A variance components/major locus likelihood approximation on quantitative data

MQScore_SNP software for multipoint parametric linkage analysis of quantitative traits in large pedigrees

We describe software for multipoint parametric linkage analysis of quantitative traits using information about SNP genotypes. A mixed model of major gene and polygene inheritance is implemented in this software. Implementation of several algorithms to avoid computational underflow and decrease running time permits application of our software to the analysis of very large pedigrees collected in human genetically isolated populations. We tested our software by performing linkage analysis of adult height in a large pedigree from a Dutch isolated population. Three significant and four suggestive loci were identified with the help of our programs, whereas variance-component-based linkage analysis, which requires the pedigree fragmentation, demonstrated only three suggestive peaks. The software package MQScore_SNP is available at http://mga.bionet.nsc.ru/soft/index.html.

Linkage analysis of adult height in a large pedigree from a Dutch genetically isolated population

Despite extensive research of genetic determinants of human adult height, the genes identified up until now allow to predict only a small proportion of the trait's variance. To identify new genes we analyzed 2,486 genotyped and phenotyped individuals in a large pedigree including 23,612 members in 18 generations. The pedigree was derived from a young genetically isolated Dutch population, where genetic heterogeneity is expected to be low and linkage disequilibrium has been shown to be increased. Complex segregation analysis confirmed high heritability of adult height, and suggested mixed model of height inheritance in this population. The estimates of the model parameters obtained from complex segregation analysis were used in parametric linkage analysis, which highlighted three genome-wide significant and additionally at least four suggestive loci involved in height. Significant peaks were located at the chromosomal regions 1p32 (LOD score = 3.35), 2p16 (LOD score = 3.29) and 16q24 (LOD score = 3.94). For the latter region, a strong association signal (FDR q < 0.05) was obtained for 19 SNPs, 17 of them were located in the CDH13 (cadherin 13) gene of which one (rs1035569) explained 1.5% of the total height variance.

Inheritance of litter size at birth in farmed arctic foxes (Alopex lagopus, Canidae, Carnivora)

Natural populations of the arctic fox (Alopex lagopus, Canidae, Carnivora) differ drastically in their reproductive strategy. Coastal foxes, which depend on stable food resources, produce litters of moderate size. Inland foxes feed on small rodents, whose populations are characterized by cycling fluctuation. In the years with low food supply, inland fox populations have a very low rate of reproduction. In the years with high food supply, they undergo a population explosion. To gain insight into the genetic basis of the reproductive strategy of this species, we performed complex segregation analysis of the litter size in the extended pedigree of the farmed arctic foxes involving 20,665 interrelated animals. Complex segregation analysis was performed using a mixed model assuming that the trait was under control of a major gene and a large number of additive genetic and random factors. To check the significance of any major gene effect, we used Elston-Stewart transmission probability test. Our analysis demonstrated that the inheritance of this trait can be described within the frameworks of a major gene model with recessive control of low litter size. This model was also supported by the pattern of its familial segregation and by comparison of the distributions observed in the population and that expected under our model. We suggest that a system of balanced polymorphism for litter size in the farmed population might have been established in natural populations of arctic foxes as a result of adaptation to the drastic fluctuations in prey availability.

A major gene influences variation in large HDL particles and their response to diet in baboons

Some baboons accumulate appreciable amounts of large apoE-rich HDLs (HDL(1)) which are similar to those reported in humans with several different dyslipoproteinemias. We estimated HDL(1) cholesterol concentrations by gradient gel electrophoresis of serum samples obtained from 634 pedigreed baboons fed with three diets differing in levels of fat and cholesterol. The HDL(1) trait was highly heritable on each diet (0.390< or =h(2)< or =0.528). Segregation analyses yielded significant evidence that a single major gene plus polygenes affected HDL(1) on a high-fat low-cholesterol diet. The major gene explained approximately 56% of total trait variance and 90% of the additive genetic variance in HDL(1) levels in these baboons. Bivariate one-locus segregation analyses indicated that this major gene exerts significant pleiotropic effects on a number of traditional HDL traits on all three diets, including HDL size distributions, and concentrations of HDL-C, apoAI, and apoE. Linkage analyses showed that this major gene was not located in chromosomal regions that contain six candidate genes whose protein products are important to HDL metabolism (LCAT, CETP, APOA1, APOE, ABCA1, LIPC). Our results suggest this major gene in baboons plays a pivotal role in HDL metabolism, but is unlikely to code for any of the proteins previously implicated in studies of human HDL(1).

