On the genetics of prelingual deafness.

In view of the many discordant findings in previous studies regarding the genetics of prelingual deafness, family data (133 nuclear families and 25 pedigrees) were gathered from India. Analysis of these data has revealed that the defect is primarily genetic, which is in agreement with earlier findings. Segregation analysis was performed to compare various autosomal diallelic one-locus and multilocus models. Our analysis revealed that the most parsimonious model for prelingual deafness is that it is controlled by recessive genes at a pair of unlinked diallelic autosomal loci. Individuals are affected if and only if they are recessive homozygous at both loci. The likelihood of the present data under this two-locus multiple recessive homozygosis model is at least 10(8) times higher than that of the one-locus models that were examined in previous studies. This model is also the best-fitting model among other plausible two-locus models.     

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.     

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.     

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.     

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.     

Constraints on the origin and maintenance of genetic kin recognition

Kin-recognition mechanisms allow helping behaviors to be directed preferentially toward related individuals, and could be expected to evolve in many cases. However, genetic kin recognition requires a genetic polymorphism on which recognition is based, and kin discriminating behaviors will affect the evolution of such polymorphism. It is unclear whether genetic polymorphisms used in kin recognition should be maintained by extrinsic selection pressures or not, as opposite conclusions have been reached by analytical one-locus models and simulations exploring different population structures. We analyze a two-locus model in a spatially subdivided population following the island model of dispersal between demes of finite size. We find that in the absence of mutation, selection eliminates polymorphism in most cases, except with extreme spatial structure and low recombination. With mutation, the population may reach a stable limit cycle over which both loci are polymorphic; however, the average frequency of conditional helping can be high only under strong structure and low recombination. Finally, we review evidence for extrinsic selection maintaining polymorphism on which kin recognition is based.     

Further analysis of complex allozyme polymorphisms in a barley population

New theory has recently been developed for two-locus models. In the light of this theory, an earlier analysis of esterase allozyme data from an experimental barley population has been modified to take proper account of initial gametic phase (linkage) disequilibria. The results show that the directions in which two-locus genotypic frequencies deviated from products of one-locus frequencies in this population followed those predicted by neutral descent theory. The observed departures were, however, much larger in size than predicted by the new descent measure theory, indicating that selection is operating in the population.     

On coding genotypes for genetic markers with multiple alleles in genetic association study of quantitative traits

Background

In genetic association study of quantitative traits using F_∞ models, how to code the marker genotypes and interpret the model parameters appropriately is important for constructing hypothesis tests and making statistical inferences. Currently, the coding of marker genotypes in building F_∞ models has mainly focused on the biallelic case. A thorough work on the coding of marker genotypes and interpretation of model parameters for F_∞ models is needed especially for genetic markers with multiple alleles.

Results

In this study, we will formulate F_∞ genetic models under various regression model frameworks and introduce three genotype coding schemes for genetic markers with multiple alleles. Starting from an allele-based modeling strategy, we first describe a regression framework to model the expected genotypic values at given markers. Then, as extension from the biallelic case, we introduce three coding schemes for constructing fully parameterized one-locus F_∞ models and discuss the relationships between the model parameters and the expected genotypic values. Next, under a simplified modeling framework for the expected genotypic values, we consider several reduced one-locus F_∞ models from the three coding schemes on the estimability and interpretation of their model parameters. Finally, we explore some extensions of the one-locus F_∞ models to two loci. Several fully parameterized as well as reduced two-locus F_∞ models are addressed.

Conclusions

The genotype coding schemes provide different ways to construct F_∞ models for association testing of multi-allele genetic markers with quantitative traits. Which coding scheme should be applied depends on how convenient it can provide the statistical inferences on the parameters of our research interests. Based on these F_∞ models, the standard regression model fitting tools can be used to estimate and test for various genetic effects through statistical contrasts with the adjustment for environmental factors.     

