Search

Phenotyping assays in plant pathology using detached plant parts are multi-phase experimental processes. Such assays involve growing plants in field or controlled-environment trials (Phase 1) and then subjecting a sample removed from each plant to disease assessment, usually under laboratory conditions (Phase 2). Each phase may be subject to non-genetic sources of variation. To be able to separate these sources of variation in both phases from genetic sources of variation requires a multi-phase experiment with an appropriate experimental design and statistical analysis. To achieve this, a separate randomization is required for each phase, with additional replication in Phase 2. In this article, Phomopsis leaf and pod blight (caused by Diaporthe toxica) of Lupinus albus was used as a case study to apply a multi-phase experimental approach to identify genetic resistance to this pathogen, and demonstrate the principles of sound experimental design and analysis in detached plant part assays. In seven experiments, 250 breeding lines, cultivars, landraces, and recombinant in-bred lines from a mapping population of L. albus were screened using detached, inoculated leaves, and/or pods. The experimental, non-genetic variance in Phase 2 varied in magnitude compared to the Phase 1 experimental, non-genetic variance. The reliability of prediction for resistance to Phomopsis pod blight was high (mean of 0.70 in seven experiments), while reliability of prediction for leaf assays was lower (mean 0.35–0.51 depending on the scoring method used).

Grey mullets (Mugilidae) are important to recreational fisheries throughout the developed world. In Australia, several species are angled and then released in large numbers; all with virtually unknown fate. In response to the need for such data to facilitate effective stock management, this study sought to quantify the post-release mortality and key causal factors for sand mullet (Myxus elongatus). A total of 125 fish were conventionally angled, and then released along with 50 controls into floating cages in a south eastern Australian estuary, where they were monitored for four days. Five treatment fish died, providing a non-significant mortality of 4%. The few fatalities were mostly explained by a significant positive relationship with the length of trace (between the float and hook) used, and bleeding during release. While sand mullet appear quite tolerant of catch and release, their welfare nevertheless could be improved through simple changes to fishing strategies.

Exploring and exploiting variety by environment (V × E) interaction is one of the major challenges facing plant breeders. In paper I of this series, we presented an approach to modelling V × E interaction in the analysis of complex multi-environment trials using factor analytic models. In this paper, we develop a range of statistical tools which explore V × E interaction in this context. These tools include graphical displays such as heat-maps of genetic correlation matrices as well as so-called E-scaled uniplots that are a more informative alternative to the classical biplot for large plant breeding multi-environment trials. We also present a new approach to prediction for multi-environment trials that include pedigree information. This approach allows meaningful selection indices to be formed either for potential new varieties or potential parents.

Roberts, L. W., Butcher, P. A., Broadhurst, M. K., and Cullis, B. R. 2011. Using a multi-experimental approach to assess the fate of angled-and-released yellowtail kingfish (Seriola lalandi). – ICES Journal of Marine Science, 68: 67–75. Yellowtail kingfish (Seriola lalandi) are angled throughout their global distribution and released in large numbers under the unsubstantiated assumption of few impacts. The validity of this supposition was tested for southeastern Australian stocks. In all, 54 fish were angled and released into cages with 36 controls and monitored for 5 d. Of the angled fish, 15% died, mostly as a consequence of gill-hooking and the associated physiological and mechanical damage. A biotelemetry experiment was then performed to determine if cutting the line on gill-hooked fish could improve their post-release fate. The attachment of transmitters was validated in an aquarium experiment before 12 jaw- and 10 gill-hooked fish were tagged, released, and tracked. One gill-hooked fish was detected motionless within 10 min, and another was last detected 7 min after release; both presumed dead. No jaw-hooked fish died within the first 24 h. The remaining fish were last detected between 3 and 49 d after release and, apart from subtle differences in their short-term responses, maintained similar wide-ranging movements and accelerations. The results justify cutting the line on deep-hooked fish to minimize post-release mortality and illustrate the utility of combining confinement and biotelemetry studies to assess the fate of released fish.

