Effect of family relatedness on characteristics of estimated IBD probabilities in relation to precision of QTL estimates

Background: A random QTL effects model uses a function of probabilities that two alleles in the same or in different animals at a particular genomic position are identical by descent (IBD). Estimates of such IBD probabilities and therefore, modeling and estimating QTL variances, depend on marker polymorphism, strength of linkage and linkage disequilibrium of markers and QTL, and the relatedness of animals in the pedigree. The effect of relatedness of animals in a pedigree on IBD probabilities and their characteristics was examined in a simulation study. Results: The study based on nine multi-generational family structures, similar to a pedigree structure of a real dairy population, distinguished by an increased level of inbreeding from zero to 28 % across the studied population. Highest inbreeding level in the pedigree, connected with highest relatedness, was accompanied by highest IBD probabilities of two alleles at the same locus, and by lower relative variation coefficients. Profiles of correlation coefficients of IBD probabilities along the marked chromosomal segment with those at the true QTL position were steepest when the inbreeding coefficient in the pedigree was highest. Precision of estimated QTL location increased with increasing inbreeding and pedigree relatedness. A method to assess the optimum level of inbreeding for QTL detection is proposed, depending on population parameters. Conclusions: An increased overall relationship in a QTL mapping design has positive effects on precision of QTL position estimates. But the relationship of inbreeding level and the capacity for QTL detection depending on the recombination rate of QTL and adjacent informative marker is not linear. © 2010 Freyer et al., licensee BioMed Central Ltd.

The relationship between CFH and ARMS2 genotypes and neuroretinal function in persons without age-related macular degeneration

Purpose: To determine whether neuroretinal function differs in healthy persons with and without common risk gene variants for age- related macular degeneration (AMD) and no ophthalmoscopic signs of AMD, and to compare those findings in persons with manifest early AMD. Methods and Participants: Neuroretinal function was assessed with the multifocal electroretinogram (mfERG) (VERIS, Redwood City, CA,) in 32 participants (22 healthy persons with no clinical signs of AMD and 10 early AMD patients). The 22 healthy participants with no AMD were risk genotypes for either the CFH (rs380390) and/or ARMS2 (rs10490920). We used a slow flash mfERG paradigm (3 inserted frames) and a 103 hexagon stimulus array. Recordings were made with DTL electrodes; fixation and eye movements were monitored online. Trough N1 to peak P1 (N1P1) response densities and P1-implicit times (IT) were analysed in 5 concentric rings. Results: N1P1 response densities (mean ± SD) for concentric rings 1-3 were on average significantly higher in at-risk genotypes (ring 1: 17.97 nV/deg2 ± 1.9, ring 2: 11.7 nV/deg2 ±1.3, ring 3: 8.7 nV/deg2 ± 0.7) compared to those without risk (ring 1: 13.7 nV/deg2 ± 1.9, ring 2: 9.2 nV/deg2 ±0.8, ring 3: 7.3 nV/deg2 ± 1.1) and compared to persons with early AMD (ring 1: 15.3 nV/deg2 ± 4.8, ring 2: 9.1 nV/deg2 ±2.3, ring 3 nV/deg2: 7.3± 1.3) (p<0.5). The group implicit times, P1-ITs for ring 1 were on average delayed in the early AMD patients (36.4 ms ± 1.0) compared to healthy participants with (35.1 ms ± 1.1) or without risk genotypes (34.8 ms ±1.3), although these differences were not significant. Conclusion: Neuroretinal function in persons with normal fundi can be differentiated into subgroups based on their genetics. Increased neuroretinal activity in persons who carry AMD risk genotypes may be due to genetically determined subclinical inflammatory and/or histological changes in the retina. Assessment of neuroretinal function in healthy persons genetically susceptible to AMD may be a useful early biomarker before there is clinical manifestation of AMD.

Mapping quantitative trait loci in a wild population using linkage and linkage disequilibrium analyses

Historical information can be used, in addition to pedigree, traits and genotypes, to map quantitative trait locus (QTL) in general populations via maximum likelihood estimation of variance components. This analysis is known as linkage disequilibrium (LD) and linkage mapping, because it exploits both linkage in families and LD at the population level. The search for QTL in the wild population of Soay sheep on St. Kilda is a proof of principle. We analysed the data from a previous study and confirmed some of the QTLs reported. The most striking result was the confirmation of a QTL affecting birth weight that had been reported using association tests but not when using linkage-based analyses. Copyright © Cambridge University Press 2010.

