#biplot

Designed experiments with replicates: Principal components or Canonical Variates?

Published at November 2, 2023 ·  16 min read

A few days ago, a colleague of mine wanted to hear my opinion about what multivariate method would be the best for a randomised field experiment with replicates. We had a nice discussion and I thought that such a case-study might be generally interesting for the agricultural sciences; thus, I decided to take my Apple Mac-Book PRO, sit down, relax and write a new post on this matter. My colleague’s research study was similar to this one: a randomised block field experiment (three replicates) with 16 durum wheat genotypes, which was repeated in four years....


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....


Biplots are everywhere: where do they come from?

Published at November 24, 2021 ·  25 min read

Principal Component Analysis (PCA) is perhaps the most widespread multivariate technique in biology and it is used to summarise the results of experiments in a wide range of disciplines, from agronomy to botany, from entomology to plant pathology. Whenever possible, the results are presented by way of a biplot, an ubiquitous type of graph with a formidable descriptive value. Indeed, carefully drawn biplots can be used to represent, altogether, the experimental subjects, the experimental variables and their reciprocal relationships (distances and correlations)....


Principal Component Analysis: a brief intro for biologists

Published at November 23, 2021 ·  24 min read

In this post I am revisiting the concept of Principal Component Analysis (PCA). You might say that there is no need for that, as the Internet is full with posts relating to such a rather old technique. However, I feel that, in those posts, the theoretical aspects are either too deeply rooted in maths or they are skipped altogether, so that the main emphasis is on interpreting the output of an R function....