The primary aim of crop variety evaluation programs is to reliably predict the performance of potential new varieties relative to existing commercial varieties. This is achieved through multienvironment trials (METs), that is, series of field trials conducted across a range of geographic trial locations and possibly over several years. Usually, a program of METs is established to take varieties through from the initial selection of potential breeding lines (often called early generation variety evaluation trials) to eventual commercial release and recommendation to farmers (late-stage variety evaluation trials). This paper is concerned with METs in the latter stages of this process, although many of our results will also apply to early generation trials. The Australian and UK late-stage variety testing systems were used as the basis of this study. In both cases, a series of trials is set up annually to test a relatively small number (• 100) of candidate varieties, which usually contains a set of standard or control varieties, highlyperforming established varieties and emerging varieties identified from earlier trials. The set of trials within (and across) years is designed to provide a range of growing conditions, and the term environments is used to describe the set of trial conditions. The aim of the statistical analysis is to use an appropriate model to provide reliable predictions of variety performance across target environments. The focus in this paper is on the use of linear mixed models which can be implemented as one-stage or two-stage analyses [1]. In a one-stage analysis individual plot data from all trials is combined in a single analysis. In a two-stage analysis variety means are first obtained from the separate analysis of individual trials (stage I), and are then combined in an overall mixed model analysis (stage II). The stage II analysis may be unweighted or weighted to reflect the relative precision of variety means from each trial. In each case, a linear mixed model may be constructed to describe the structure of the data, and this model is usually fitted using REML estimation. Two sets of trials from Australia and the UK are used to provide realistic scenarios for a simulation study to evaluate the different methods of analysis. This study showed that a one-stage approach gave the most accurate predictions of variety performance overall or within each environment, across a range of models, as measured by mean squared error of prediction or realised genetic gain. A weighted two-stage approach performed adequately for both overall variety predictions and variety predictions within environments. A two-stage unweighted approach performed poorly both for overall variety predictions and for variety predictions at individual environments. The performance of the two-stage methods was related to the change in heritability between the methods.

We report an analysis of a series of uniformity field trials using the technique proposed by Gilmour, Cullis, and Verbyla. In particular, we clarify the role of the sample variogram and present a range of enhanced graphical diagnostics to aid the spatial modeling process. We highlight the implications of the presence of extraneous variation related to commonly used agronomic practices, such as serpentine harvesting.

Butcher, P. A., Broadhurst, M. K., Hall, K. C., Cullis, B. R., and Nicoll, R. G. 2010. Scale loss and mortality in angled-and-released eastern sea garfish (Hyporhamphus australis). – ICES Journal of Marine Science, 67: 522–529. The eastern sea garfish (Hyporhamphus australis) is an endemic Australian marine teleost that is angled in large numbers throughout its distribution. Most fish are retained, although some are released, mainly because of size-grading in response to bag limits. Owing to their fragility, there are concerns that few released fish survive. To investigate this assumption, 185 angled and 90 control eastern sea garfish were released in groups of five into holding cages, then monitored for up to 24 h. One control and 93 angled fish died, providing an adjusted angled mortality rate of 49.2%. All fish that ingested their hooks (n=7) subsequently died. Generalized linear mixed models for the remaining mouth-hooked garfish revealed that mortalities were mainly caused by scale loss (p

Background and Aims: The influence of grapevine rootstocks on vine vigour and crop yield is recognized as an integral part of viticultural management. However, the genetic potential of Vitis species rootstock hybrids for vigour and yield control is not fully exploited in Australian viticulture. The effect of 55 novel inter- and intra-species hybrids and five traditional hybrid rootstock cultivars on winter pruning weight, berry size and fruit yield of grafted Shiraz vines is presented. The genetic predictions that resulted from this analysis were used to illustrate how rootstocks that best perform for a combination of traits may be selected. Methods and Results: The use of linear mixed models and residual maximum likelihood procedures took into account repeated measures and spatial variation within a large field trial (720 vines). Over 6 years of assessment, variation of up to 93.9% in winter pruning weight, 81.9% in fruit yield and 21.0% in berry weight between rootstocks was estimated. Conclusions: The effect of rootstock genotype accounted for marked differences in conferred pruning weight, berry weight and fruit yield from trial averages. Comparison of statistical analysis techniques illustrated that the choice of such techniques may influence the outcome of genetic selection from field trial data. Significance of the Study: Such quantification of the variation between vines in vigour, fruit yield and berry size due to rootstock genotype provides a framework for selection of well-performing genotypes for inclusion in advanced generations of the CSIRO vine rootstock breeding program.

Earthworm populations were monitored annually over 10 years in an acidic soil on the south-western slopes of New South Wales, Australia. The Typic Fragiochrept soil at the experimental site has a strong texture-contrast profile with a soil pH of 4.0–4.2 in 0.01 M CaCl2 in the 0–20 cm horizon. We found that the site was dominated by two native species, the megascolecids Spenceriella macleayi and Spenceriella montana, and accompanied by three exotic species, the lumbricid Aporrectodea trapezoides, and the acanthodrilids Microscolex dubius and Microscolex phosphoreus. Total earthworm abundance varied from 61 to 188 m−2. Lime, applied as a treatment, favoured all exotic earthworm species; their abundance was 3 times greater in limed soil than in unlimed soil. This strongly indicated that severe soil acidity was the most likely factor limiting, directly and indirectly, these species at this site. In contrast, the responses of the two native species to lime varied from negative (S. montana) to non-responsive (S. macleayi), suggesting that these native species are well adapted to acidic soil conditions, and perhaps to the dry seasonal conditions experienced during 5 of the 10 years the site was sampled.