A web application to perform linkage disequilibrium and linkage analyses on a computational grid

Motivation: Unravelling the genetic architecture of complex traits requires large amounts of data, sophisticated models and large computational resources. The lack of user-friendly software incorporating all these requisites is delaying progress in the analysis of complex traits. Methods: Linkage disequilibrium and linkage analysis (LDLA) is a high-resolution gene mapping approach based on sophisticated mixed linear models, applicable to any population structure. LDLA can use population history information in addition to pedigree and molecular markers to decompose traits into genetic components. Analyses are distributed in parallel over a large public grid of computers in the UK. Results: We have proven the performance of LDLA with analyses of simulated data. There are real gains in statistical power to detect quantitative trait loci when using historical information compared with traditional linkage analysis. Moreover, the use of a grid of computers significantly increases computational speed, hence allowing analyses that would have been prohibitive on a single computer. © The Author 2009. Published by Oxford University Press. All rights reserved.

Prediction of multilocus identity-by-descent

Previous studies have enabled exact prediction of probabilities of identity-by-descent (IBD) in randommating populations for a few loci (up to four or so), with extension to more using approximate regression methods. Here we present a precise predictor of multiple-locus IBD using simple formulas based on exact results for two loci. In particular, the probability of non-IBD X ABC at each of ordered loci A, B, and C can be well approximated by XABC = XABXBC/XB and generalizes to X123. . .k = X12X23. . .Xk-1,k/ Xk-2, where X is the probability of non-IBD at each locus. Predictions from this chain rule are very precise with population bottlenecks and migration, but are rather poorer in the presence of mutation. From these coefficients, the probabilities of multilocus IBD and non-IBD can also be computed for genomic regions as functions of population size, time, and map distances. An approximate but simple recurrence formula is also developed, which generally is less accurate than the chain rule but is more robust with mutation. Used together with the chain rule it leads to explicit equations for non-IBD in a region. The results can be applied to detection of quantitative trait loci (QTL) by computing the probability of IBD at candidate loci in terms of identity-by-state at neighboring markers.

Prediction of IBD based on population history for fine gene mapping

A novel multiple regression method (RM) is developed to predict identity-by-descent probabilities at a locus L (IBDL), among individuals without pedigree, given information on surrounding markers and population history. These IBDL probabilities are a function of the increase in linkage disequilibrium (LD) generated by drift in a homogeneous population over generations. Three parameters are sufficient to describe population history: effective population size (Ne), number of generations since foundation (T), and marker allele frequencies among founders (p). IBD L are used in a simulation study to map a quantitative trait locus (QTL) via variance component estimation. RM is compared to a coalescent method (CM) in terms of power and robustness of QTL detection. Differences between RM and CM are small but significant. For example, RM is more powerful than CM in dioecious populations, but not in monoecious populations. Moreover, RM is more robust than CM when marker phases are unknown or when there is complete LD among founders or Ne is wrong, and less robust when p is wrong. CM utilises all marker haplotype information, whereas RM utilises information contained in each individual marker and all possible marker pairs but not in higher order interactions. RM consists of a family of models encompassing four different population structures, and two ways of using marker information, which contrasts with the single model that must cater for all possible evolutionary scenarios in CM.

Mapping of multiple quantitative trait loci affecting bovine spongiform encephalopathy

A whole-genome scan was conducted to map quantitative trait loci (QTL) for BSE resistance or susceptibility. Cows from four half-sib families were included and 173 microsatellite markers were used to construct a 2835-cM (Kosambi) linkage map covering 29 autosomes and the pseudoautosomal region of the sex chromosome. Interval mapping by linear regression was applied and extended to a multiple-QTL analysis approach that used identified QTL on other chromosomes as cofactors to increase mapping power. In the multiple-QTL analysis, two genome-wide significant QTL (BTA17 and X/Y ps) and four genome-wide suggestive QTL (BTA1, 6, 13, and 19) were revealed. The QTL identified here using linkage analysis do not overlap with regions previously identified using TDT analysis. One factor that may explain the disparity between the results is that a more extensive data set was used in the present study. Furthermore, methodological differences between TDT and linkage analyses may affect the power of these approaches.

On the prediction of simultaneous inbreeding coefficients at multiple loci

A new deterministic method for predicting simultaneous inbreeding coefficients at three and four loci is presented. The method involves calculating the conditional probability of IBD (identical by descent) at one locus given IBD at other loci, and multiplying this probability by the prior probability of the latter loci being simultaneously IBD. The conditional probability is obtained applying a novel regression model, and the prior probability from the theory of digenic measures of Weir and Cockerham. The model was validated for a finite monoecious population mating at random, with a constant effective population size, and with or without selfing, and also for an infinite population with a constant intermediate proportion of selfing. We assumed discrete generations. Deterministic predictions were very accurate when compared with simulation results, and robust to alternative forms of implementation. These simultaneous inbreeding coefficients were more sensitive to changes in effective population size than in marker spacing. Extensions to predict simultaneous inbreeding coefficients at more than four loci are now possible.

