[Functional linear models for region-based association analysis].

Regional association analysis is one of the most powerful tools for gene mapping because instead analysis of individual variants it simultaneously considers all variants in the region. Recent development of the models for regional association analysis involves functional data analysis approach. In the framework of this approach, genotypes of variants within region as well as their effects are described by continuous functions. Such approach allows us to use information about both linkage and linkage disequilibrium and reduce the influence of noise and/or observation errors. Here we define a functional linear mixed model to test association on independent and structured samples. We demonstrate how to test fixed and random effects of a set of genetic variants in the region on quantitative trait. Estimation of statistical properties of new methods shows that type I errors are in accordance with declared values and power is high especially for models with fixed effects of genotypes. We suppose that new functional regression linear models facilitate identification of rare genetic variants controlling complex human and animal traits. New methods are implemented in computer software FREGAT which is available for free download at http://mga.bionet.nsc.ru/soft/FREGAT/.

A genome-wide linkage study of individuals with high scores on NEO personality traits.

The NEO-Five-Factor Inventory divides human personality traits into five dimensions: neuroticism, extraversion, openness, conscientiousness and agreeableness. In this study, we sought to identify regions harboring genes with large effects on the five NEO personality traits by performing genome-wide linkage analysis of individuals scoring in the extremes of these traits (>90th percentile). Affected-only linkage analysis was performed using an Illumina 6K linkage array in a family-based study, the Erasmus Rucphen Family study. We subsequently determined whether distinct, segregating haplotypes found with linkage analysis were associated with the trait of interest in the population. Finally, a dense single-nucleotide polymorphism genotyping array (Illumina 318K) was used to search for copy number variations (CNVs) in the associated regions. In the families with extreme phenotype scores, we found significant evidence of linkage for conscientiousness to 20p13 (rs1434789, log of odds (LOD)=5.86) and suggestive evidence of linkage (LOD >2.8) for neuroticism to 19q, 21q and 22q, extraversion to 1p, 1q, 9p and12q, openness to 12q and 19q, and agreeableness to 2p, 6q, 17q and 21q. Further analysis determined haplotypes in 21q22 for neuroticism (P-values = 0.009, 0.007), in 17q24 for agreeableness (marginal P-value = 0.018) and in 20p13 for conscientiousness (marginal P-values = 0.058, 0.038) segregating in families with large contributions to the LOD scores. No evidence for CNVs in any of the associated regions was found. Our findings imply that there may be genes with relatively large effects involved in personality traits, which may be identified with next-generation sequencing techniques.

Some pitfalls in application of functional data analysis approach to association studies.

One of the most effective methods for gene-based mapping employs functional data analysis, which smoothes data using standard basis functions. The full functional linear model includes a functional representation of genotypes and their effects, while the beta-smooth only model smoothes the genotype effects only. Benefits and limitations of the beta-smooth only model should be studied before using it in practice. Here we analytically compare the full and beta-smooth only models under various scenarios. We show that when the full model employs two sets of basis functions equal in type and number, genotypes smoothing is eliminated from the model and it becomes analytically equivalent to the beta-smooth only model. If the basis functions differ only in type, genotypes smoothing is also eliminated from the full model, but the type of basis functions used for smoothing genotype effects becomes redefined. This leads to misinterpretation of the results and may reduce statistical power. When basis functions differ in number, no analytical comparison of the full and beta-smooth only models is possible. However, we show that the numbers of basis functions set unequal can become equal during the analysis, and the full model becomes disadvantageous.

Segregation analysis of Scheuermann disease in ninety families from Siberia.

Scheuermann disease [OMIM number 181440] is the most common cause of structural kyphosis in adolescence. Segregation analysis using a model with gender effects was applied to 90 pedigrees from Barnaul (West Siberia, Russia) ascertained through a proband with Scheuermann disease. The transmission probability model was used to detect major gene effect. A significant contribution of a major gene to the control of the pathology was established. Inheritance of the disease can be described within the framework of a dominant major gene diallele model. According to this model, Scheuermann disease should never occur in the absence of the mutant allele. All male carriers of the mutant allele develop the disease, while only a half of female carriers manifest it. We found a high frequency of idiopathic scoliosis in the families with Scheuermann disease (0.08 vs. 0.01-0.02 in general population). We also observed a succession of idiopathic scoliosis and Scheuermann disease in consecutive generations. The familial aggregation of these two spinal pathologies in the present sample may indicate a genetic unity of Scheuermann disease and idiopathic scoliosis.

Segregation analysis of idiopathic scoliosis: demonstration of a major gene effect.