SUMMARYPrime lamb live weight response to lime application on pasture was measured in a grazing experiment in the high rainfall zone of the southwestern slopes of New South Wales, Australia. The pastures were limed every 6 years over 15 years. First cross South African Meat Merino lambs were used as test animals. Pre- and post-grazing pasture dry matter (DM) yield, botanical composition, feed quality and lamb live weight were monitored over 12 weeks in 2007. Results showed that liming significantly increased pasture DM yield of high quality species and improved overall pasture quality due to increased digestibility and metabolic energy content. As a result, the limed perennial and annual pastures carried 24.0% (3.6 lambs ha−1) and 29.0% (4.4 lambs ha−1) more stock than the unlimed perennial and annual pastures, respectively. Averaged across pasture types, the limed pastures produced 30.6% (131 kg ha−1) more lamb live weight gain than the unlimed pastures over 12 weeks. The live weight gain varied between grazing cycles depending on the availability of feed-on-offer and feed quality, which were closely related to the rainfall pattern. The perennial pastures did not show any advantage in animal production over annual pastures during the experimental period due to lack of moisture in the deep soil profile because of severe drought in the previous year. More seasons with normal or above average rainfall are needed to compare animal production on perennial pastures and annual pastures to investigate the advantage of perennial pastures in animal production.

The design of large-scale field trials where the residuals are correlated has been of recent interest, in large part because of advances in statistical and computational methods of analysis. The construction of designs for correlated data has typically used A-optimality and is computationally intensive. This involves calculating the inverse of the information matrix for treatments under the supervision of an optimization strategy that explores the design space. We propose an approximation to A-optimality, using nearest-neighbour balance, that is less computationally demanding and can achieve at least 95% efficiency relative to A-optimality in many practical situations.

A long-term rotation experiment was established in 2001 to compare conservation tillage techniques with conventional tillage in a semi-arid environment in the western Loess Plateau of China. We examined resource use efficiencies and crop productivity in a spring wheat (Triticum aestivum L.)-field pea (Pisum arvense L.) rotation. The experimental design included a factorial combination of tillage with different ground covers (complete stubble removal, stubble retained and plastic film mulch). Results showed that there was more soil water in 0-30 cm at sowing under the no-till with stubble retained treatment than the conventional tillage with stubble removed treatment for both field pea (60 mm vs. 55 mm) and spring wheat (60 mm vs. 53 mm). The fallow rainfall efficiency was up to 18% on the no-till with stubble retained treatment compared to only 8% for the conventional tillage with stubble removed treatment. The water use efficiency was the highest in the no-till with stubble retained treatment for both field pea (10.2 kg/ha mm) and spring wheat (8.0 kg/ha mm), but the lowest on the no-till with stubble removed treatment for both crops (8.4 kg/ha mm vs. 6.9 kg/ha mm). Spring wheat also had the highest nitrogen use efficiency on the no-till with stubble retained treatment (24.5%) and the lowest on the no-till with stubble removed treatment (15.5%). As a result, grain yields were the highest under no-till with stubble retained treatment, but the lowest under no-till with no ground cover treatment for both spring wheat (2.4 t/ha vs. 1.9 t/ha) and field pea (1.8 t/ha vs. 1.4 t/ha). The important finding from this study is that conservation tillage has to be adopted as a system, combining both no-tillage and retention of crop residues. Adoption of a no-till system with stubble removal will result in reductions in grain yields and a combination of soil degradation and erosion. Plastic film mulch increased crop yields in the short-term compared with the conventional tillage practice. However, use of non-biodegradable plastic film creates a disposal problem and contamination risk for soil and water resources. It was concluded that no-till with stubble retained treatment was the best option in terms of higher and more efficient use of water and nutrient resources and would result in increased crop productivity and sustainability for the semi-arid region in the Loess Plateau. The prospects for adoption of conservation tillage under local conditions were also discussed.

Mixing measurements provide valuable information about dough strength and stability (STAB) traits. These measurements are important in milling and baking operations, and for varietal selection in wheat breeding programmes. There are several techniques with different sample sizes used for measuring these traits so there is interest in examining the agreement between methods in terms of genotypic (varietal) rankings. This issue has been investigated by using two different mixing methods, a small-scale Mixograph (2 g) and large-scale Farinograph (50 g) using data from a doubled haploid population (190 lines) from a Chara (excellent dough strength)×WW2449 (poor dough strength) cross. The cross was grown in a field trial at the Wagga Wagga Agricultural Institute (WWAI) in 2000. Eleven mixing traits were measured and compared according to a statistical design. The estimated genetic correlation matrix for six of the 11 mixing traits, dough development time (DDT), STAB, mixing tolerance index (MTI), maximum bandwidth (MBW), bandwidth at peak resistance (BWPR) and peak resistance (PR) revealed that for these dough-strength-related parameters, both methods were measuring equivalent traits, although individual parameters had widely different coefficients of variation. In this population, PR was correlated with the extensibility trait length determined by large-scale extension testing. None of the large-scale or small-scale mixing traits was an effective predictor of the small-scale extensibility parameter extensibility at Rmax (Ext_Rmax). The data verified that small-scale Mixograph tests are a robust and efficient alternative to large-scale Farinograph tests for both commercial breeding and research.