Technical note: determining peeling order using sparse matrix algorithms

To study the effect of individual genes by segregation or linkage analyses, the likelihood of the model needs to be evaluated. The likelihood can be computed efficiently using the Elston-Stewart algorithm. This algorithm involves summing over the unobserved genotypes in the pedigree, which is called peeling. An important aspect of this algorithm is to determine the order of peeling to maximize efficiency. This paper shows how determining peeling order is related to a problem in solving systems of symmetric sparse linear equations. It also shows how algorithms developed to efficiently solve those systems, can be used to determine the optimal order of peeling in the Elston-Stewart algorithm.

Association of growth hormone loci with milk yield traits in Holstein bulls

A pedigree analysis was used to investigate the association of bovine growth hormone loci with milk production traits of Holstein cattle. Holstein bulls were typed for three bovine growth hormone loci located in exon V, intron C, and the 3' region of the gene. Phenotypic data were daughter yield deviations for milk, fat, and protein yields and for fat and protein percentages. Analysis of linkage across families was applied to the data using one or two bovine growth hormone loci as markers linked to a putative biallelic quantitative trait locus. Estimated parameters were allele frequency, genotypic means, within-genotype standard deviation of a putative quantitative trait locus, and recombination fraction between the markers and the quantitative trait locus. Parameters were estimated by maximum likelihood techniques. The estimated frequency of the quantitative trait locus allele that decreased the value of the phenotype ranged from 0.1 for milk yield to 0.6 for protein yield. The estimated effect of an allele substitution at the quantitative trait locus, given in phenotypic standard deviation units, ranged from 0.75 for fat percentage to 1.6 for milk yield. The standard deviation within genotype ranged from 0.67 for fat yield to 0.87 for milk yield. The estimated recombination fraction was close to zero for protein percentage, indicating physical linkage between a quantitative trait locus affecting the trait and the bovine growth hormone loci.

Detection and utilization of single genes without DNA assays

Quantitative traits are often assumed to be controlled by a large number of loci that each have a small effect. Under this assumption, the distribution of genotypic and phenotypic values can be adequately modeled by a multivariate normal distribution. Thus, most genetic analyses are based on mixed linear models. Evidence is accumulating, however, for the presence of loci that have large effects on traits of economic importance. If the genotypes for such loci can be observed without error, then--conditional on these observed genotypes--genotypic and phenotypic values follow a multivariate normal distribution, and data from very large pedigrees can be analyzed using a mixed linear model that includes the genotypic effects for these loci as fixed effects. However, when the major genotype is not observed, the genotypic and phenotypic values follow a mixture of multivariate normal distributions, and analyses based on fitting a mixed linear model may not be optimum, especially for populations undergoing selection and nonrandom mating. Several approaches are discussed for the genetic analysis of data when the major genotypes are not known.

The finite polygenic mixed model: An alternative formulation for the mixed model of inheritance

This paper presents a mixed model of inheritance with a finite number of polygenic loci. This model leads to a likelihood that can be calculated using efficient algorithms developed for oligogenic models. For comparison, likelihood profiles were obtained for the finite polygenic mixed model, the usual mixed model, with exact and approximate calculations, and for a class D regressive model. The profiles for the finite polygenic mixed model were closest to the profiles for the usual mixed model with exact calculations.

Genetic epidemiologic studies in the etiology of skin diseases

Genetic epidemiologic studies have provided critical insights into the etiology of both rare and common skin diseases. Designs for these studies are distinct from those generally employed in epidemiologic studies. Here, we review the types of data collected for various genetic epidemiologic designs, inherent strengths and weaknesses, and their similarities to more classic epidemiologic methods. Examples from the study of skin diseases are provided to highlight the successful application of these methods.

A gene-environment interaction between inferred kallikrein genotype and potassium

Urinary kallikrein excretion has been shown statistically to be partially determined by a major gene in large Utah pedigrees with the use of segregation analysis. A previous twin analysis of environmental factors influencing urinary kallikrein level showed that urinary potassium twin differences were strongly related to differences in urinary kallikrein. The present study uses 769 individuals in 58 Utah pedigrees to analyze the association of urinary potassium with urinary kallikrein within statistically inferred kallikrein genotypes. Fitting genotype-specific curves relating urinary kallikrein level to 12-hour urinary potassium amount within a major gene, polygene, and common environment model, we showed a significant statistical urinary potassium interaction with the inferred major gene for kallikrein (P = .0002). The heterozygotes (with a frequency of 50%) had a significant association between urinary kallikrein and potassium (slope, 0.51 +/- 0.04 SD), whereas there was no association with potassium in the low homozygotes, suggesting a genetic defect involving the kallikrein response to potassium. The model predicted that an increase in urinary potassium excretion of 0.8 SD above the mean in these pedigrees would be associated with high kallikrein levels in the heterozygotes similar to the high homozygotes. A decrease of 1.3 SD in urinary potassium excretion in heterozygous individuals was associated with kallikrein levels similar to the homozygous individuals with low kallikrein. Because in the steady state urinary potassium represents dietary potassium intake, this study suggests that an increase in dietary potassium intake in 50% of these pedigree members, estimated to be heterozygous at the kallikrein locus, would be associated with an increase in an underlying genetically determined low kallikrein level.(ABSTRACT TRUNCATED AT 250 WORDS)

