A CONDITIONAL DERIVATION OF RESIDUAL MAXIMUM LIKELIHOOD

WGNAM: whole-genome nested association mapping

A powerful QTL analysis method for nested association mapping populations is presented. Based on a one-stage multi-locus model, it provides accurate predictions of founder specific QTL effects. Nested association mapping (NAM) populations have been created to enable the identification of quantitative trait loci (QTL) in different genetic backgrounds. A whole-genome nested association mapping (WGNAM) method is presented to perform QTL analysis in NAM populations. The WGNAM method is an adaptation of the multi-parent whole genome average interval mapping approach where the crossing design is incorporated through the probability of inheriting founder alleles for every marker across the genome. Based on a linear mixed model, this method provides a one-stage analysis of raw phenotypic data, molecular markers, and crossing design. It simultaneously scans the whole-genome through an iterative process leading to a model with all the identified QTL while keeping the false positive rate low. The WGNAM approach was assessed through a simulation study, confirming to be a powerful and accurate method for QTL analysis for a NAM population. This novel method can also accommodate a multi-reference NAM (MR-NAM) population where donor parents are crossed with multiple reference parents to increase genetic diversity. Therefore, a demonstration is presented using a MR-NAM population for wheat (Triticum aestivum L.) to perform a QTL analysis for plant height. The strength and size of the putative QTL were summarized enhancing the understanding of the QTL effects depending on the parental origin. Compared to other methods, the proposed methodology based on a one-stage analysis provides greater power to detect QTL and increased accuracy in the estimation of their effects. The WGNAM method establishes the basis for accurate QTL mapping studies for NAM and MR-NAM populations.

Copula miss-specification in REML multivariate genetic animal model estimation

BACKGROUND

In animal genetics, linear mixed models are used to deal with genetic and environmental effects. The variance and covariance terms of these models are usually estimated by restricted maximum likelihood (REML), which provides unbiased estimators. A strong hypothesis of REML estimation is the multi-normality of the response variables. However, in practice, even if the marginal distributions of each phenotype are normal, the multi-normality assumption may be violated by non-normality of the cross-sectional dependence structure, that is to say when the copula of the multivariate distribution is not Gaussian. This study uses simulations to evaluate the impact of copula miss-specification in a bivariate animal model on REML estimations of variance components.

RESULT

Bivariate phenotypes were simulated for populations undergoing selection, considering different copulas for the dependence structure between the error components. Two multi-trait situations were considered: two phenotypes were measured on the selection candidates, or only one phenotype was measured on the selection candidates. Three generations with random selection and five generations with truncation selection based on estimated breeding values were simulated. When selection was performed at random, no significant differences were observed between the REML estimations of variance components and the true parameters even for the non-Gaussian distributions. For the truncation selections, when two phenotypes were measured on candidates, biases were systematically observed in the variance components for high residual dependence in the case of non-Gaussian distributions, especially in the case of a heavy-tailed or asymmetric distribution when the two traits were measured. Conversely, when only one phenotype was measured on candidates, no difference was observed between the Gaussian and non-Gaussian distributions in REML estimations.

CONCLUSIONS

This study confirms that REML can be used by geneticists to evaluate breeding values in the multivariate case even if the multivariate phenotypes deviate from normality in the situation of random selection or if one trait is not measured for the candidate under selection. Nevertheless, when the two traits are measured, the violation of the normality assumption may lead to non-negligible biases in the REML estimations of the variance-covariance components.

