#Multi_environment_studies

GGE analyses for multi-environment studies

Published at May 31, 2023 ·  12 min read

In a recent post we have seen that we can use Principal Component Analyses (PCA) to elucidate the ‘genotype by environment’ relationship (see this post). Whenever the starting point for PCA is the doubly-centered (centered by rows and columns) matrix of yields across environments, we talk about AMMI analysis, which is often used to get insight into the stability of genotype yields across environments. By changing the starting matrix, we can obtain a different perspective and put focus on the definition of macroenvironments and on the selection of winning genotypes....


AMMI analyses for multi-environment studies

Published at May 26, 2023 ·  19 min read

Again into a subject that is rather important for most agronomists, i.e. the selection of crop varieties. All farmers are perfectly aware that crop performances are affected both by the genotype and by the environment. These two effects are not purely additive and they often show a significant interaction. By this word, we mean that a genotype can give particularly good/bad performances in some specific environmental situations, which we may not expect, considering its average behaviour in other environmental conditions....


Meta-analysis for a single study. Is it possible?

Published at July 21, 2022 ·  12 min read

We all know that the word meta-analysis encompasses a body of statistical techniques to combine quantitative evidence from several independent studies. However, I have recently discovered that meta-analytic methods can also be used to analyse the results of a single research project. That happened a few months ago, when I was reading a paper from Damesa et al. (2017), where the authors describe some interesting methods of data analyses for multi-environment genotype experiments....


lmDiallel: a new R package to fit diallel models. Multienvironment diallel experiments

Published at March 5, 2021 ·  7 min read

In recent times, a few colleagues at my Department and I have devoted some research effort to data management for diallel mating experiments, which we have summarised in a paper (Onofri et al., 2020) and a series of five blog posts (see here). A final topic that remains to be covered relates to the frequent possibility that these diallel experiments are repeated across years and/or locations. How should the resulting dataset be analysed?...


lmDiallel: a new R package to fit diallel models. The Gardner-Eberhart models

Published at February 22, 2021 ·  15 min read

Another post for this series about diallel mating experiments. So far, we have published a paper in Plant Breeding (Onofri et al., 2020), where we presented lmDiallel, a new R package to fit diallel models. We followed up this paper with a series of four blog posts, giving more detail about the package (see here), about the Hayman’s models type 1 (see here) and type 2 (see here) and about the Griffing’s family of models (see here)....


lmDiallel: a new R package to fit diallel models. The Griffing's models (1956)

Published at January 12, 2021 ·  10 min read

Diallel mating designs are often used by plant breeders to compare the possible crosses between a set of genotypes. In spite of such widespread usage, the process of data analysis in R is not yet strightforward and it is not clear which tool should be routinely used. We recently gave a small contribution by publishing a paper in Plant Breeding (Onofri et al., 2020 ), where we advocated the idea that models for diallel crosses are just a class of general linear models, that should be fit by Ordinary Least Squares (OLS) or REstricted Maximum Likelihood methods (REML)....


lmDiallel: a new R package to fit diallel models. The Hayman's model (type 2)

Published at January 5, 2021 ·  9 min read

This posts follows two other previously published posts, where we presented our new ‘lmDiallel’ package (see here) and showed how we can use it to fit the Hayman’s model type 1, as proposed in Hayman (1954) (see here). In this post, we will give a further example relating to another very widespread model from the same author, the Hayman’s model type 2. We apologise for some overlapping with previous posts: we think this is necessary so that each post can be read on its own....


lmDiallel: a new R package to fit diallel models. The Hayman's model (type 1)

Published at November 26, 2020 ·  15 min read

In a previous post we have presented our new ‘lmDiallel’ package (see this link here and see also the original paper in Theoretical and Applied Genetics). This package provides an extensions to fit a class of linear models of interest for plant breeders or geneticists, the so-called diallel models. In this post and other future posts we would like to present some examples of how to use this package: please, sit back and relax and, if you have comments, let us know, using the email link at the bottom of this post....


lmDiallel: a new R package to fit diallel models. Introduction

Published at November 11, 2020 ·  7 min read

Together with some colleagues from the plant breeding group, we have just published a new paper, where we presented a bunch of R functions to analyse the data from diallel experiments. The paper is titled ‘Linear models for diallel crosses: a review with R functions’ and it is published in the ‘Theoretical and Applied Genetics’ Journal. If you are interested, you can take a look here at this link....


Building ANOVA-models for long-term experiments in agriculture

Published at August 20, 2020 ·  29 min read

This is the follow-up of a manuscript that we (some colleagues and I) have published in 2016 in the European Journal of Agronomy (Onofri et al., 2016). I thought that it might be a good idea to rework some concepts to make them less formal, simpler to follow and more closely related to the implementation with R. Please, be patient: this lesson may be longer than usual. What are long-term experiments?...


Fitting complex mixed models with nlme. Example #5

Published at June 5, 2020 ·  14 min read

A Joint Regression model Let’s talk about a very old, but, nonetheless, useful technique. It is widely known that the yield of a genotype in different environments depends on environmental covariates, such as the amount of rainfall in some critical periods of time. Apart from rain, also temperature, wind, solar radiation, air humidity and soil characteristics may concur to characterise a certain environment as good or bad and, ultimately, to determine yield potential....


Fitting 'complex' mixed models with 'nlme'. Example #1

Published at August 20, 2019 ·  9 min read

The environmental variance model Fitting mixed models has become very common in biology and recent developments involve the manipulation of the variance-covariance matrix for random effects and residuals. To the best of my knowledge, within the frame of frequentist methods, the only freeware solution in R should be based on the ‘nlme’ package, as the ‘lmer’ package does not easily permit such manipulations. The ‘nlme’ package is fully described in Pinheiro and Bates (2000)....


Genotype experiments: fitting a stability variance model with R

Published at June 6, 2019 ·  8 min read

Yield stability is a fundamental aspect for the selection of crop genotypes. The definition of stability is rather complex (see, for example, Annichiarico, 2002); in simple terms, the yield is stable when it does not change much from one environment to the other. It is an important trait, that helps farmers to maintain a good income in most years. Agronomists and plant breeders are continuosly concerned with the assessment of genotype stability; this is accomplished by planning genotype experiments, where a number of genotypes is compared on randomised complete block designs, with three to five replicates....