Segregation analysis using a model with age and gender effects was applied to 101 pedigrees ascertained through a proband with idiopathic scoliosis. The transmission probability model was used to detect major gene effect. When we analyzed the pedigrees where affected status was assigned to persons with a Cobb's angle of more than 5 degrees we did not detect a significant major gene effect. However, when the affected status was assigned to persons with pronounced forms of disease only (a curve of at least 11 degrees) a significant contribution of a major causal gene could be established and inheritance could be described according to a dominant major gene diallele model, assuming incomplete sex and age dependent penetrance of genotypes. According to this model, the pronounced forms of idiopathic scoliosis should never occur in the absence of the mutant allele. This indicates that only the carriers of the mutant allele develop pronounced forms of the disease. At the same time, only a fraction of the carriers of the mutant gene should manifest the disease (30% of males and 50% of females).

Segregation analysis of animal pedigree data from inter-population crosses.

The general method of segregation analysis of pedigree data has been developed and widely used in human genetics. We modified this method to examine pedigree data coming from inter-population crosses. These kinds of pedigrees are common in laboratory and farm animal breeding. This paper describes a rationale for the method and illustrates its application to the study of inheritance of litter size and of male sterility in hybrid stock of the house musk shrew (Suncus murinus) derived from crosses of two geographically isolated populations.

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.

Prediction of linkage phase by parental phenotypes.

This paper answers the question as to which parental phenotypes are useful in prediction of the linkage phase of the progeny under conditions of linkage equilibrium. I demonstrate that 1) the parents with the same disease status or marker genotype carry no information about phase of the diheterozygous offspring; 2) the linkage phase can be inferred unambiguously only under recessive or dominant control of disease. In any other situations, only the probability of linkage phase is inferred. It has been shown that the relative difference between the probabilities of coupling phase and repulsion phase, epsilon, which is regarded as a measure of accuracy of linkage phase prediction by parental phenotypes, is the same in all informative crosses and is dependent on the genetic model of the disease. Furthermore, epsilon is the same for the di- and polyallelic marker genes.

Sample size required for predefined linkage decision quality.

A method for estimating the sample size required to attain a predefined linkage decision quality (type I and type II errors) is proposed using the linkage test power estimate developed by Ginsburg et al. [(1996) Genet Epidemiol 13:355-366]. The method is applicable for samples of arbitrarily structured pedigrees collected via proband. Comparison of different ascertainment schemes and pedigree structures by their consequent minimal sample size was performed. For recessive and dominant inheritance with complete penetrance, the relative ranks of the ascertainment schemes are invariant regardless of the true recombination fraction value and the trait and marker gene frequencies, which enables one to point out the better scheme. The feasibility of evaluating a sampling strategy by the cost of pedigree collection is also considered, and comparison between these two methods of sample planning is performed.

A cooperative binomial ascertainment model.

It has been shown that the classical binomial form of ascertainment, assuming a constant probability pi that any affected individual may become a proband for his pedigree, cannot describe a rather wide range of ascertainment procedures that might arise in practice. Some more general heuristic ascertainment formulas might then be preferred, and in this paper we consider the probabilistic basis for these formulas. We retain the binomial assumption of the classical scheme but allow the ascertainment probability to depend on the number of potential probands per pedigree. This probability can be expressed by an increasing or a decreasing function of that number. Various illustrations are given and situations where the "cooperative" binomial scheme should be valuable are discussed.

On planning of samples for linkage analysis: two ways of a sample size reduction.

The sample size required for a given type I and type II errors of linkage decision is determined by using the earlier proposed method of the linkage test power estimation [Ginsburg et al., 1996]. Dependence of the sample size on the heterozygotic genotype penetrance is investigated. Two approaches to sample size reduction are considered: the choice of marker gene and the special extension of analyzed pedigree structures. Their effects are quantitatively evaluated in some illustrative situations. It is shown that a practical reduction in sample size can be achieved only when the added part of a pedigree has a special set of phenotypic characteristics in its members.

Comparison of asymptotic tests of the Hardy-Weinberg distribution.

Nine asymptotic tests of the Hardy-Weinberg distribution have been analysed. It is shown that the usual chi 2 test is the most appropriate one, considering type I and II errors.

On estimation of linkage test power.

Two methods of estimating linkage test power are proposed. The first method is based on the maximum likelihood (ML) estimate of the recombination fraction and is intended for use with a likelihood ratio test (LRT) in the form of a chi 2 or lod score. The power is estimated through a noncentral chi 2 distribution with a specially chosen noncentrality parameter. The second method uses the LRT constructed for a simple alternative hypothesis regarding the recombination fraction value. The approximate distribution of this test and a method of estimating its power is proposed. Using simulated pedigree data, the power estimates for these two methods were shown to be satisfactory. Comparisons among these two methods and the computer simulation approach of Boehnke [1986] are performed.