On the use of GBLUP and its extension for GWAS with additive and epistatic effects

Genomic best linear unbiased prediction (GBLUP) is the most widely used model for genome-wide predictions. Interestingly, it is also possible to perform genome-wide association studies (GWAS) based on GBLUP. Although the estimated marker effects in GBLUP are shrunken and the conventional test based on such effects has low power, it was observed that a modified test statistic can be produced and the result of test was identical to a standard GWAS model. Later, a mathematical proof was given for the special case that there is no fixed covariate in GBLUP. Since then, the new approach has been called “GWAS by GBLUP”. Nevertheless, covariates such as environmental and subpopulation effects are very common in GBLUP. Thus, it is necessary to confirm the equivalence in the general case. Recently, the concept was generalized to GWAS for epistatic effects and the new approach was termed rapid epistatic mixed-model association analysis (REMMA) because it greatly improved the computational efficiency. However, the relationship between REMMA and the standard GWAS model has not been investigated. In this study, we first provided a general mathematical proof of the equivalence between “GWAS by GBLUP” and the standard GWAS model for additive effects. Then, we compared REMMA with the standard GWAS model for epistatic effects by a theoretical investigation and by empirical data analyses. We hypothesized that the similarity of the two models is influenced by the relative contribution of additive and epistatic effects to the phenotypic variance, which was verified by empirical and simulation studies.

Desert island papers-A life in variance parameter and quantitative genetic parameter estimation reviewed using 16 papers

I review my scientific career in terms of eight areas and 16 papers. The first two areas are associated with childhood. The other six are associated with residual maximum likelihood (REML), canonical transformation, inbreeding in selected populations, average information residual maximum likelihood (AIREML), the computer program ASReml and sampling-based estimation.

Comparison of intra-individual coefficients of variation on the paired sampling data when inter-individual variations are different between measures

Background

Pain intensities of patients are repeatedly measured by Visual Analog Scale (VAS) and Pain Vision (PV) in a clinical research. Two measurements by VAS and PV are performed at the same time. In order to evaluate within patient consistency, intra-individual coefficient of variations (CVs) are compared between measures assuming that the pain status of each patient is stable during the research period. The correlated samples and different inter-individual variation due to different scales of the measures should be taken into account in statistical analysis. The adjustment of covariates will improve the estimation of population mean values of the measures.

Methods

In this paper, statistical approach to compare the intra-individual CVs is proposed. The approach consists of two steps: (1) estimating population mean values and intra-individual variances of the pain intensities by measure in a mixed effect model framework, (2) computing intra-individual CVs and comparing them between measures. The mixed effect model includes measure and some variables as fixed effects and subject by measure as a random effect. The different inter-individual variations between measures and their covariance reflect the paired sampling in the variance component. The confidence interval of the difference of intra-individual CVs is constructed using the asymptotic normality and the delta method. Bootstrap method is available if sample size is small.

Results

The proposed approach is illustrated using pain research data. Measure (VAS and PV), age and sex are included in the model as fixed effects. The confidence intervals of the difference of intra-individual CVs between measures are estimated by the asymptotic theory and by bootstrap using a subgroup resampling, respectively. Both confidence intervals are similar.

Conclusion

The proposed approach is useful to compare two intra-individual CVs taking it into account to reflect the paired sampling, different inter-individual variations between measures and some covariates. Although the inclusion of covariates did not improve the goodness-of-fit in the illustration, the proposed model with covariates will improve the accuracy and/or precision if covariates truly influence response variable. This approach can be applicable with small modification to various situations.

Electronic supplementary material

The online version of this article (doi:10.1186/s13104-016-1912-y) contains supplementary material, which is available to authorized users.

Refining multivariate disease phenotypes for high chip heritability

Background

Statistical genetics shows that the success of both genetic association studies and genomic prediction methods is positively associated with the heritability of the trait used in the analysis. Identifying highly heritable components of a complex disease can thus enhance genetic studies of the disease. Existing heritable component analysis methods use data from related individuals to compute linearly-combined traits to maximize heritability. Recent advances in acquiring genome-wide markers have enhanced heritability estimation using genotypic data from apparently unrelated individuals, which is referred to as the chip heritability. Novel statistical models are thus needed to identify disease components (subtypes) with high chip heritability.

