So far in this course we have dealt entirely with the evolution of characters that are controlled by simple Mendelian inheritance at a single locus. There are notes on the course website about gametic disequilibrium and how allele frequencies change at two loci simultaneously, but we didn’t discuss them. In every example we’ve considered we’ve imagined that we could understand something about evolution by examining the evolution of a single gene. That’s the domain of classical population genetics. For the next few weeks we’re going to be exploring a field that’s actually older than classical population genetics, although the approach we’ll be taking to it involves the use of population genetic machinery. If you know a little about the history of evolutionary biology, you may know that after the rediscovery of Mendel’s work in 1900 there was a heated debate between the “biometricians” (e.g., Galton and Pearson) and the “Mendelians” (e.g., de Vries, Correns, Bateson, and Morgan). Biometricians asserted that the really important variation in evolution didn’t follow Mendelian rules. Height, weight, skin color, and similar traits seemed to

Human biochemical genetics

ASREML user guide release 3.0

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.

/pdf/on-the-design-of-early-generation-variety-trials-with-4hji1yz8uv.pdf

On the design of early generation variety trials with correlated data

Best linear unbiased prediction (BLUP) is a standard method for estimating random effects of a mixed model. This method was originally developed in animal breeding for estimation of breeding values and is now widely used in many areas of research. It does not, however, seem to have gained the same popularity in plant breeding and variety testing as it has in animal breeding. In plants, application of mixed models with random genetic effects has up until recently been mainly restricted to the estimation of genetic and non- genetic components of variance, whereas estimation of genotypic values is mostly based on a model with fixed effects. This paper reviews recent developments in the application of BLUP in plant breeding and variety testing. These include the use of pedigree information to model and exploit genetic correlation among relatives and the use of flexible variance-covariance structures for genotype-by-environment interaction. We demonstrate that BLUP has good predictive accuracy compared to other procedures. While pedi- gree information is often included via the so-called numerator relationship matrix ðAÞ, we stress that it is frequently straightforward to exploit the same infor- mation by a simple mixed model without explicit reference to the A-matrix.

https://www.esalq.usp.br/departamentos/lce/arquivos/aulas/2012/LCE5872/Piepho%20et%20al.,%202008.pdf

BLUP for phenotypic selection in plant breeding and variety testing

This study had as objective to propose a new approach for quality evaluation of variety trials for determination of cropping and use values (VCU), which considers three attributes simultaneously: magnitude of the residual variation, replication number, and genetic control of the trait under selection. It was also emphasized the need for using shrinkage estimators/predictors of genotypic values instead of unshrunk phenotypic means of varieties, i.e., the procedures should consider the genetic coefficient of determination of the traits, as well as the eventual heterogeneity of residual variance within varieties. Targeting an accuracy of 90%, it was concluded that Snedecor F test values associated to treatment effects in the analysis of variance should be above 5.0. The magnitude of genotypic variability of the traits is also involved in the F statistics. This means that the approach of fixing minimum values for replication number and maximum values for residual variation coefficient (CVe) is not sufficient. For traits related to yield (with low genetic coefficient of determination) the normally used replication number, between two and four, does not permit to reach the targeted accuracy, even if residual variation coefficients below 10% are aimed, and the experimentation is conducted on several sites and years. For that target accuracy it is recommended the use of at least six replications. It was also shown that shrinkage estimators provide more precise and reliable inferences concerning genotypic means of the varieties, and their use is encouraged. KEY-WORDS: Accuracy; shrinkage estimator; variance heterogeneity; biased estimator; variation coefficent.

https://revistas.ufg.br/pat/article/download/1867/1773

Precisão e controle de qualidade em experimentos de avaliação de cultivares

The analysis of series of crop variety trials has a long history with the earliest approaches being based on ANOVA methods. Kempton (1984) discussed the inadequacies of this approach, summarized the alternatives available at that time and noted that all of these approaches could be classified as multiplicative models. Recently, mixed model approaches have become popular for the analysis of series of variety trials. There are numerous reasons for their use, including the ease with which incomplete data (not all varieties in all trials) can be handled and the ability to appropriately model within-trial error variation. Currently, the most common mixed model approaches for series of variety trials are mixed model versions of the methods summarized by Kempton (1984). In the present paper a general formulation that encompasses all of these methods is described, then individual methods are considered in detail.

/pdf/the-analysis-of-crop-cultivar-breeding-and-evaluation-trials-4gp5287540.pdf

The analysis of crop cultivar breeding and evaluation trials: an overview of current mixed model approaches

The recommendation of new plant varieties for commercial use requires reliable and accurate predictions of the average yield of each variety across a range of target environments and knowledge of important interactions with the environment. This information is obtained from series of plant variety trials, also known as multi-environment trials (MET). Cullis, Gogel, Verbyla, and Thompson (1998) presented a spatial mixed model approach for the analysis of MET data. In this paper we extend the analysis to include multiplicative models for the variety effects in each environment. The multiplicative model corresponds to that used in the multivariate technique of factor analysis. It allows a separate genetic variance for each environment and provides a parsimonious and interpretable model for the genetic covariances between environments. The model can be regarded as a random effects analogue of AMMI (additive main effects and multiplicative interactions). We illustrate the method using a large set of MET data from a South Australian barley breeding program.

Analyzing variety by environment data using multiplicative mixed models and adjustments for spatial field trend.

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.

Applications: The Analysis of Crop Variety Evaluation Data in Australia

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

Alison B. Smith

Papers

On the design of early generation variety trials with correlated data

The analysis of crop cultivar breeding and evaluation trials: an overview of current mixed model approaches

Analyzing variety by environment data using multiplicative mixed models and adjustments for spatial field trend.

Applications: The Analysis of Crop Variety Evaluation Data in Australia

The accuracy of varietal selection using factor analytic models for multi-environment plant breeding trials