The effect on neutral gene flow of selection at a linked locus

The effect on gene flow at a neutral locus of a selective cline at a linked locus is investigated. A diffusion approximation for a two-locus island model is derived in which only one locus is subject to selection. The moments of the stationary distribution are obtained and compared to the corresponding moments from a one-locus, neutral island model. This comparison yields an effective migration rate. The effective migration rate is always less than the actual migration rate, but this effect is seen to be small for weak selection and loose linkage in the case of adult migration. The importance of selection at linked loci to the question of genetic differentiation in a subdivided population is discussed.     

Considerations on study designs using the extreme sibpairs methods under multilocus oligogenic models

Several issues pertinent to study designs employing extreme sibpairs (ESP) methods to detect complex oligogenic quantitative trait loci (QTL) are investigated in the setting of genome-wide multipoint scans. We demonstrate that when stringent alpha-levels are imposed (e.g., alpha = 0.00022 as recommended by Landers and Kruglyak), the power to detect a susceptibility locus could drop from 83.6% under a one-locus model down to a hopeless 22.8% under a two-locus model of the same heritability h(2) = 0.5 and gene frequency (p = 0.1). We introduce the notion of joint power that is the power to detect linkage to at least one location over a given panel of markers across a genomic region and describe the effect of several design factors on such joint power in a multipoint scan. Moreover, power of analysis conditional on the IBD sharings of ESPs at a known/detected locus is examined and shown to increase substantively (to 93.3% under the previous two-locus model) in detecting novel trait loci. We conclude that with such remedies, the ESP design continues to be a relatively powerful design for mapping oligogenic QTL. However, when the effect of individual contributing loci becomes less tractable, especially when their contributions are "asymmetric," deliberation on balancing two types of statistical errors and a careful examination of possible contributions from multiple genetic factors and/or interaction effects are a must in designing an efficient study.     

Partial selfing and linkage: the effect of a heterotic locus on a neutral locus

Equilibria are determined for the two-locus model in a partially selfing population when one locus is neutral and the other locus is heterotic. At an equilibrium point, the frequency of heterozygotes at the neutral locus is greater than that expected from one-locus theory, even if the heterotic locus is on a different chromosome. Thus, the neutral locus also appears to be heterotic. The magnitude of this effect is determined for several different proportions of selfing and amounts of recombination.     

GLIDE: GPU-Based Linear Regression for Detection of Epistasis

Due to recent advances in genotyping technologies, mapping phenotypes to single loci in the genome has become a standard technique in statistical genetics. However, one-locus mapping fails to explain much of the phenotypic variance in complex traits. Here, we present GLIDE, which maps phenotypes to pairs of genetic loci and systematically searches for the epistatic interactions expected to reveal part of this missing heritability. GLIDE makes use of the computational power of consumer-grade graphics cards to detect such interactions via linear regression. This enabled us to conduct a systematic two-locus mapping study on seven disease data sets from the Wellcome Trust Case Control Consortium and on in-house hippocampal volume data in 6 h per data set, while current single CPU-based approaches require more than a year's time to complete the same task.     

Properties of Equilibria in Multi-Locus Genetic Systems

The classical mathematical theory of population genetics considered, for simplicity, almost exclusively one-locus systems. In the last two decades much work has been done on two-locus and, less frequently, multi-locus systems. This research has usually involved investigating properties of systems with given, and usually rather special, fitness parameters. Real genetic fitness systems are undoubtedly multi-locus and seldom will possess simplifying characteristics. One aim of this paper is to study generalized systems where no special assumptions are made about fitness structure, the number of alleles at each locus, the number of loci involved or the recombination structure between loci. A second aim is to consider marginal properties (often one-locus properties) of complex systems: the fact that many observations involve data from only on locus makes this second aim relevant.     

Sex determination in hymenoptera: A need for genetic and molecular studies

Sex-determining mechanisms appear to be very diverse in invertebrates. Haplodiploidy is a widespread mode of reproduction in insects: males are haploid and females are diploid. Several models have been proposed for the genetic mechanisms of sex determination in haplodiploid Hymenoptera. Although a one-locus multi-allele model is valid for several species, sex determination in other species cannot be explained by any of the existing models. Evidence for and predictions of two recently proposed models are discussed. Some genetic and molecular approaches are proposed to study sex determination in Hymenoptera.     