Methods

We propose an optimization approach to identify highly heritable components of a complex disease as a function of multiple clinical variables. The heritability of the components is estimated directly from unrelated individuals using their genome-wide single nucleotide polymorphisms. The proposed approach can also model the fixed effects due to covariates, such as age and race, so that the derived traits have high chip heritability after correcting for fixed effects. A new sequential quadratic programming algorithm is developed to efficiently solve the proposed optimization problem.

Results

The proposed algorithm was validated both in simulations and the analysis of a real-world dataset that was aggregated from genetic studies of cocaine, opoid, and alcohol dependence. Simulation studies demonstrated that the proposed approach could identify the hypothesized component from multiple synthesized features. A case study on cocaine dependence (CD) identified a quantitative trait that achieved chip heritability of 0.86 estimated using a cross-validation process. This quantitative trait corresponded to the likelihood of an individual's membership in a CD subtype. Clinical analysis showed that the subtype enclosed individuals who reported heavy use of cocaine but few withdrawal symptoms.

Conclusions

Extensive experiments on both synthetic and real-world data demonstrate the effectiveness of the proposed approach as a means to find meaningful disease components with high chip heritability.

Whole-genome analysis of multienvironment or multitrait QTL in MAGIC

Multiparent Advanced Generation Inter-Cross (MAGIC) populations are now being utilized to more accurately identify the underlying genetic basis of quantitative traits through quantitative trait loci (QTL) analyses and subsequent gene discovery. The expanded genetic diversity present in such populations and the amplified number of recombination events mean that QTL can be identified at a higher resolution. Most QTL analyses are conducted separately for each trait within a single environment. Separate analysis does not take advantage of the underlying correlation structure found in multienvironment or multitrait data. By using this information in a joint analysis—be it multienvironment or multitrait — it is possible to gain a greater understanding of genotype- or QTL-by-environment interactions or of pleiotropic effects across traits. Furthermore, this can result in improvements in accuracy for a range of traits or in a specific target environment and can influence selection decisions. Data derived from MAGIC populations allow for founder probabilities of all founder alleles to be calculated for each individual within the population. This presents an additional layer of complexity and information that can be utilized to identify QTL. A whole-genome approach is proposed for multienvironment and multitrait QTL analysis in MAGIC. The whole-genome approach simultaneously incorporates all founder probabilities at each marker for all individuals in the analysis, rather than using a genome scan. A dimension reduction technique is implemented, which allows for high-dimensional genetic data. For each QTL identified, sizes of effects for each founder allele, the percentage of genetic variance explained, and a score to reflect the strength of the QTL are found. The approach was demonstrated to perform well in a small simulation study and for two experiments, using a wheat MAGIC population.

Whole-genome QTL analysis for MAGIC

An efficient whole genome method of QTL analysis is presented for Multi-parent advanced generation integrated crosses. Multi-parent advanced generation inter-cross (MAGIC) populations have been developed for mice and several plant species and are useful for the genetic dissection of complex traits. The analysis of quantitative trait loci (QTL) in these populations presents some additional challenges compared with traditional mapping approaches. In particular, pedigree and marker information need to be integrated and founder genetic data needs to be incorporated into the analysis. Here, we present a method for QTL analysis that utilizes the probability of inheriting founder alleles across the whole genome simultaneously, either for intervals or markers. The probabilities can be found using three-point or Hidden Markov Model (HMM) methods. This whole-genome approach is evaluated in a simulation study and it is shown to be a powerful method of analysis. The HMM probabilities lead to low rates of false positives and low bias of estimated QTL effect sizes. An implementation of the approach is available as an R package. In addition, we illustrate the approach using a bread wheat MAGIC population.