The Matern correlation function provides great flexibility for modeling spatially correlated random processes in two dimensions, in particular via a smoothness parameter, whose estimation allows data to determine the degree of smoothness of a spatial process. The extension to include anisotropy provides a very general and flexible class of spatial covariance functions that can be used in a model-based approach to geostatistics, in which parameter estimation is achieved via REML and prediction is within the E-BLUP framework. In this article we develop a general class of linear mixed models using an anisotropic Matern class with an extended metric. The approach is illustrated by application to soil salinity data in a rice-growing field in Australia, and to fine-scale soil pH data. It is found that anisotropy is an important aspect of both datasets, emphasizing the value of a straightforward and accessible approach to modeling anisotropy.

Modeling of cultivar x trial effects for multienvironment trials (METs) within a mixed model framework is now common practice in many plant breeding programs. The factor analytic (FA) model is a parsimonious form used to approximate the fully unstructured form of the genetic variance-covariance matrix in the model for MET data. In this study, we demonstrate that the FA model is generally the model of best fit across a range of data sets taken from early generation trials in a breeding program. In addition, we demonstrate the superiority of the FA model in achieving the most common aim of METs, namely the selection of superior genotypes. Selection is achieved using best linear unbiased predictions (BLUPs) of cultivar effects at each environment, considered either individually or as a weighted average across environments. In practice, empirical BLUPs (E-BLUPs) of cultivar effects must be used instead of BLUPs since variance parameters in the model must be estimated rather than assumed known. While the optimal properties of minimum mean squared error of prediction (MSEP) and maximum correlation between true and predicted effects possessed by BLUPs do not hold for E-BLUPs, a simulation study shows that E-BLUPs perform well in terms of MSEP.

Varietal selection for yield from a series of multi-environment trials can be regarded as a multi-trait selection problem in which the yields in different environments are synonymous with traits. As such an analysis of the data combined across environments should be conducted in order to form an index for selection. Analytical methods that include appropriate models for both the genetic variance structure (that is, the variances and covariances of genotype effects from different environments) and the residual variance structure (which typically comprises spatial covariance models for each trial) have been published previously. In the case of perennial crops, yields are often obtained from multiple harvests which implies that the data comprise short sequences of repeated measurements. Varietal performance in individual harvests is important for selection so that a combined analysis across both trials and harvests is required. The repeated measures nature of the data provides additional modelling challenges. In this paper we propose an approach for the analysis of multi-environment, multi-harvest data that accommodates the major sources of variation and correlation (including temporal). The approach is illustrated using two examples from sugarcane breeding programmes. The proposed models were found to provide a superior fit to the data and thence more accurate selection decisions than the common practice of conducting separate analyses of individual trials and harvests.

Three types of polynomial mixed model splines have been proposed: smoothing splines, P-splines and penalized splines using a truncated power function basis. The close connections between these models are demonstrated, showing that the default cubic form of the splines differs only in the penalty used. A general definition of the mixed model spline is given that includes general constraints and can be used to produce natural or periodic splines. The impact of different penalties is demonstrated by evaluation across a set of functions with specific features, and shows that the best penalty in terms of mean squared error of prediction depends on both the form of the underlying function and the signal:noise ratio.

The domestication of cereal crops such as wheat, maize, rice and barley has included the modification of inflorescence architecture to improve grain yield and ease harvesting(1). Yield increases have often been achieved through modifying the number and arrangement of spikelets, which are specialized reproductive branches that form part of the inflorescence. Multiple genes that control spikelet development have been identified in maize, rice and barley(2-5). However, little is known about the genetic underpinnings of this process in wheat. Here, we describe a modified spikelet arrangement in wheat, termed paired spikelets. Combining comprehensive QTL and mutant analyses, we show that Photoperiod-1 (Ppd-1), a pseudo-response regulator gene that controls photoperiod-dependent floral induction, has a major inhibitory effect on paired spikelet formation by regulating the expression of FLOWERING LOCUS T (FT)(6,7). These findings show that modulated expression of the two important flowering genes, Ppd-1 and FT, can be used to form a wheat inflorescence with a more elaborate arrangement and increased number of grain producing spikelets.

This article considers the design of early generation variety trials with a prespecified spatial correlation structure and introduces a new class of partially replicated designs called p-rep designs in which the plots of standard varieties are replaced by additional plots of test lines. We show how efficient p-rep designs can be readily generated using the modified Reactive TABU search algorithm. The expected and realized genetic gain of p-rep and grid plot designs is compared in a simulation study.

Despite the importance of selection for quality characteristics in plant improvement programmes, literature on experimental design and statistical analysis for these traits is scarce. Most quality traits are obtained from multi-phase experiments in which plant varieties are first grown in a field trial then further processed in the laboratory. In the present paper a general mixed model approach for the analysis of multi-phase data is described, with particular emphasis on quality trait data that are often highly unbalanced and involve substantial sources of non-genetic variation and correlation. Also detailed is a new approach for experimental design that employs partial replication in all phases. The motivation for this was the high cost of obtaining quality trait data, thus the need to limit the total number of samples tested, but still allow use of the mixed model analysis. A simulation study is used to show that the combined use of the new designs and mixed model analysis has substantial benefits in terms of the genetic gain from selection.

