deterministic algorithms were employed to integrate and maximize likelihoods. A simulation study was conducted to evaluate model selection and parameter estimation. Three designs were simulated that differed in the number of sires/number of dams within sires (10/10, 30/30, 100/30). Major gene effects of at least one SD of the liability were detected with satisfactory power under the mixed model of inheritance, except for the smallest design. Parameter estimates were empirically unbiased with acceptable standard errors, except for the smallest design, and allowed to distinguish clearly between the genetic models. Distributions of the likelihood ratio statistic were evaluated empirically, because asymptotic theory did not hold. For each simulation model, the Average Information Criterion was computed for all models of analysis. The model with the smallest value was chosen as the best model and was equal to the true model in almost every case studied.     

Evidence for recessive and against dominant inheritance at the HLA-"linked" locus in coeliac disease.

It has been proposed that gluten sensitive enteropathy (GSE) results from the interaction of two loci: one locus linked to HLA and associated with dominant inheritance, and the other, a non-HLA-linked GSE-associated B-cell alloantigen, exhibiting recessive inheritance. We have shown in previous analyses that a two-locus, dominant-recessive model is less compatible with the existing population prevalence and observed familial segregation data than is a recessive-recessive two-locus model. Here we present additional analyses of reported population and familial HLA data that support the recessive mode of inheritance for the HLA-linked disease locus. Reported data from HLA typing of affected sib pairs, the association of GSE with DR3 and DR7 in different populations, and the proportions of different HLA phenotypes and genotypes were compared with expected data derived by three different methods. The HLA data analyses consistently reject a dominant mode of inheritance for the presumed HLA-linked disease allele but do not reject a recessive model. The affected sib-pair data also support a recessive model. These analyses are consistent with our previous prediction that the HLA-"linked" disease allele in GSE is recessive inherited.     

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.     

Recessive inheritance of a relative fat pattern.

We defined a relative-fat-pattern index (RFPI) as the ratio of subscapular skinfold thickness to the sum of subscapular and suprailiac skinfold thicknesses and computed RFPI for 774 adults (age greater than or equal to 25 years) in 59 pedigrees ascertained through cases of cardiovascular disease. Likelihood analysis of RFPI supported recessive inheritance of an allele with a frequency of 46%, which elevated mean RFPI from .412 to .533 when homozygous. The analysis apportioned the variance in RFPI as 42.3% due to the major locus, 9.5% due to polygenic inheritance, and 48.2% due to random environmental effects. Homozygotes for the recessive allele tended to have small suprailiac skinfold thicknesses rather than large subscapular skinfold thicknesses. Homozygotes were more frequent in younger than in older cases of obesity, coronary heart disease, essential hypertension, and diabetes mellitus; the increase was significant for all but diabetes.     

Sib mating designs for mapping quantitative trait loci

The power to separate the variance of a quantitative trait locus (QTL) from the polygenic variance is determined by the variability of genes identical by descent (IBD) at the QTL. This variability may increase with inbreeding. Selfing, the most extreme form of inbreeding, increases the variability of the IBD value shared by siblings, and thus has a higher efficiency for QTL mapping than random mating. In self-incompatible organisms, sib mating is the closest form of inbreeding. Similar to selfing, sib mating may also increase the power of QTL detection relative to random mating. In this study, we develop an IBD-based method under sib mating designs for QTL mapping. The efficiency of sib mating is then compared with random mating. Monte Carlo simulations show that sib mating designs notably increase the power for QTL detection. When power is intermediate, the power to detect a QTL using full-sib mating is, on average, 7% higher than under random mating. In addition, the IBD-based method proposed in this paper can be used to combine data from multiple families. As a result, the estimated QTL parameters can be applied to a wide statistical inference space relating to the entire reference population. This revised version was published online in July 2006 with corrections to the Cover Date.     

Genome‐wide association study for jumping performances in French sport horses

A genome‐wide association study was performed to identify single nucleotide polymorphisms (SNPs) associated with jumping performances of warmbloods in France. The 999 horses included in the study for jumping performances were sport horses [mostly Selle Français (68%), Anglo‐Arabians (13%) and horses from the other European studbooks]. Horses were genotyped using the Illumina EquineSNP50 BeadChip. Of the 54 602 SNPs available on this chip, 44 424 were retained after quality testing. Phenotypes were obtained by deregressing official breeding values for jumping competitions to use all available information, that is, the performances of each horse as well as those of its relatives. Two models were used to test the effects of the genotypes on deregressed phenotypes: a single‐marker mixed model and a haplotype‐based mixed model (significant: P < 1E‐05; suggestive: P < 1E‐04). Both models included a polygenic effect to take into account familial structures. For jumping performances, one suggestive quantitative trait locus (QTL) located on chromosome 1 (BIEC2_31196 and BIEC2_31198) was detected with both models. This QTL explains 0.7% of the phenotypic variance. RYR2, a gene encoding a major calcium channel in cardiac muscle in humans and mice, is located 0.55 Mb from this potential QTL.     

An indication of major genes affecting hip and elbow dysplasia in four Finnish dog populations

The aim of the study was to assess the possible existence of major genes influencing hip and elbow dysplasia in four dog populations. A Bayesian segregation analysis was performed separately on each population. In total, 34 140 dogs were included in the data set. Data were analysed with both a polygenic and a mixed inheritance model. Polygenic models included fixed and random environmental effects and additive genetic effects. To apply mixed inheritance models, the effect of a major gene was added to the polygenic models. The major gene was modelled as an autosomal biallelic locus with Mendelian transmission probabilities. Gibbs sampling and a Monte Carlo Markov Chain algorithm were used. The goodness-of-fit of the different models were compared using the residual sum-of-squares. The existence of a major gene was considered likely for hip dysplasia in all the breeds and for elbow dysplasia in one breed. Several procedures were followed to exclude the possible false detection of major genes based on non-normality of data: permuted datasets were analysed, data-transformations were applied, and residuals were judged for normality. Allelic effects at the major gene locus showed nearly to complete dominance, with a recessive, unfavourable allele in both traits. Relatively high estimates of the frequencies of unfavourable alleles in each breed suggest that considerable genetic progress would be possible by selection against major genes. However, the major genes that are possibly affecting hip and elbow dysplasia in these populations will require further study.     

Linkage analysis for diseases with variable age of onset

We present a method for the multivariate linkage analysis of the age of onset of a disease. The approach allows the incorporation of covariates for the study of gene by environment interactions. It is applicable to general pedigrees. The likelihood of the data is expressed as a function of the number of alleles identical by descent at a marker, the censored ages of onset and disease status, and environmental exposures. In a simulation study, we compare the power to detect linkage under different sampling schemes for either a dominant or recessive trait when approximately 10% of individuals are gene carriers. The majority of the linkage information from a sample of randomly selected sib pairs was retained when the analyses were limited to sibships with one sibling having early-onset disease (<59 years old). Incorporating parental phenotypes could improve the power to detect the gene. When the sample consists of affected sib pairs (ASPs) having variable age of onset, the likelihood ratio (LR) test had higher power than the means (t(2)) test for detecting a locus with a large genetic relative risk (R(g) = 20). However, the power of the two tests was similar when ASPs are selected so that the proband has an early onset of disease. Lastly, the LR test had more power than the t(2) test to detect linkage in the presence of gene by environment interactions.