Accounting for Natural and Extraneous Variation in the Analysis of Field Experiments

Gilmour, A.; Cullis, Brian R; Verbyla, A. P.

doi:10.2307/1400446

Cited by 637 publications

(752 citation statements)

References 22 publications

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“…In the first stage, best spatial models for yield, anthesis and height were determined for each trial (environment) following Gilmour et al (1997) using Residual Maximum Likelihood (REML) in GenStat Release 9.0 (Payne et al 2006) and assuming random genotype effects. Following the notation of Welham et al (2006), for an individual trial, j (j = 1,…, t), the mixed model in vector notation can be written as:…”

Section: Phenotypic Analysismentioning

confidence: 99%

“…The within-trial residuals e j were modelled such that experimental design parameters (such as replicate and sub-block within replicate for the two-replicate alphalattice designs) were fitted as random; and the checks were fitted as fixed effects in the single-replicate augmentedcheck designs. An autoregressive process in each of the row and column directions (separable AR 9 AR model) modelled the spatial trend while further global effects (broad trends such as gradient or fertility trends in the column and/or row direction) and extraneous spatial effects (trial management practices such as irrigation pipe placement or harvest order) were fitted as fixed and random effects, respectively (Gilmour et al 1997).…”

Section: Phenotypic Analysismentioning

confidence: 99%

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Multi-environment QTL mixed models for drought stress adaptation in wheat

et al. 2008

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Many quantitative trait loci (QTL) detection methods ignore QTL-by-environment interaction (QEI) and are limited in accommodation of error and environment-specific variance. This paper outlines a mixed model approach using a recombinant inbred spring wheat population grown in six drought stress trials. Genotype estimates for yield, anthesis date and height were calculated using the best design and spatial effects model for each trial. Parsimonious factor analytic models best captured the variance-covariance structure, including genetic correlations, among environments. The 1RS.1BL rye chromosome translocation (from one parent) which decreased progeny yield by 13.8 g m -2 was explicitly included in the QTL model. Simple interval mapping (SIM) was used in a genome-wide scan for significant QTL, where QTL effects were fitted as fixed environmentspecific effects. All significant environment-specific QTL were subsequently included in a multi-QTL model and evaluated for main and QEI effects with non-significant QEI effects being dropped. QTL effects (either consistent or environment-specific) included eight yield, four anthesis, and six height QTL. One yield QTL co-located (or was linked) to an anthesis QTL, while another co-located with a height QTL. In the final multi-QTL model, only one QTL for yield (6 g m -2 ) was consistent across environments (no QEI), while the remaining QTL had significant QEI effects (average size per environment of 5.1 g m -2 ). Compared to single trial analyses, the described framework allowed explicit modelling and detection of QEI effects and incorporation of additional classification information about genotypes.

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Section: Phenotypic Analysismentioning

confidence: 99%

Section: Phenotypic Analysismentioning

confidence: 99%

Multi-environment QTL mixed models for drought stress adaptation in wheat

et al. 2008

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“…Spatial analysis can capture both local gradient variations within blocks (patches) and a global gradient trend along the row and column of the trial, so it is becoming a popular method to use for both agricultural and forestry field trials (Anekonda and Libby 1996;Brownie and Gumpertz 1997;Cullis et al 1998;Cullis and Gleeson 1989;Cullis and Gleeson 1991;Fox et al 2007a, b;Gilmour et al 1997;Qiao et al 2000;Yang et al 2004;Ye and Jayawickrama 2008;Chen et al 2017). In forestry, there are several spatial analysis methods used, such as post-blocking (Dutkowski et al 2002;Ericsson 1997), nearest-neighbor adjustment (Anekonda and Libby 1996;Joyce et al 2002;Wright 1978), and kriging (Hamann et al 2002;Zas 2006).…”

Section: Introductionmentioning

confidence: 99%

“…In forestry, there are several spatial analysis methods used, such as post-blocking (Dutkowski et al 2002;Ericsson 1997), nearest-neighbor adjustment (Anekonda and Libby 1996;Joyce et al 2002;Wright 1978), and kriging (Hamann et al 2002;Zas 2006). However, the most common method used in crop and forestry trials seems to be a combination of experimental design with a spatial component, in the form of separable first-order twodimensional autoregressive residual variation as recommended by Gilmour et al (1997).…”