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.

Geostatistical estimates of a soil property by kriging are equivalent to the best linear unbiased predictions (BLUPs). Universal kriging is BLUP with a fixed-effect model that is some linear function of spatial coordinates, or more generally a linear function of some other secondary predictor variable when it is called kriging with external drift. A problem in universal kriging is to find a spatial variance model for the random variation, since empirical variograms estimated from the data by method-of-moments will be affected by both the random variation and that variation represented by the fixed effects. The geostatistical model of spatial variation is a special case of the linear mixed model where our data are modelled as the additive combination of fixed effects (e.g. the unknown mean, coefficients of a trend model), random effects (the spatially dependent random variation in the geostatistical context) and independent random error (nugget variation in geostatistics). Statisticians use residual maximum likelihood (REML) to estimate variance parameters, i.e. to obtain the variogram in a geostatistical context. REML estimates are consistent (they converge in probability to the parameters that are estimated) with less bias than both maximum likelihood estimates and method-of-moment estimates obtained from residuals of a fitted trend. If the estimate of the random effects variance model is inserted into the BLUP we have the empirical BLUP or E-BLUP. Despite representing the state of the art for prediction from a linear mixed model in statistics, the REML-E-BLUP has not been widely used in soil science, and in most studies reported in the soils literature the variogram is estimated with methods that are seriously biased if the fixed-effect structure is more complex than just an unknown constant mean (ordinary kriging). In this paper we describe the REML-E-BLUP and illustrate the method with some data on soil water content that exhibit a pronounced spatial trend.

Summary The general linear model encompasses statistical methods such as regression and analysis of variance (anova) which are commonly used by soil scientists. The standard ordinary least squares (OLS) method for estimating the parameters of the general linear model is a design-based method that requires that the data have been collected according to an appropriate randomized sample design. Soil data are often obtained by systematic sampling on transects or grids, so OLS methods are not appropriate. Parameters of the general linear model can be estimated from systematically sampled data by model-based methods. Parameters of a model of the covariance structure of the error are estimated, then used to estimate the remaining parameters of the model with known variance. Residual maximum likelihood (REML) is the best way to estimate the variance parameters since it is unbiased. We present the REML solution to this problem. We then demonstrate how REML can be used to estimate parameters for regression and anova-type models using data from two systematic surveys of soil. We compare an efficient, gradient-based implementation of REML (ASReml) with an implementation that uses simulated annealing. In general the results were very similar; where they differed the error covariance model had a spherical variogram function which can have local optima in its likelihood function. The simulated annealing results were better than the gradient method in this case because simulated annealing is good at escaping local optima.

Increasing crop competitiveness using higher seeding rates is a possible technique for weed management in low input and organic farming systems or when herbicide resistance develops in weeds. A range of wheat seeding rates were sown and resulted in crop densities between 50–400 plants/m2 (current recommendations are 100–150 plants/m2) in the presence and absence of annual ryegrass (Lolium rigidum Gaud.) in three wheat cultivars at nine experiments in southern Australia. Wheat densities of at least 200 plants/m2 were required to suppress L. rigidum and to a lesser extent increase crop yield across a wide range of environments (seasonal rainfall between 200–420 mm) and weed densities (50–450 L. rigidum plants/m2). Doubling crop density of all cultivars from 100 to 200 plants/m2 halved L. rigidum dry weight (averaged over all experiments) from 100 g/m2 to about 50 g/m2. Higher crop densities gave diminishing marginal reductions in weed biomass, while cultivar differences in weed suppression were small. Grain yields ranged from 0·5 t/ha to over 5 t/ha depending on site and season. Maximum yields in the weed-free plots (averaged over environments and cultivars) were at 200 crop plants/m2, and yield declined only slightly by 4–5% at densities up to 425 plants/m2. In the weedy plots grain yield continued to increase up to the highest density but at a slower rate. The percentage yield loss from weed competition was of a smaller magnitude than the suppression of L. rigidum by wheat. For example, 100 wheat plants/m2 led to an average 23% yield loss compared with 17% at 200 plants/m2, and the probability of reduced crop grain size and increased proportion of small seeds was negligible at these densities. Cultivar differences in yield loss from weed competition were small compared with differences due to crop density. Adoption of higher wheat seed rates as part of integrated weed management is now strongly promoted to farmers.

After estimation of effects from a linear mixed model, it is often useful to form predicted values for certain factor/variate combinations. This process has been well-defined for linear models, but the introduction of random effects means that a decision has to be made about the inclusion or exclusion of random model terms from the predictions, including the residual error. For spatially correlated data, kriging then becomes prediction from the fitted model. In many cases, the size of the matrices required to calculate predictions and their covariance matrix directly can be prohibitive. An efficient computational strategy for calculating predictions and their standard errors is given, which includes the ability to detect the invariance of predictions to the parameterisation used in the model.