Power of QTL detection using association tests with family controls

The power of testing for a population-wide association between a biallelic quantitative trait locus and a linked biallelic marker locus is predicted both empirically and deterministically for several tests. The tests were based on the analysis of variance (ANOVA) and on a number of transmission disequilibrium tests (TDT). Deterministic power predictions made use of family information, and were functions of population parameters including linkage disequilibrium, allele frequencies, and recombination rate. Deterministic power predictions were very close to the empirical power from simulations in all scenarios considered in this study. The different TDTs had very similar power, intermediate between one-way and nested ANOVAs. One-way ANOVA was the only test that was not robust against spurious disequilibrium. Our general framework for predicting power deterministically can be used to predict power in other association tests. Deterministic power calculations are a powerful tool for researchers to plan and evaluate experiments and obviate the need for elaborate simulation studies.

Candidate gene analysis for quantitative traits using the transmission disequilibrium test : the example of the melanocortin 4-receptor in pigs

Population-wide associations between loci due to linkage disequilibrium can be used to map quantitative trait loci (QTL) with high resolution. However, spurious associations between markers and QTL can also arise as a consequence of population stratification. Statistical methods that cannot differentiate between loci associations due to linkage disequilibria from those caused in other ways can render false-positive results. The transmission-disequilibrium test (TDT) is a robust test for detecting QTL. The TDT exploits within-family associations that are not affected by population stratification. However, some TDTs are formulated in a rigid-form, with reduced potential applications. In this study we generalize TDT using mixed linear models to allow greater statistical flexibility. Allelic effects are estimated with two independent parameters: one exploiting the robust within-family information and the other the potentially biased between-family information. A significant difference between these two parameters can be used as evidence for spurious association. This methodology was then used to test the effects of the fourth melanocortin receptor (MC4R) on production traits in the pig. The new analyses supported the previously reported results; i.e., the studied polymorphism is either causal of in very strong linkage disequilibrium with the causal mutation, and provided no evidence for spurious association.

Genome-wide search for markers associated with bovine spongiform encephalopathy

A genome-wide search for markers associated with BSE incidence was performed by using Transmission-Disequilibrium Tests (TDTs). Significant segregation distortion, i.e., unequal transmission probabilities of alleles within a locus, was found for three marker loci on Chromosomes (Chrs) 5, 10, and 20. Although TDTs are robust to false associations owing to hidden population substructures, it cannot distinguish segregation distortion caused by a true association between a marker and bovine spongiform encephalopathy (BSE) from a population-wide distortion. An interaction test and a segregation distortion analysis in half-sib controls were used to disentangle these two alternative hypotheses. None of the markers showed any significant interaction between allele transmission rates and disease status, and only the marker on Chr 10 showed a significant segregation distortion in control individuals. Nevertheless, the control group may have been a mixture of resistant and susceptible but unchallenged individuals. When new genotypes were generated in the vicinity of these three markers, evidence for an association with BSE was confirmed for the locus on Chr 5.

Cell death control : the interplay of apoptosis and autophagy in the pathogenicity of sclerotinia sclerotiorum

Programmed cell death is characterized by a cascade of tightly controlled events that culminate in the orchestrated death of the cell. In multicellular organisms autophagy and apoptosis are recognized as two principal means by which these genetically determined cell deaths occur. During plant-microbe interactions cell death programs can mediate both resistant and susceptible events. Via oxalic acid (OA), the necrotrophic phytopathogen Sclerotinia sclerotiorum hijacks host pathways and induces cell death in host plant tissue resulting in hallmark apoptotic features in a time and dose dependent manner. OA-deficient mutants are non-pathogenic and trigger a restricted cell death phenotype in the host that unexpectedly exhibits markers associated with the plant hypersensitive response including callose deposition and a pronounced oxidative burst, suggesting the plant can recognize and in this case respond, defensively. The details of this plant directed restrictive cell death associated with OA deficient mutants is the focus of this work. Using a combination of electron and fluorescence microscopy, chemical effectors and reverse genetics, we show that this restricted cell death is autophagic. Inhibition of autophagy rescued the non-pathogenic mutant phenotype. These findings indicate that autophagy is a defense response in this necrotrophic fungus/plant interaction and suggest a novel function associated with OA; namely, the suppression of autophagy. These data suggest that not all cell deaths are equivalent, and though programmed cell death occurs in both situations, the outcome is predicated on who is in control of the cell death machinery. Based on our data, we suggest that it is not cell death per se that dictates the outcome of certain plant-microbe interactions, but the manner by which cell death occurs that is crucial.

Bayesian computation via empirical likelihood

Approximate Bayesian computation has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable. However, the well-established statistical method of empirical likelihood provides another route to such settings that bypasses simulations from the model and the choices of the approximate Bayesian computation parameters (summary statistics, distance, tolerance), while being convergent in the number of observations. Furthermore, bypassing model simulations may lead to significant time savings in complex models, for instance those found in population genetics. The Bayesian computation with empirical likelihood algorithm we develop in this paper also provides an evaluation of its own performance through an associated effective sample size. The method is illustrated using several examples, including estimation of standard distributions, time series, and population genetics models.