Pedigree analysis of vitiligo: Further support for multilocus involvement

Vitiligo is a dermatological disorder in man that shows familial aggregation. We performed segregation analysis on data pertaining to vitiligo on members of 147 pedigrees each ascertained through a single proband, and tested various non-genetic, and one-locus and two-locus genetic models. Non-genetic and one-locus genetic models were rejected in favour of a two-locus model postulating epistatic interaction of recessive alleles in the aetiology of vitiligo. The present results show that vitiligo is not a single-locus disorder and substantiate our earlier inference, drawn on the basis of nuclear-family data, of multilocus involvement in the pathogenesis of vitiligo.     

Schizophrenia: the testing of genetic models by pedigree analysis.

Simulated pedigrees of schizophrenia generally show a clear peak in their likelihood surface corresponding to analysis by the genetic models, which served as the basis for the simulation. The likelihood surface obtained with real data permits determination of the allelic frequency and the selection of an optimal one-locus, two-locus, and four-locus model. These three models have certain features in common, notably, a relatively high frequency of the allele predisposing to schizophrenia (about 20%) and a relatively low index of genetic determination (23%--34%). However, direct likelihood comparisons do not permit distinctions between the one-locus, two-locus, and four-locus models. The most likely interpretation of this finding is that the etiology of schizophrenia is heterogeneous or even nongenetic. However, a simple model with a single completely recessive locus and incomplete penetrance in the homozygote also produces a flat likelihood surface closely resembling that obtained with the real data. With reservation, this single-locus model may be put forward as a potentially useful working hypothesis.     

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.     

Evidence for two unlinked loci regulating total serum IgE levels.

Studies investigating the genetic control of total serum IgE levels are of major importance in understanding basic pathophysiologic mechanisms in atopy and asthma, since IgE levels predict onset and correlate with the clinical expression of these disorders. Previous analysis of data from 92 families, ascertained through a parent with asthma, showed evidence for recessive inheritance of high IgE levels with linkage to chromosome 5q. Since there was significant residual familial correlation in the one-locus segregation analysis, two-locus segregation and linkage analyses were performed. Segregation analyses provided evidence for a second major locus unlinked to the locus on 5q. Utilization of this two-locus model corroborates the previous evidence for linkage between this trait and markers on 5q31-q33. The LODs for the most informative marker D5S436 increased from 3.00 at 10% recombination to 4.67 at 9% recombination, when the two-locus model was used. Additional linkage studies are needed to map this second locus. These results demonstrate the importance of performing multilocus segregation and linkage analyses for quantitative traits that are related to the phenotype of a complex disorder. This approach has given further insight into the genetics of allergy and asthma by providing evidence for a two-locus model.     

A complete enumeration and classification of two-locus disease models

There are 512 two-locus, two-allele, two-phenotype, fully penetrant disease models. Using the permutation between two alleles, between two loci, and between being affected and unaffected, one model can be considered to be equivalent to another model under the corresponding permutation. These permutations greatly reduce the number of two-locus models in the analysis of complex diseases. This paper determines the number of nonredundant two-locus models (which can be 102, 100, 96, 51, 50, or 58, depending on which permutations are used, and depending on whether zero-locus and single-locus models are excluded). Whenever possible, these nonredundant two-locus models are classified by their property. Besides the familiar features of multiplicative models (logical AND), heterogeneity models (logical OR), and threshold models, new classifications are added or expanded: modifying-effect models, logical XOR models, interference and negative interference models (neither dominant nor recessive), conditionally dominant/recessive models, missing lethal genotype models, and highly symmetric models. The following aspects of two-locus models are studied: the marginal penetrance tables at both loci, the expected joint identity-by-descent (IBD) probabilities, and the correlation between marginal IBD probabilities at the two loci. These studies are useful for linkage analyses using single-locus models while the underlying disease model is two-locus, and for correlation analyses using the linkage signals at different locations obtained by a single-locus model.     