RWGAIM: an efficient high-dimensional random whole genome average (QTL) interval mapping approach

Mapping of quantitative trait loci (QTLs) underlying variation in quantitative traits continues to be a powerful tool in genetic study of plants and other organisms. Whole genome average interval mapping (WGAIM), a mixed model QTL mapping approach using all intervals or markers simultaneously, has been demonstrated to outperform composite interval mapping, a common approach for QTL analysis. However, the advent of high-throughput high-dimensional marker platforms provides a challenge. To overcome this, a dimension reduction technique is proposed for WGAIM for efficient analysis of a large number of markers. This approach results in reduced computing time as it is dependent on the number of genetic lines (or individuals) rather than the number of intervals (or markers). The approach allows for the full set of potential QTL effects to be recovered. A proposed random effects version of WGAIM aims to reduce bias in the estimated size of QTL effects. Lastly, the two-stage outlier procedure used in WGAIM is replaced by a single stage approach to reduce possible bias in the selection of putative QTL in both WGAIM and the random effects version. Simulation is used to demonstrate the efficiency of the dimension reduction approach as well as demonstrate that while the approaches are very similar, the random WGAIM performs better than the original and modified fixed WGAIM by reducing bias and in terms of mean square error of prediction of estimated QTL effects. Finally, an analysis of a doubled haploid population is used to illustrate the three approaches.

Modeling and testing treated tumor growth using cubic smoothing splines

Human tumor xenograft models are often used in preclinical study to evaluate the therapeutic efficacy of a certain compound or a combination of certain compounds. In a typical human tumor xenograft model, human carcinoma cells are implanted to subjects such as severe combined immunodeficient (SCID) mice. Treatment with test compounds is initiated after tumor nodule has appeared, and continued for a certain time period. Tumor volumes are measured over the duration of the experiment. It is well known that untreated tumor growth may follow certain patterns, which can be described by certain mathematical models. However, the growth patterns of the treated tumors with multiple treatment episodes are quite complex, and the usage of parametric models is limited. We propose using cubic smoothing splines to describe tumor growth for each treatment group and for each subject, respectively. The proposed smoothing splines are quite flexible in modeling different growth patterns. In addition, using this procedure, we can obtain tumor growth and growth rate over time for each treatment group and for each subject, and examine whether tumor growth follows certain growth pattern. To examine the overall treatment effect and group differences, the scaled chi-squared test statistics based on the fitted group-level growth curves are proposed. A case study is provided to illustrate the application of this method, and simulations are carried out to examine the performances of the scaled chi-squared tests.

Bioinsecticidal activity of Archidendron ellipticum trypsin inhibitor on growth and serine digestive enzymes during larval development of Spodoptera litura

The roles of serine proteases involved in the digestion mechanism of the cutworm Spodoptera litura (Lepidoptera: Noctuidae) were examined (in vitro and in vivo) following feeding of plant protease inhibitors. A trypsin inhibitor from Archidendron ellipticum (AeTI) was purified by ammonium sulfate fractionation, ion-exchange chromatography and size-exclusion chromatography (HPLC) and its bioinsecticidal properties against S. litura were compared with Soybean Kunitz trypsin inhibitor (SBTI). AeTI inhibited the trypsin-like activities of the midgut proteases of fifth instar larvae of S. litura by over 70%. Dixon plot analysis revealed competitive inhibition of larval midgut trypsin and chymotrypsin by AeTI, with an inhibition constant (K(i)) of 3.5x10(-9) M and 1.5x10(-9) M, respectively. However, inhibitor kinetics using double reciprocal plots for both trypsin and chymotrypsin inhibitions demonstrated a mixed inhibition pattern. Feeding experiments conducted on different (neonate to ultimate) instars suggested a dose-dependent decrease for both the larval body weight as well as % survival of larva fed on diet containing 50, 100 and 150 microM AeTI. Influence of AeTI on the larval gut physiology indicated a 7-fold decrease of trypsin-like protease activity and a 5-fold increase of chymotrypsin-like protease activity, after being fed with a diet supplemented with 150 microM AeTI. This study suggests that although the early (1st to 3rd) larval instars of S. litura are susceptible to the trypsin inhibitory action of AeTI, the later instars may facilitate the development of new serine proteases, insensitive to the inhibitor.