The major aim of crop variety evaluation is to predict the future performance of varieties. This paper presents the routine statistical analysis of data from late-stage testing of crop varieties in Australia. It uses a two-stage approach for analysis. The data from individual trials from the current year are analysed using spatial techniques. The resultant table of variety-by-trial means is combined with tables from previous years to form the data for an overall mixed model analysis. Weights allow for the data being estimates with varying accuracy. In view of the predictive aim of the analysis, variety effects and interactions are regarded as random effects. Appropriate inferential tools have been developed to assist with interpretation of the results. Analyses must be conducted in a timely manner so that variety predictions can be published and disseminated to growers immediately after harvest each year. Factors which facilitate this include easy access to historic data and the use of specialist mixed model software.

In this paper we present the analysis of yield data from a broad cross-section of crop variety evaluation programmes (CVEP) conducted in Australia. The main sources of variety by environment interaction are ‘non-static’ interactions, namely those linked to seasonal influences. These contributed an average of 41·3% of the total variance. In contrast the static component accounts for only 5·3% of the total.We develop methods for determining the relative accuracy of CVEP based on selection of newly promoted entries. The accuracy of the current testing regimes for the Australian CVEP under study is determined. The accuracy of alternative schemes, with different numbers of years of testing, numbers of locations per year and numbers of replicates per trial is also examined. Cost effective methods for improving the accuracy of CVEP are discussed.

The versatility of mixed model procedures in investigating large, unbalanced sets of genotype by environment data is illustrated on an historic set of yields from a South Australian oat evaluation program. Information on specific genotypic traits is included in the analysis in order to isolate unexplained genotype by environment interaction.

The high cost of transporting limestone for distances up to 300 km to acidic cropping soils in Australia has caused interest in evaluating the effect of management practices on soil acidification. Practices which minimise acidification will minimise the use and hence cost of liming. A long term rotation trial which started in 1979 at Wagga Wagga in southeastern Australia provided an ideal opportunity to evaluate the effects of some rotations, stubble handling and tillage practices on the relative rates of soil profile acidification over a period of 12 years. The soil had an initial pH (CaCl 2 ) of 4.93 and 0.13% total N. All 13 treatments acidified the soil over the 12 years of the trial, at rates equivalent to a loss of 46 to 95 kg CaCO 3 ha −1 year −1 . Although there were differences between treatments in their relative rates of acidification only the management of N, as fertiliser or via legumes in the rotation, appears to offer any scope for minimising acidification rates. Most treatments influenced the stratification of the soil profile more than they influenced the net rate of acidification. All 13 treatments had minimum pH and minimum variance in pH at 5–10 cm depth, the depth range into which crop seed is generally placed. Direct drilling resulted in a higher pH (CaCl 2 ) at 0–5 cm depth than conventional (2 or 3 passes) cultivation but the reverse was true at 5–10 cm. Direct drilling resulted in a stratification of soil pH which was exaggerated by burning stubble, as opposed to retaining it, and minimised by an increasing intensity of cultivation. There was no difference in soil profile acidification between lupin crops ( Lupinus augustifolius ), L, and subterranean clover pasture ( Trifolium subterraneum ), C, in 1:1 rotations with wheat ( Triticum aestivum ), W. The addition of a second wheat phase, LWW, made no difference to the soil pH compared to the LW rotation. The effects of mowing and mulching of subterranean clover on soil pH were not significantly different to the effects of grazing by sheep. The addition of 100 kg N ha −1 year −1 as urea in three split applications to continuous crops of wheat caused the surface 10 cm of soil to be acidified by 0.4 pH units compared with where no N fertiliser was applied. The greater acidification extended to at least 15 cm depth. In our system, which uses only annual species and relies on N inputs from legumes or fertiliser, there has so far been little evidence that realistic management practices will minimise acidification and the requirement for lime.

The efficiency of various trialling systems for wheat variety evaluation in New South Wales (NSW) is considered. This involved the estimation of the variance components due to genotype, genotype-by-year, genotype-by-location and genotype-by-year-by-location. It is shown that there is a significant reduction in the magnitude of these variance components by the inclusion of the interaction of genotype maturity, winter habit and aluminium tolerance with environment.

Summary Field trials for evaluating plant varieties are conducted to obtain information on a range of traits including grain yield and grain quality. Some grain quality traits are costly to measure so it is not possible to test all plots individually. It has therefore become common practice to test a single composite sample for each variety in the trial but this precludes the use of an efficient statistical analysis. We propose an approach in which a proportion of varieties is tested by using individual replicate samples. The remaining varieties may either be tested as composite samples or with reduced replication. This allows application of efficient mixed model analyses for both the inexpensive traits (using data from the complete set of individual replicate plots) and expensive traits (using data from a subset of the plots or a mixture of composite and individual plot samples).

