Arūnas P. Verbyla

Joint modeling of additive and non-additive genetic line effects in single field trials

A statistical approach is presented for selection of best performing lines for commercial release and best parents for future breeding programs from standard agronomic trials. The method involves the partitioning of the genetic effect of a line into additive and non-additive effects using pedigree based inter-line relationships, in a similar manner to that used in animal breeding. A difference is the ability to estimate non-additive effects. Line performance can be assessed by an overall genetic line effect with greater accuracy than when ignoring pedigree information and the additive effects are predicted breeding values. A generalized definition of heritability is developed to account for the complex models presented.

Adjusted likelihood methods for modelling dispersion in generalized linear models

This paper considers double generalized linear models, which allow the mean and dispersion to be modelled simultaneously in a generalized linear model context. Estimation of the dispersion parameters is based on a X 2 1 approximation to the unit deviances, and the accuracy of the saddle-point approximation which underlies this is discussed. Approximate REML methods are developed for estimation of the dispersion. The approximate REML methods can be implemented with very little added complication in a generalized linear model setting by adjusting the working vector and working weights. S-Plus functions for double generalized linear models are described. Through two data examples it is shown that the approximate REML methods are more robust than maximum likelihood, in the sense of being less sensitive to perturbations in the mean model.

Curation of wheat maps to improve map accuracy and QTL detection

Three Australian doubled haploid populations were used to illustrate the importance of map curation in order to improve the quality of linkage maps and quantative trait locus (QTL) detection. The maps were refined and improved by re-examining the order of markers, inspection of the genetic maps in relation to a consensus map, editing the marker data for double crossovers, and determining estimated recombination fractions for all pairs of markers. The re-ordering of markers and replacing genotypes at double crossovers with missing values resulted in an overall decrease in the length of the maps. Fewer apparent genotyping errors, associated with the presence of double recombinants, were identified with restriction fragment length polymorphisms (RFLPs) than with other types of markers used in this study. The complications that translocations may cause in the ordering of markers and subsequent QTL analysis were investigated. QTL analysis using both the original and revised maps indicated that QTL peaks were more sharply located or had improved log-likelihood (LOD) scores in the revised maps. An accurate indication of the QTL peak and a significant LOD score are both essential for the identification of markers suitable for marker-assisted selection. Recommendations are provided for the improvement of the quality of linkage maps.

Joint modeling of additive and non-additive (genetic line) effects in multi-environment trials.

A statistical approach for the analysis of multi-environment trials (METs) is presented, in which selection of best performing lines, best parents, and best combination of parents can be determined. The genetic effect of a line is partitioned into additive, dominance and residual non-additive effects. The dominance effects are estimated through the incorporation of the dominance relationship matrix, which is presented under varying levels of inbreeding. A computationally efficient way of fitting dominance effects is presented which partitions dominance effects into between family dominance and within family dominance line effects. The overall approach is applicable to inbred lines, hybrid lines and other general population structures where pedigree information is available.

The analysis of QTL by simultaneous use of the full linkage map

An extension of interval mapping is presented that incorporates all intervals on the linkage map simultaneously. The approach uses a working model in which the sizes of putative QTL for all intervals across the genome are random effects. An outlier detection method is used to screen for possible QTL. Selected QTL are subsequently fitted as fixed effects. This screening and selection approach is repeated until the variance component for QTL sizes is not statistically significant. A comprehensive simulation study is conducted in which map uncertainty is included. The proposed method is shown to be superior to composite interval mapping in terms of power of detection of QTL. There is an increase in the rate of false positive QTL detected when using the new approach, but this rate decreases as the population size increases. The new approach is much simpler computationally. The analysis of flour milling yield in a doubled haploid population illustrates the improved power of detection of QTL using the approach, and also shows how vital it is to allow for sources of non-genetic variation in the analysis.

Joint modelling of location and scale parameters of the t distribution

Joint modelling of location and scale parameters has generally been confined to exponential families. In this paper the location and scale parameters of the t distribution are allowed to depend on covariates. The closed form of the likelihood allows inference to proceed in a similar fashion to the Gaussian location and scale model and provides a framework for a simple scoring algorithm to estimate the parameters. The algorithm includes a procedure to estimate the degrees of freedom parameter of the t distribution. Homogeneity and asymptotic tests are discussed and a methodology is derived to detect heteroscedasticity when the response is t distributed. Simulations reveal considerable bias in the estimates of the degrees of freedom parameter and only minor bias in the estimated fixed effects associated with the scale parameter. In comparison, the estimated location effects are well behaved. To illustrate the joint modelling of location and scale parameters of the t distribution the methodology is applied to two data sets.

Modelling in Repeated Measures Experiments

In repeated measures experiments how treatment contrasts change over time is often of prime interest and modelling these contrasts is the aim of any analysis. We present an approach to the analysis of repeated measures data in which both the mean and the covariance matrix are modelled parametrically. We use the correlogram and semivariogram for identification of the covariance structure and linear models for specifying the change over time of the treatment contrasts. Incomplete data are handled in the approach and estimation is based on residual maximum likelihood. Examples which motivated the work are presented to illustrate the applicability of the method

The analysis of quantitative trait loci in multi-environment trials using a multiplicative mixed model

A new approach for multi-environment quantitative trait locus (QTL) analysis based on an appropriate genetic model is presented. To accommodate a multi-environment analysis, the size of a QTL effect is assumed to be a random effect. The approach results in a multiplicative mixed model for QTL × environment interaction of the factor analytic type. The full genetic model may also include a factor analytic model for the residual genotype × environment interaction, whereas the environmental model for the non-genetic variation involves local, global, and extraneous variation. The approach is used to determine QTLs for yield in the Arapiles × Franklin doubled haploid population of the National Barley Molecular Marker Program. Analysis leads to the determination of 8 QTLs. Many of these QTLs are associated with other traits.

The analysis of quantitative traits in wheat mapping populations

This paper discusses the analysis of quantitative trait loci (QTLs) using molecular markers from a doubled haploid wheat mapping population arising from the Cranbrook Halberd cross. Two field trials are used to provide phenotypic information on the trait of interest, which is grain percentage protein. Methods for QTL analysis are reviewed together with methods for the analysis of field trials. The aim of the paper is to examine different approaches for QTL analysis, namely the conventional approach available in standard software, which ignores field variation, a 2-stage approach that provides adjusted phenotypic effects for a subsequent QTL analysis, and a joint marker and spatial analysis. The major effect, however, is the maturity class of the doubled haploid lines. Maturity and percent protein appear highly correlated genetically so QTL analysis shows marked changes if maturity is included as a covariate. More subtle changes occur due to field variation but this may not be the standard situation.

Mapping and QTL analysis of the barley population Alexis × Sloop

Two populations between the German malting variety Alexis and the Australian malting variety Sloop were constructed, mapped, phenotyped, and subjected to quantitative trait loci analysis. One population consisted of 153 F4-derived recombinant inbred lines and the other of 111 doubled haploid lines. This paper describes 18 field and laboratory experiments conducted with the populations and summarises the traits mapped and analysed. The genetic basis of 5 traits (malt extract, resistance to leaf rust, resistance to powdery mildew, early flowering, plant stature) important to Australian efforts to improve malting barley varieties was elucidated. Detailed maps for these populations are shown in this paper, while a consensus map incorporating these maps and further experiments on the populations are described elsewhere in this issue.