Quantitative genetics of sexual dimorphism in body fat measurements

A variance decomposition analysis using maximum likelihood methods was employed to examine the genetic architecture of sexual dimorphism in anthropometric traits in a large pedigreed sample of Mexican American individuals from San Antonio, Texas. For this analysis the magnitude of sexual dimorphism was viewed as arising from a special case of genotype by environment interaction (G × E), that of genotype by sex (G × S). Evidence indicates a marked G × S interaction for 9 of the 12 traits examined and 1 of the 4 indices, findings which are interpreted as indicators of a strong genetic component to the degree of sexual dimorphism expressed in these traits. Such results have important implications for the use and interpretation of these traits in an epidemiological as well as an evolutionary context. © 1993 Wiley-Liss, Inc.

Variance components/major locus likelihood approximation for quantitative, polychotomous, and multivariate data

Pearson [Philos Trans R Soc Lond [A] 200:1-66, 1903], Mendell and Elston [Biometrics 30:41-57, 1974], and Rice et al. [Biometrics 35:451-459, 1979] approximated the likelihood of the multifactorial model on a dichotomous phenotype by a procedure of successive univariate computation and conditioning. Hasstedt [Pap: Pedigree Analysis Package, Rev. 3. 1989] and Demenais [Am J Hum Genet 49:773-785, 1991] extended the algorithm to include a major locus. Here I extend the algorithm to polychotomous, quantitative, and multivariate phenotypes, add a major locus to the model, and describe and evaluate the accuracy of an approximation of the resulting variance components/major locus model.

Segregation analysis of height-adjusted weight with generation- and age-dependent effects: the Nancy Family Study

A segregation analysis using a regressive model with generation- and age-dependent effects was applied to familial data of height-adjusted weight to investigate the major gene hypothesis. The sample included 629 nuclear families with 2,534 members volunteering for a free health check-up in the Preventive Medicine Center of Vandoeuvre-lès-Nancy, France. The familial correlations were 0.094 +/- 0.040 between spouses, 0.198 +/- 0.023 between parent and offspring, and 0.327 +/- 0.034 between siblings. The variability of the trait was higher in parents than in offspring. The most parsimonious genetic model indicated a codominant major effect increasing with age in childhood, then stabilizing in adulthood. The same data were analyzed using the classical mixed model, assuming equality of variances between parents and offspring, no resemblance between spouses, similar parent-offspring and sib-sib correlations, and identical effects in parents and offspring. This analysis indicated a recessive solution. In both analyses, mendelian transmission was rejected. However, the mixture of two distributions in the recessive model, instead of three in the codominant one, was less constraining with respect to the test of transmission probabilities, and the rejection of mendelian transmission was due to a single family in the recessive case, instead of several families in the codominant one. This could possibly explain why previous studies, all using the mixed model, found evidence for a recessive major gene. Although the major gene hypothesis cannot be definitely ruled out from our results, the mechanism appears more complex than the effect of one single gene.

Extended pedigree patterned covariance matrix mixed models for quantitative phenotype analysis

Overt computational constraints in the formation of mixed models for the analysis of large extended-pedigree quantitative trait data which allow one to reliably characterize and partition sources of variation resulting from a variety sources have proven difficult to overcome. The present paper suggests that by combining a restricted patterned covariance matrix approach to modeling and partitioning the variation arising from polygenic and environmental forces with an Elston-Stewart like algorithmic approach to modeling variation resulting from a single genetic locus with large phenotypic effects one can produce a model that is at once intuitively appealing, efficient computationally, and reliable numerically. Extensions and variations of this approach are also discussed, as are some simulation and timing studies carried out in an effort to validate the accuracy and computational efficiency of the proposed methodology.

A variance components/major locus likelihood approximation on quantitative data

The variance components/major locus model encompasses a major locus, a polygenic component, and shared environmental effects. The model attributes familial correlations to polygenic and shared environmental effects when testing for major locus inheritance or accounts for the major locus when estimating variance components. Because exact computation of the likelihood of the variance components/major locus model on quantitative data requires excessive computer time, I developed an approximation. The approximation retained the general shape of the likelihood surface. Accuracy of the approximation did not vary consistently with allele frequency or the size of the major locus effect.