Trials in the early stages of selection are often subject to variation arising from spatial variability and interplot competition, which can seriously bias the assessment of varietal performance and reduce genetic progress. An approach to jointly model both sources of bias is presented. It models genotypic and residual competition and also global and extraneous spatial variation. Variety effects were considered random and residual maximum likelihood was used for parameter estimation. Competition at the residual level was examined using two special simultaneous autoregressive models. An equal-roots second-order autoregressive (EAR(2)) model is proposed for trials where competition is dominant. An equal-roots third-order autoregressive (EAR(3)) model allows for competition and spatial variability. These models are applied to two yield data sets from an Australian sugarcane selection program. One data set is in the paper and the other is in supplementary material available online. To determine the effect of simultaneously adjusting for spatial variability and interplot competition on selection, the percentages of superior varieties in common in the top 15% for the joint model and classical approaches were compared. Agreement between the two approaches was 45 and 84%. Hence, for some trials there are large differences in varieties advanced to the next stage of selection.

A major aim in some plant-based studies is the determination of quantitative trait loci (QTL) for multiple traits or across multiple environments. Understanding these QTL by trait or QTL by environment interactions can be of great value to the plant breeder. A whole genome approach for the analysis of QTL is presented for such multivariate applications. The approach is an extension of whole genome average interval mapping in which all intervals on a linkage map are included in the analysis simultaneously. A random effects working model is proposed for the multivariate (trait or environment) QTL effects for each interval, with a variance–covariance matrix linking the variates in a particular interval. The significance of the variance–covariance matrix for the QTL effects is tested and if significant, an outlier detection technique is used to select a putative QTL. This QTL by variate interaction is transferred to the fixed effects. The process is repeated until the variance–covariance matrix for QTL random effects is not significant; at this point all putative QTL have been selected. Unlinked markers can also be included in the analysis. A simulation study was conducted to examine the performance of the approach and demonstrated the multivariate approach results in increased power for detecting QTL in comparison to univariate methods. The approach is illustrated for data arising from experiments involving two doubled haploid populations. The first involves analysis of two wheat traits, α-amylase activity and height, while the second is concerned with a multi-environment trial for extensibility of flour dough. The method provides an approach for multi-trait and multi-environment QTL analysis in the presence of non-genetic sources of variation.

Summary The procedure of Verbyla & Cullis (1990) is extended to cater for the analysis of repeated measures data in which either non-linear modelling of the treatment contrasts is required and or there are time dependent covariates. These extensions are illustrated via two agricultural data sets.

SUMMARYA simulation study was conducted to determine the relative response to selection of a one-dimensional spatial analysis of field experiments (SAFE) specifically adapted for early generation trials. The primary purpose of the analysis in these trials is to obtain accurate estimates of genotypic effects of the unreplicated test lines by adjusting for local variation, using either the yields of all neighbouring plots or the yields of neighbouring plots of (replicated) check varieties. The response to selection of the SAFE analysis, relative to the use of unadjusted yields of test line plots, was consistently greater than the relative response to selection of check-plot-only analyses. The relative response to selection of SAFE increased as the percentage of trend variance increased.

There has been much work on the use of neighbouring plots to control environmental variation in the analysis of agricultural field experiments. In particular, the Residual Maximum Likelihood Neighbour (REMLN) analysis of Gleeson&Cullis (1987) appears very promising. The application of the REMLN analysis to an unequally replicated field trial augmented with an additional variety planted every six plots in a grid system is here compared with a covariance (COV) analysis using the neighbouring grid or check plot values as the covariate. The results indicate that the REMLN analysis gives more accurate estimates of treatment contrasts than the COV analyses, but that the estimate of treatment means can be biased. The bias depends on the mean of the check plot. This bias can be removed by adjusting the estimates of the treatment means such that their average equals the average of the raw means rather than that of the raw data.

Genetic models partitioning additive and non-additive genetic effects for populations tested in replicated multi-environment trials (METs) in a plant breeding program have recently been presented in the literature. For these data, the variance model involves the direct product of a large numerator relationship matrix A, and a complex structure for the genotype by environment interaction effects, generally of a factor analytic (FA) form. With MET data, we expect a high correlation in genotype rankings between environments, leading to non-positive definite covariance matrices. Estimation methods for reduced rank models have been derived for the FA formulation with independent genotypes, and we employ these estimation methods for the more complex case involving the numerator relationship matrix. We examine the performance of differing genetic models for MET data with an embedded pedigree structure, and consider the magnitude of the non-additive variance. The capacity of existing software packages to fit these complex models is largely due to the use of the sparse matrix methodology and the average information algorithm. Here, we present an extension to the standard formulation necessary for estimation with a factor analytic structure across multiple environments.

Models for repeated measures or growth curves consist of a mean response plus error and the errors are usually correlated. Both maximum likelihood and residual maximum likelihood (REML) estimators of a regression model with dependent errors are derived for cases in which the variance matrix of the error model admits a convenient Cholesky factorisation. This factorisation may be linked to methods for producing recursive estimates of the regression parameters and recursive residuals to provide a convenient computational method. The method is used to develop a general approach to repeated measures analysis.

