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PubMed1990

Linkage strategies for genetically complex traits. II. The power of affected relative pairs.

The power to detect disease-susceptibility loci through linkage analysis using pairs of affected relatives and affected-unaffected pairs is examined. Allelic identity by descent (ibd) for a completely polymorphic marker for sibling, uncle-nephew, grandparent-grandchild, half-sib, and first-cousin pairs is considered. Affected-unaffected pairs generally represent a poor strategy. For single-locus models, ibd depends on lambda R, the risk ratio for type R relatives compared with population prevalence, and the recombination fraction theta. The ibd for grandparent-grandchild pairs is least affected by recombination, followed by sibs, half-sib, uncle-nephew, and first-cousin pairs. For diseases with large lambda values and for small theta values, distant relatives offer greater power. For larger theta values, grandparent-grandchild pairs are best; for small lambda values, sibs are best. Additive and multiplicative multilocus models are considered. For the multiplicative model, the same formulas as in the single-locus model apply, except that lambda iR (for the ith contributing locus) is substituted for lambda R. For the additive model, the deviation from null expectation for ibd is divided among all contributing loci. Compared with the multiplicative model, for an additive model there is usually greater advantage in distant relationships. Multipoint analysis using linked marker loci for affected relative pairs is described. Simultaneous use of multiple markers diminishes the effect of recombination and allows for localization of the disease-susceptibility locus.

Alleles↗
PubMed1990

Linkage strategies for genetically complex traits. III. The effect of marker polymorphism on analysis of affected relative pairs.

The results from the second paper of this series are reexamined for markers that are not completely polymorphic. A maximum lod score (MLS) criterion is defined for affected relative pairs. The expected MLS (EMLS) is calculated as a function of the marker polymorphic information content (PIC) for various values of lambda R (relative risk ratio) and different relative types by using simulations. An m-allele model with equal allele frequencies is employed. The EMLS is calculated for two sampling strategies: scheme 1, which uses pairs only, and scheme 2, which also includes additional informative relatives. For scheme 2, the percent of the maximum achievable EMLS (i.e., for a marker with a PIC of 1.0) is approximately equal to the marker PIC value for all relative types. For scheme 1, the EMLS is greatly diminished unless PIC is high, especially for distant relatives. For example, scheme 1 is not cost-effective for sibs unless PIC greater than .7; for second- and third-degree relatives, PIC must be greater than .85. Therefore, in general, it will be worthwhile to type additional relatives in linkage studies using affected pairs. The comparative value of sibs versus distant relatives depends on lambda R, recombination theta, and PIC. For large lambda R and PIC values, distant relatives are preferred. Alternatively, for smaller lambda R and PIC values, sibs are best.

Female↗
PubMed1997

Combining information within and between pedigrees for mapping complex traits.

This paper is concerned with efficient strategies for gene mapping using pedigrees containing small numbers of affecteds and identity-by-descent data from closely spaced markers throughout the genome. Particular attention is paid to additive traits involving phenocopies and/or locus heterogeneity. For a sample of pedigrees containing a particular configuration of affecteds, e.g., pairs of siblings together with a first cousin, we use a likelihood analysis to find 1-df statistics that are very efficient over a broad range of penetrances and allele frequencies. We identify configurations of affecteds that are particularly powerful for detecting linkage, and we show how pedigrees containing different numbers and configurations of affecteds can be efficiently combined in an overall test statistic.

Chromosome Mapping↗
PubMed2000

Bayesian mapping of quantitative trait loci for complex binary traits.