Section: Introductionmentioning

confidence: 99%

Efficiency of using spatial analysis for Norway spruce progeny tests in Sweden

Chen

Helmersson

Westin

et al. 2017

Annals of Forest Science

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Key message Spatial analysis could improve the accuracy of genetic analyses, as well as increasing the accuracy of predicting breeding values and genetic gain for Norway spruce trials. Context Spatial analysis has been increasingly used in genetic evaluation of field trials in tree species. However, the efficiency of spatial analysis relative to the analysis using the conventional experimental designs or pre- and post-blocking method in Swedish genetic trials has not been systematically evaluated. Aims This study aims to examine the effectiveness of spatial analysis in improving the accuracy of predicting breeding values and genetic gain. Methods Spatial analysis, using separable first-order autoregressive processes of residuals in rows and columns, was used in nine types of trait classes from 145 field trials of Norway spruce (Picea abies (L.) Karst.) in Sweden. Results Ninety-six percent of variables (traits) were converged for the spatial model. Large trials with a large block variance tend to have a larger improvement from the model of experimental design to spatial model in accuracy. Growth and Pilodyn measurement traits showed greater improvements in log likelihood, accuracy, and genetic gain. Block variance was reduced by more than 80% for trait height and diameter using spatial analysis, indicating that it is more effective using both pre-blocking and post-blocking analyses in Swedish Norway spruce trials. The prediction accuracy for diameter and height for progeny breeding values showed an increase of 3.6 and 3.4%, respectively. The improvement of efficiency for growth traits is also related to the geographical location of test sites, tree age, number of survival trees, and the spacing of the trial. Conclusion The spatial analysis approach is more efficient in Swedish Norway spruce trials than the conventional methods using models based on the experimental design.

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“…Commonly-used experimental designs, often practiced by the crop improvement programmes, are based on anticipated, though often not confirmed, homogeneous blocks of suitable sizes (incomplete blocks) [2,4,6,10]. Coupled with the incomplete block design, the possibility of accounting for any possible correlation between the plot errors, particularly auto-correlations along rows and columns, has been found useful in enhancing the efficiency of crop variety trials [3,5,12,13]. These experimental designs and analysis led to higher efficiency for genotypic comparisons and genetic gain over analyses based on complete blocks.…”

Section: Introductionmentioning

confidence: 99%

Increasing Precision of Even Otherwise Well-Run Trials by Capturing Heterogeneity of Plot Error Variances

et al. 2012

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Application of an experimental design based on blocking of homogeneous experimental units is an objective approach to reduce experimental error. Often, the experimental design and analysis efforts are considered to be executed satisfactory as long as the coefficient of variation is estimated to be below 10 %, say for yield, as a generally accepted guide for a well-run trial. Most of the statistical analyses of data are based on the assumption of a homogeneous variance of plot errors. In field plot experimentation, the question of heterogeneity of error variances has been addressed here. This study introspects a set of four such supposedly well-run trials in lentil and chickpea conducted in lattice designs. The presence of, in fact, heterogeneous error variances exhibits a distribution of coefficient of variation as opposed to a single index to measure heterogeneity of a field. This further suggests that it is more realistic to view the distribution of the heritability of a trait and its genetic advance due to selection, when assessing them, even in a single field. Objectives of the study were to examine the possibility of heterogeneous error variances, identify the associated experimental units and estimate the predicted means of the genotypes and gain due to selection. We show that accounting heterogeneous variances allows a significant increase in the efficiency of genotypic comparisons and the power of genotypic discrimination, higher heritability and genetic advance. Thus, it is likely to help shorten the breeding cycle for an expected genetic gain, and is in principle relevant to all experiments that use replications, involving crops or not.

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Accounting for Natural and Extraneous Variation in the Analysis of Field Experiments

Cited by 637 publications

References 22 publications

Multi-environment QTL mixed models for drought stress adaptation in wheat

Multi-environment QTL mixed models for drought stress adaptation in wheat

Efficiency of using spatial analysis for Norway spruce progeny tests in Sweden

Increasing Precision of Even Otherwise Well-Run Trials by Capturing Heterogeneity of Plot Error Variances

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