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....

Analysing seed germination and emergence data with R: a tutorial. Part 3

Published at October 19, 2021 ·  11 min read

This is a follow-up post. If you are interested in other posts of this series, please go to: https://www.statforbiology.com/tags/drcte/ Reshaping time-to-event data The first thing we should consider before working through this tutorial is the structure of germination/emergence data. To our experience, seed scientists are used to storing their datasets in several formats, that may not be immediately usable with the ‘drcte’ and ‘drc’ packages, which this tutorial is built upon....

Analysing seed germination and emergence data with R (a tutorial). Part 2

Published at October 9, 2021 ·  16 min read

Survival analysis and germination/emergence data: an overlooked connection Seed germination and emergence data describe the time until the event of interest occurs and, therefore, they can be put together in the wide group of time-to-event data. You may wonder: what’s the matter with time-to-event data? Do they have anything special that needs our attention? The answer is, definitely, yes! Indeed, with very few exceptions, time-to-event data are affected by a peculiar form of uncertainty, which takes the name of censoring....

Analysing seed germination and emergence data with R (a tutorial). Part 1

Published at October 7, 2021 ·  3 min read

Introduction to the tutorial Germination/emergence assays are relatively easy to perform, by following standardised procedures, as described, e.g., by the International Seed Testing Association (see here ). In short, we take a sample of seeds and we put them in an appropriate container. We put the container in the right environmental conditions (e.g., relating to humidity content and temperature) and we inspect the seeds according to a regular schedule (e....

Why are derivatives important in biology? A case-study with nonlinear regression

Published at June 9, 2021 ·  7 min read

In general, undergraduate students in biology/ecology courses tend to consider the derivatives as a very abstract entity, with no real usefulness in the everyday life. In my work as a teacher, I have often tried to fight against such an attitude, by providing convincing examples on how we can use the derivatives to get a better understanding about the changes on a given system. In this post I’ll tell you about a recent situation where I was involved with derivatives....

Other useful functions for nonlinear regression: threshold models and all that

Published at May 1, 2021 ·  13 min read

In a recent post I presented several equations and just as many self-starting functions for nonlinear regression analyses in R. Today, I would like to build upon that post and present some further equations, relating to the so-called threshold models. But, … what are threshold models? In some instances, we need to describe relationships where the response variable changes abruptly, following a small change in the predictor. A typical threshold model looks like that in the Figure below, where we see three threshold levels:...

The R-squared and nonlinear regression: a difficult marriage?

Published at March 25, 2021 ·  4 min read

Making sure that a fitted model gives a good description of the observed data is a fundamental step of every nonlinear regression analysis. To this aim we can (and should) use several techniques, either graphical or based on formal hypothesis testing methods. However, in the end, I must admit that I often feel the need of displaying a simple index, based on a single and largely understood value, that reassures the readers about the goodness of fit of my models....

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)....