A complex binary trait is a character that has a dichotomous expression but with a polygenic genetic background. Mapping quantitative trait loci (QTL) for such traits is difficult because of the discrete nature and the reduced variation in the phenotypic distribution. Bayesian statistics are proved to be a powerful tool for solving complicated genetic problems, such as multiple QTL with nonadditive effects, and have been successfully applied to QTL mapping for continuous traits. In this study, we show that Bayesian statistics are particularly useful for mapping QTL for complex binary traits. We model the binary trait under the classical threshold model of quantitative genetics. The Bayesian mapping statistics are developed on the basis of the idea of data augmentation. This treatment allows an easy way to generate the value of a hypothetical underlying variable (called the liability) and a threshold, which in turn allow the use of existing Bayesian statistics. The reversible jump Markov chain Monte Carlo algorithm is used to simulate the posterior samples of all unknowns, including the number of QTL, the locations and effects of identified QTL, genotypes of each individual at both the QTL and markers, and eventually the liability of each individual. The Bayesian mapping ends with an estimation of the joint posterior distribution of the number of QTL and the locations and effects of the identified QTL. Utilities of the method are demonstrated using a simulated outbred full-sib family. A computer program written in FORTRAN language is freely available on request.

Algorithms↗
PubMed2005

Genetic studies to identify genes underlying menopausal age.

Menopausal age is important as a retrospective marker for ovarian senescence, an early menopausal age is associated with an increased risk of cardiovascular diseases and osteoporosis, whereas a later menopausal age has been associated with an increased risk of breast cancer. The worldwide average for age at natural menopause is approximately 51 years and is more or less normally distributed with a range roughly between 40 and 60 years. Environmental factors explain only a small part of the variance and it has been proposed that genetic factors are the main source of variation. Menopausal age may be considered a continuous complex trait. Complex traits are defined as traits that are influenced by both multiple genetic and environmental factors. A category of complex traits comprises those that are measured on a continuous scale. The genomic loci that make up the genetic component are called 'quantitative trait loci' or QTLs. The first linkage study on menopausal age suggests that the involvement of the X-chromosome may not be limited to premature ovarian failure (POF), but may influence the broader spectrum of menopausal age. A potentially new locus for variation in menopausal age was allocated to chromosome 9. Further studies need to identify new candidate genes to help unravel the pathophysiology of menopausal age. It is becoming increasingly clear that, in any speciality, it should be acknowledged that genetic factors are involved in many traits and that uncovering these factors may provide insight into pathogenesis and ultimately advance prevention and treatment of disease. In this review we discuss methods and basic principles of gene finding for such traits, exemplified by menopausal age as phenotype. Furthermore, we give an overview of the state of the art of candidate gene studies and linkage studies.

Aging↗
PubMed1999

Mapping quantitative trait loci for complex binary traits in outbred populations.

Complex binary traits have a dichotomous phenotypic expression but do not show a simple Mendelian segregation ratio. These traits are considered to be jointly controlled by the actions of several genes and a random environmental effect. The binary phenotype and the underlying factor are assumed to be linked through a threshold model. The underlying factor, referred to as the liability, is treated as a regular but unobservable quantitative character. Mapping quantitative trait loci (QTL) can be performed directly on the liability. Methods of QTL mapping for the liability of a complex binary trait have been well developed in line-crossing experiments. However, such a method is not available in outbred populations which usually consist of many independent pedigrees (families). In this study, we develop a method to analyse jointly multiple families of an outbred population. The method is developed based on a fixed-model approach, i.e. the QTL effects, rather than the variance, are estimated and tested. After the test, the estimated effects are then converted into a single estimate of the QTL variance by taking into consideration errors in the estimated effects. The QTL effects and variance-covariance matrix of the estimates are obtained by a fast Fisher-scoring method. Monte Carlo simulations show that the method is not only powerful but also generates very accurate estimates of QTL variances.

Algorithms↗
PubMed1999

A random model approach to mapping quantitative trait loci for complex binary traits in outbred populations.