The deafness locus (dn) maps to mouse Chromosome 19

The deafness mouse has profound sensorineural hearing loss with degeneration of hair cells soon after birth. The mode of inheritance is recessive, and there are no associated phenotypic anomalies. Thus, this mouse provides a model for recessive, nonsyndromic, prelingual deafness. We have mapped the gene causing deafness in the mouse to Chromosome (Chr) 19 by analysis of 230 intersubspecific backcross progeny. No recombinants were found with the microsatellite marker D19Mit14. The loci for two guanine nucleotide-binding proteins are tightly linked to this marker, and they are being investigated as possible candidate genes. The identification of the defective gene in the mouse will help to explain the mechanism that causes hair cell degeneration and is likely to identify a homologous gene for deafness in humans.     

The contribution of the DFNB1 locus to neurosensory deafness in a Caucasian population.

Classical studies have demonstrated genetic heterogeneity for nonsyndromic autosomal recessive congenital neurosensory deafness, with at least six loci postulated. Linkage analysis in two consanguineous Tunisian kindreds has demonstrated that one such deafness locus, DFNB1, maps near chromosome 13 markers D13S175, D13S143, and D13S115. We tested these markers for cosegregation with deafness in 18 New Zealand and 1 Australian nonconsanguineous kindreds, each of which included at least two siblings with nonsyndromic presumed congenital sensorineural deafness and that had a pedigree structure consistent with autosomal recessive inheritance. When all families were combined, a peak two-point lod score of 2.547 (theta = .1) was obtained for D13S175, 0.780 (theta = .2) for D13S143, and 0.664 (theta = .3) for D13S115. While there was no statistically significant evidence for heterogeneity at any of the three loci tested, nine families showed cosegregation of marker haplotypes with deafness. These observations suggest that the DFNB1 locus may make an important contribution to autosomal recessive neurosensory deafness in a Caucasian population. In the nine cosegregating families, phenotypic variation was observed both within sibships (in four families), which indicates that variable expressivity characterizes some genotypes at the DFNB1 locus, and between generations (in two families), which suggests allelic heterogeneity.     

On the inheritance of abdominal aortic aneurysm.

To determine the mode of inheritance of abdominal aortic aneurysm, data on first-degree relatives of 91 probands were collected. Results of segregation analysis performed on these data are reported. Many models, including nongenetic and genetic models, were compared using likelihood methods. The nongenetic model was rejected; statistically significant evidence in favor of a genetic model was found. Among the many genetic models compared, the most parsimonious genetic model was that susceptibility to abdominal aortic aneurysm is determined by a recessive gene at an autosomal diallelic major locus. A multifactorial component in addition to the major locus does not increase the likelihood of the data significantly.     

Strategies for conditional two-locus nonparametric linkage analysis

In this article we deal with two-locus nonparametric linkage (NPL) analysis, mainly in the context of conditional analysis. This means that one incorporates single-locus analysis information through conditioning when performing a two-locus analysis. Here we describe different strategies for using this approach. Cox et al. [Nat Genet 1999;21:213-215] implemented this as follows: (i) Calculate the one-locus NPL process over the included genome region(s). (ii) Weight the individual pedigree NPL scores using a weighting function depending on the NPL scores for the corresponding pedigrees at speci fi c conditioning loci. We generalize this by conditioning with respect to the inheritance vector rather than the NPL score and by separating between the case of known (prede fi ned) and unknown (estimated) conditioning loci. In the latter case we choose conditioning locus, or loci, according to prede fi ned criteria. The most general approach results in a random number of selected loci, depending on the results from the previous one-locus analysis. Major topics in this article include discussions on optimal score functions with respect to the noncentrality parameter (NCP), and how to calculate adequate p values and perform power calculations. We also discuss issues related to multiple tests which arise from the two-step procedure with several conditioning loci as well as from the genome-wide tests.     