On the possibility of pleiotropic monogenic control of hereditary polyposis and primary cancer of the colon.

The results of the segregation analysis of hereditary adenomatous polyposis and primary cancer of the colon are given, taking into account the age-dependent manifestation of genotypes and the specificity of pedigree sampling. The results are used for testing the hypothesis of pleiotropic monogenic control of these two colon pathologies.

Inheritance of litter size at birth in the house musk shrew (Suncus murinus, Insectivora, Soricidae).

In this research we estimated the contribution of a major-gene effect to the control of litter size in hybrids between two local populations of the house musk shrew (Suncus murinus). Segregation analysis was performed on the basis of a mixed polygene and major-gene model. The model presumes that two parental populations may differ from each other in gene frequencies and in the values of polygenic effects but not in the major-gene contribution of the trait. Moreover, the peculiarity of the trait--litter size--is taken into account. This trait is not an individual attribute. It characterizes the parental couple and may depend on the genotypes of both parents. Results of segregation analysis of a large hybrid pedigree of Suncus murinus indicate that the parental populations differ in the allele frequency of the major gene (one population is homozygous, while the other contains the two alleles in approximately equal proportions) and in the values of average polygenic effects. Both major-gene and polygenic components are necessary for the correct description of litter size inheritance in interracial hybrids of S murinus, inasmuch as the exclusion of either of them leads to a significant drop in likelihood. The Elston-Stewart criterion also confirms the Mendelian inheritance of the major gene.

Inheritance of male hybrid sterility in the house musk shrew (Suncus murinus, Insectivora, Soricidae).

Two geographic races of the house musk shrew (Suncus murinus) were crossed and intercrossed in the laboratory. Many cases of male sterility were detected among the hybrids. Segregation analysis of the pedigree data showed that the inheritance of male sterility in interracial hybrids of S. murinus can be described within the framework of monogene polyallele model with sterility of a single allele combination. This model is similar if not identical to that proposed by Dobzhansky and Muller.

miLD and booLD programs for calculation and analysis of corrected linkage disequilibrium.

We describe software which calculates a set of linkage disequilibrium statistics, including multiallelic D' corrected by the bootstrap and permutation. The software also provides a tool for maximum likelihood and least squares estimation and testing of a set of hierarchical hypotheses formulated within the framework of the Malecot model of the decay of linkage disequilibrium with distance. Additionally, the bootstrap approach is used for estimation of the model parameter's confidence intervals and for hypothesis testing. The programs are available from http://www.geneticepi.com/Research/software/software.html

Inheritance of white head spotting in natural populations of South American water rat (Nectomys squamipes Rodentia: Sigmodontinae).

Specimens with white head spots are present at low frequency in the natural populations of South American water rat (Nectomys squamipes) and absent in the sibling species Nectomys rattus. We analyzed the pattern of inheritance of the phenotype using complex segregation analysis of pedigrees of a captive-bred population of N. squamipes. We found that the inheritance of the white head spot in this species can be described within the framework of the major gene recessive model with incomplete penetrance of genotypes.

Chromosomal segregation and fertility in Robertsonian chromosomal heterozygotes of the house musk shrew (Suncus murinus, Insectivora, Soricidae).

Crucial to our understanding of chromosomal variation and evolution in mammals are detailed studies of chromosomal heterozygotes, with analyses of chromosomal segregation and chromosome-derived infertility. We studied segregation and fertility in hybrids between karyotypic races of the house musk shrew Suncus murinus. These individuals were heterozygous for up to five Robertsonian fusions (Rbs) and an insertion of heterochromatin in an autosome. All variant chromosomes showed Mendelian segregation and all Rbs segregated independently of each other in the progeny of double heterozygotes. Litter size in single and even multiple Rb heterozygotes was no smaller than that in the less fertile parental strain. The effects of genetic background were more important in determining litter size than Rb heterozygosity for the shrews that we examined.

Inheritance of pendulum movements in rats.

The stereotyped hyperkinesis referred to as pendulum movements (PM) may be found in up to 50% of the animals in stocks of Wistar rats. The mode of inheritance of predisposition to PM was studied by two methods: 1) a classical Mendelian analysis of hybrids of the strains PM+ and PM- bred from Wistar stock for enhancement and absence of PM, respectively, and 2) a segregation analysis of pedigree data from the archive records of breeding the cataleptic GC strain. The two methods gave the same result: the inheritance of predisposition to PM can be explained by a major gene model with an incomplete penetrance of heterozygous genotype.