Mapping quantitative trait loci (QTL) for complex binary traits is more challenging than for normally distributed traits due to the nonlinear relationship between the observed phenotype and unobservable genetic effects, especially when the mapping population contains multiple outbred families. Because the number of alleles of a QTL depends on the number of founders in an outbred population, it is more appropriate to treat the effect of each allele as a random variable so that a single variance rather than individual allelic effects is estimated and tested. Such a method is called the random model approach. In this study, we develop the random model approach of QTL mapping for binary traits in outbred populations. An EM-algorithm with a Fisher-scoring algorithm embedded in each E-step is adopted here to estimate the genetic variances. A simple Monte Carlo integration technique is used here to calculate the likelihood-ratio test statistic. For the first time we show that QTL of complex binary traits in an outbred population can be scanned along a chromosome for their positions, estimated for their explained variances, and tested for their statistical significance. Application of the method is illustrated using a set of simulated data.

Breeding↗
PubMed1999

Visual signalling by asymmetry: a review of perceptual processes.

Individual levels of asymmetry in traits that display fluctuating asymmetry could be used as visual signals of phenotypic (and perhaps genotypic) quality, as asymmetry can often be negatively related to fitness parameters. There are some data to support this hypothesis but the experimental protocols employed have commonly resulted in asymmetries far larger than those observed in nature. To date, there has been little consideration of the ability of animals to accurately discriminate small asymmetries (of the magnitude observed in the wild) from perfect symmetry. This is key to assessing the plausibility of the asymmetry-signalling hypothesis. Here, I review the perceptual processes that may lead to the discrimination of asymmetry and discuss a number of ecologically relevant factors that may influence asymmetry signalling. These include: signal orientation, distance of trait elements from the axis of symmetry, trait complexity, trait contrast and colour, and the behaviour of both signaller and receiver. I also discuss the evolution of symmetry preferences and make suggestions as to where researchers should focus attention to examine the generality of asymmetry-signalling theory. In highly developmentally stable signalling systems the magnitude of asymmetry may be too small to be detected accurately and reliably, hence asymmetry signalling is unlikely to have evolved in these situations.

Animals↗
PubMed1989

Estimating the power of a proposed linkage study for a complex genetic trait.

Many genetic traits have complex modes of inheritance; they may exhibit incomplete or age-dependent penetrance or fail to show any clear Mendelian inheritance pattern. As primary linkage maps for the human genome near completion, it is becoming increasingly possible to map these traits. Prior to undertaking a linkage study, it is important to consider whether the pedigrees available for the proposed study are likely to provide sufficient information to demonstrate linkage, assuming a linked marker is tested. In the current paper, we describe a computer simulation method to estimate the power of a proposed study to detect linkage for a complex genetic trait, given a hypothesized genetic model for the trait. Our method simulates trait locus genotypes consistent with observed trait phenotypes, in such a way that the probability to detect linkage can be estimated by sample statistics of the maximum lod score distribution. The method uses terms available when calculating the likelihood of the trait phenotypes for the pedigree and is applicable to any trait determined by one or a few genetic loci; individual-specific environmental effects can also be dealt with. Our method provides an objective answer to the question, Will these pedigrees provide sufficient information to map this complex genetic trait?

Genetic Linkage↗
PubMed2003

Bayesian model choice and search strategies for mapping interacting quantitative trait Loci.

Most complex traits of animals, plants, and humans are influenced by multiple genetic and environmental factors. Interactions among multiple genes play fundamental roles in the genetic control and evolution of complex traits. Statistical modeling of interaction effects in quantitative trait loci (QTL) analysis must accommodate a very large number of potential genetic effects, which presents a major challenge to determining the genetic model with respect to the number of QTL, their positions, and their genetic effects. In this study, we use the methodology of Bayesian model and variable selection to develop strategies for identifying multiple QTL with complex epistatic patterns in experimental designs with two segregating genotypes. Specifically, we develop a reversible jump Markov chain Monte Carlo algorithm to determine the number of QTL and to select main and epistatic effects. With the proposed method, we can jointly infer the genetic model of a complex trait and the associated genetic parameters, including the number, positions, and main and epistatic effects of the identified QTL. Our method can map a large number of QTL with any combination of main and epistatic effects. Utility and flexibility of the method are demonstrated using both simulated data and a real data set. Sensitivity of posterior inference to prior specifications of the number and genetic effects of QTL is investigated.

Bayes Theorem↗