Two-locus identity probabilities and identity disequilibrium in a partially selfing subdivided population

Measures of association of genes at different loci (linkage disequilibrium) are widely used to determine whether the structure of natural populations is clonal or not, to map genes from population data, or to test for the homogeneity of response of molecular markers to background selection, for example. However, the usual definitions of parameters for gametic associations may not be suitable for all these purposes. In this paper, we derive the recursion equations for one- and two-locus identity probabilities in an infinite island model. We study the role of drift, gene flow, partial selfing and mutation model on the expected association of genes across loci. We define the 'within-subpopulation identity disequilibrium' as the difference between the joint two-locus probability of identity in state and the expected product of one-locus identity probabilities. We evaluate this parameter as a function of recombination rate, effective size, gene flow and selfing rate. Within-subpopulation identity disequilibrium attains maximum values for intermediate immigration rates, whatever the selfing rate. Moreover, identity disequilibrium may be very small, even for high selfing rates. We discuss the implications of these findings for the analysis of data from natural populations.     

A simple method for testing two-locus models of inheritance

A graphic method for testing simple two-locus models of inheritance is developed. The model assumes two alleles at each locus where both loci exhibit dominant, both exhibit recessive, or one locus exhibits dominant and one locus exhibits recessive inheritance. Examples of applying the graphs using published data on three diseases are given.     

Selective sweeps in multilocus models of quantitative traits

We study the trajectory of an allele that affects a polygenic trait selected toward a phenotypic optimum. Furthermore, conditioning on this trajectory we analyze the effect of the selected mutation on linked neutral variation. We examine the well-characterized two-locus two-allele model but we also provide results for diallelic models with up to eight loci. First, when the optimum phenotype is that of the double heterozygote in a two-locus model, and there is no dominance or epistasis of effects on the trait, the trajectories of selected mutations rarely reach fixation; instead, a polymorphic equilibrium at both loci is approached. Whether a polymorphic equilibrium is reached (rather than fixation at both loci) depends on the intensity of selection and the relative distances to the optimum of the homozygotes at each locus. Furthermore, if both loci have similar effects on the trait, fixation of an allele at a given locus is less likely when it starts at low frequency and the other locus is polymorphic (with alleles at intermediate frequencies). Weaker selection increases the probability of fixation of the studied allele, as the polymorphic equilibrium is less stable in this case. When we do not require the double heterozygote to be at the optimum we find that the polymorphic equilibrium is more difficult to reach, and fixation becomes more likely. Second, increasing the number of loci decreases the probability of fixation, because adaptation to the optimum is possible by various combinations of alleles. Summaries of the genealogy (height, total length, and imbalance) and of sequence polymorphism (number of polymorphisms, frequency spectrum, and haplotype structure) next to a selected locus depend on the frequency that the selected mutation approaches at equilibrium. We conclude that multilocus response to selection may in some cases prevent selective sweeps from being completed, as described in previous studies, but that conditions causing this to happen strongly depend on the genetic architecture of the trait, and that fixation of selected mutations is likely in many instances.     

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.     

Contribution of DFNB1 and DFNB2 loci to neurosensory deafness in affected Tunisian families

Classical studies have demonstrated genetic heterogeneity for nonsyndromic autosomal recessive congenital neurosensory deafness. The first two DFNB1 and DFNB2 locations were found using two consanguineous Tunisian families respectively from north and south. We tested these loci for cosegregation with deafness in twenty four southern families with nonsyndromic presumed congenital sensorineural deafness and a pedigree structure consistent with autosomal recessive inheritance. Only in our families, did deafness cosegregate with DFNB1. Although our families are from the south, none of them showed linkage to DFNB2.     

Estimation of effective population size and migration rate from one- and two-locus identity measures

Standard methods for inferring demographic parameters from genetic data are based mainly on one-locus theory. However, the association of genes at different loci (e.g., two-locus identity disequilibrium) may also contain some information about demographic parameters of populations. In this article, we define one- and two-locus parameters of population structure as functions of one- and two-locus probabilities for the identity in state of genes. Since these parameters are known functions of demographic parameters in an infinite island model, we develop moment-based estimators of effective population size and immigration rate from one- and two-locus parameters. We evaluate this method through simulation. Although variance and bias may be quite large, increasing the number of loci on which the estimates are derived improves the method. We simulate an infinite allele model and a K allele model of mutation. Bias and variance are smaller with increasing numbers of alleles per locus. This is, to our knowledge, the first attempt of a joint estimation of local effective population size and immigration rate.     