Body weight and traits associated with production of wool were measured over a 2-year period between 1985 and 1987 in south-western New South Wales in a flock of Merino wethers experimentally infected with footrot. The disease was allowed to spread freely amongst 150 of the flock but kept at very low prevalence in the remaining 50 by preventive footbathing during transmission periods. Severe, underrunning footrot had a significant adverse effect on body weight, for each year of the trial. Body weight was most severely reduced at times of the year when footrot was spreading among animals and lesions were severe. The mean body weight of the infected group at the end of the 2 years of observation was 7.3 kg (11.6%) below that of the control group. Footrot also depressed wool growth, with the mean clean fleece weight of the infected group being 0.4 kg (8%) lighter than that of the controls at each of the 2 annual shearings. There were no consistent differences between the groups for the other wool characteristics measured.

While the genetic control of wheat processing characteristics such as dough rheology is well understood, limited information is available concerning the genetic control of baking parameters, particularly sponge and dough (SD) baking. In this study, a quantitative trait loci (QTL) analysis was performed using a population of doubled haploid lines derived from a cross between Australian cultivars Kukri x Janz grown at sites across different Australian wheat production zones (Queensland in 2001 and 2002 and Southern and Northern New South Wales in 2003) in order to examine the genetic control of protein content, protein expression, dough rheology and sponge and dough baking performance. The study highlighted the inconsistent genetic control of protein content across the test sites, with only two loci (3A and 7A) showing QTL at three of the five sites. Dough rheology QTL were highly consistent across the 5 sites, with major effects associated with the Glu-B1 and Glu-D1 loci. The Glu-D1 5 + 10 allele had consistent effects on SD properties across sites; however, there was no evidence for a positive effect of the high dough strength Glu-B1-al allele at Glu-B1. A second locus on 5D had positive effects on SD baking at three of five sites. This study demonstrated that dough rheology measurements were poor predictors of SD quality. In the absence of robust predictive tests, high heritability values for SD demonstrate that direct selection is the current best option for achieving genetic gain in this product category.

Composition, dough mixing, extensional rheological properties and baking properties of a set of 160 double haploid lines grown in two different environments were assessed in order to establish linkages between regions of the wheat genome and wheat quality traits. Further studies are required to rigorously test the impact of loci associated with rheological parameters on baking properties, as there are clear differences between the genetic control of rheological and baking parameters.

Variety selection in perennial pasture crops involves identifying best varieties from data collected from multiple harvest times in field trials. For accurate selection, the statistical methods for analysing such data need to account for the spatial and temporal correlation typically present. This paper provides an approach for analysing multi-harvest data from variety selection trials in which there may be a large number of harvest times. Methods are presented for modelling the variety by harvest effects while accounting for the spatial and temporal correlation between observations. These methods provide an improvement in model fit compared to separate analyses for each harvest, and provide insight into variety by harvest interactions. The approach is illustrated using two traits from a lucerne variety selection trial. The proposed method provides variety predictions allowing for the natural sources of variation and correlation in multi-harvest data.

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.

L-splines are a large family of smoothing splines defined in terms of a linear differential operator. This article develops L-splines within the context of linear mixed models and uses the resulting mixed model L-spline to analyze longitudinal data from a grassland experiment. In the spirit of time-series analysis, a periodic mixed model L-spline is developed, which partitions data into a smooth periodic component plus smooth long-term trend.

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.

‘Managing Acid Soils Through Efficient Rotations (MASTER)’ is a long-term pasture–crop rotation experiment commenced in 1992. One of the objectives was to demonstrate the extent of crop, pasture, and animal responses to lime on a typical acidic soil in the 500–800 mm rainfall zone in south-eastern Australia. Two types of pastures (perennial v. annual pastures) with or without lime application were established in 1992. This paper presents the results of the pasture dry matter (DM) responses to lime application over 6 years from 1992 to 1997. Results showed that both perennial and annual pastures responded positively to lime on a highly acidic soil on the south-west slopes of New South Wales. Averaged across pasture types and 5 growing seasons, the limed pastures produced 18% more pasture DM (520 kg/ha, P < 0.05) than the unlimed pastures. Significant responses to lime were detected on perennial pastures (610 kg DM/ha, P < 0.05), but not on annual pastures, although the limed annual pastures produced more DM (420 kg/ha, P = 0.20) than the unlimed annual pastures. There was a large seasonal variation in pasture growth rate with the significant lime responses in winter and spring on both perennial pastures (P < 0.05) and annual pastures (P < 0.10 in winter and P < 0.05 in spring), but no responses in autumn and summer on either perennial or annual pastures. The extra growth in winter is of importance as winter is the period when feed is normally inadequate and limits stocking rates. It is recommended that perennial-based pastures should be promoted for the purposes of productivity, in terms of increasing pasture production and improving feed quality, and for the environmental benefits in terms of alleviating the soil acidity problem and reducing the risk of dryland salinity in the high-rainfall zone in south-eastern Australia.