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.     

Analysis of Schizophrenia Data Using A Nonlinear Threshold Index Logistic Model

Genetic information, such as single nucleotide polymorphism (SNP) data, has been widely recognized as useful in prediction of disease risk. However, how to model the genetic data that is often categorical in disease class prediction is complex and challenging. In this paper, we propose a novel class of nonlinear threshold index logistic models to deal with the complex, nonlinear effects of categorical/discrete SNP covariates for Schizophrenia class prediction. A maximum likelihood methodology is suggested to estimate the unknown parameters in the models. Simulation studies demonstrate that the proposed methodology works viably well for moderate-size samples. The suggested approach is therefore applied to the analysis of the Schizophrenia classification by using a real set of SNP data from Western Australian Family Study of Schizophrenia (WAFSS). Our empirical findings provide evidence that the proposed nonlinear models well outperform the widely used linear and tree based logistic regression models in class prediction of schizophrenia risk with SNP data in terms of both Types I/II error rates and ROC curves.     

Segregation analyses of 1,476 population-based Australian families affected by prostate cancer

Segregation analyses aim to detect genetic factors that have a major effect on an individual's risk of disease and to describe them in terms of mode of inheritance, age-specific cumulative risk (penetrance), and allele frequency. We conducted single- and two-locus segregation analyses of data from 1,476 men with prostate cancer diagnosed at age <70 years and ascertained through population registries in Melbourne, Sydney, and Perth, Australia, and from their brothers, fathers, and both maternal and paternal lineal uncles. Estimation and model selection were based on asymptotic likelihood theory and were performed through use of the software MENDEL. All two-locus models gave better fits than did single-locus models, even if lineal uncles were excluded or if we censored data (age and disease status) for relatives at 1992, when prostate-specific-antigen testing started to have a major impact on the incidence of prostate cancer in Australia. Among the genetic models that we considered, the best-fitting ones included a dominantly inherited increased risk that was greater, in multiplicative terms, at younger ages, as well as a recessively inherited or X-linked increased risk that was greater, in multiplicative terms, at older ages. The recessive and X-linked effects were strongly confounded, and it was not possible to fit them together. Penetrance to age 80 years was approximately 70% (95% confidence interval [CI] 57%-85%) for the dominant effect and virtually 100% for the recessive and X-linked effects. Approximately 1/30 (95% CI 1/80-1/12) men would carry the dominant risk, and 1/140 (95% CI 1/220-1/90) would carry the recessive risk or 1/200 (95% CI 1/380-1/100) would carry the X-linked risk. Within discussed limitations, these analyses confirm the genetic heterogeneity, of prostate cancer susceptibility, that is becoming evident from linkage analyses, and they may aid future efforts in gene discovery.     

A single-locus minisatellite discriminates chinook salmon (Oncorhynchus tshawytscha) populations

A knowledge of genetic structure in natural populations is often necessary for conservation and management purposes, especially in declining Pacific salmon populations. To test for genetic differentiation between nine populations of chinook salmon, Oncorhynchus tshawytscha, from south-western British Columbia, Canada, DNA was extracted from 603 fish and hybridized with a single-locus minisatellite probe. Multivariate statistical analyses of the resulting allele size data permitted successful overall population identification of 52% (individual population range: 24–78%; P < 0.005), indicating a high level of genetic differentiation among the nine populations. Two of the nine populations were further analysed using data from a second minisatellite locus. The discrimination success rate improved from 81.1% (one-locus analyses) to 90.0% (two-locus analyses), indicating the potential for greatly increased resolution gained by the addition of more loci. These results indicate that variation at minisatellite loci can be used for assessing population-level genetic structure, even with artificial gene flow.     

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.