Variational principles in evolution

For a one-locus selection model, Svirezhev introduced an integral variational principle by defining a Lagrangian which remained stationary on the trajectory followed by the population undergoing selection. It is shown here (i) that this principle can be extended to multiple loci in some simple cases and (ii) that the Lagrangian is defined by a straightforward generalization of the one-locus case, but (iii) that in two-locus or more general models there is no straightforward extension of this principle if linkage and epistasis are present. The population trajectories can be constructed as trajectories of steepest ascent in a Riemannian metric space. A general method is formulated to find the metric tensor and the surface in the metric space on which the trajectories, which characterize the variations in the gene structure of the population, lie. The local optimality principle holds good in such a space. In the special case when all possible linkage disequilibria are zero, the phase point of then-locus genetic system moves on the surface of the product space ofn higher dimensional unit spheres in a certain Riemannian metric space of gene frequencies so that the rate of change of mean fitness is maximum along the trajectory. In the two-locus case the corresponding surface is a hyper-torus.     

Linkage of congenital recessive deafness (gene DFNB10) to chromosome 21q22.3.

Deafness is a heterogeneous trait affecting approximately 1/1,000 newborns. Genetic linkage studies have already implicated more than a dozen distinct loci causing deafness. We conducted a genome search for linkage in a large Palestinian family segregating an autosomal recessive form of nonsyndromic deafness. Our results indicate that in this family the defective gene, DFNB10, is located in a 12-cM region near the telomere of chromosome 21. This genetic distance corresponds to <2.4 Mbp. Five marker loci typed from this region gave maximum LOD scores > or = to 3. Homozygosity of marker alleles was evident for only the most telomeric marker, D21S1259, suggesting that DFNB10 is closest to this locus. To our knowledge, this is the first evidence, at this location, for a gene that is involved in the development or maintenance of hearing. As candidate genes at these and other deafness loci are isolated and characterized, their roles in hearing will be revealed and may lead to development of mechanisms to prevent deafness.     

Molecular analysis of the TMPRSS3 gene in Moroccan families with non-syndromic hearing loss

Autosomal recessive non-syndromic hearing impairment (ARNSHI) is the most common type of inherited hearing impairment, accounting for approximately 80% of inherited prelingual hearing impairment. Hearing loss is noted to be both phenotypically and genetically heterogeneous. Mutations in the TMPRSS3 gene, which encodes a transmembrane serine protease, are known to cause autosomal recessive non-syndromic hearing impairment DFNB8/10. In order to elucidate if the TMPRSS3 gene is responsible for ARNSHI in 80 Moroccan families with non-syndromic hearing impairment, the gene was sequenced using DNA samples from these families. Nineteen TMPRSS3 variants were found, nine are located in the exons among which six are missense and three are synonymous. The 10 remaining variations are located in non-coding regions. Missense variants analysis show that they do not have a significant pathogenic effect on protein while pathogenicity of some variant remains under discussion. Thus we show that the TMPRSS3 gene is not a major contributor to non-syndromic deafness in the Moroccan population.     

How to model a complex trait. 2. Analysis with two disease loci

Complex traits are often governed by more than one trait locus. The first step towards an adequate model for such diseases is a linkage analysis with two trait loci. Such an analysis can be expected to have higher power to detect linkage than a standard single-trait-locus linkage analysis. However, it is crucial to accurately specify the parameters of the two-locus model. Here, we recapitulate the general two-locus model with and without genomic imprinting. We relate heterogeneity, multiplicative, and additive two-locus models to biological or pathophysiological mechanisms, and give the corresponding averaged ("best-fitting") single-trait-locus models for each of the two loci. Furthermore, we derive the two-locus penetrances from the averaged single-locus models, under the assumption of one of the three model classes mentioned above. Using these formulae, if the best-fitting single-locus models are available, investigators may perform a two-trait-locus linkage analysis under a realistic model. This procedure will maximize the power to detect linkage for traits which are governed by two or more loci, and lead to more accurate estimates of the disease-locus positions.