Getting the Absolute/Relative Growth Rate from growth curves

Published at November 27, 2025 ·  7 min read

Yesterday, a colleague of mine pointed me to the article “How to fit nonlinear plant growth models and calculate growth rates: an update for ecologists” (Paine et al., 2012). It addresses a relevant topic: many plant scientists are involved in growth analyses and need to determine Absolute Growth Rates (AGRs) and Relative Growth Rates (RGRs).

The main point made by Paine et al. is that we can use the observed data to fit a growth model via nonlinear regression and then calculate model-derived growth rates together with their standard errors. In principle, the process is straightforward: we select a suitable growth model to predict biomass at any given time \(t\); the AGR at time \(t\) is the derivative of the selected growth function with respect to time, and the RGR is simply the AGR at time \(t\) divided by the biomass at that same time point.

Field Research methods in Agriculture

Published at November 25, 2025 ·  2 min read

Hi everybody, I have exciting news!

After a few months of silence, I’m thrilled to finally share the reason why: I’ve been working intensely on a new book project, which has taken up most of my spare time. And now… the book is out!

This book is titled ‘Field Research Methods in Agriculture’ and it is published by Springer Nature. It offers a clear, accessible, and practical introduction to experimental design and basic data analysis for field experiments in agriculture and related disciplines. It’s specifically designed for students, researchers, and practitioners who want to strengthen their methodological skills without getting lost in heavy mathematics.

Dealing with correlation in designed field experiments: part II

Published at February 10, 2025 ·  11 min read

With field experiments, studying the correlation between the observed traits may not be an easy task. For example, we can consider a genotype experiment, laid out in randomised complete blocks, with 27 wheat genotypes and three replicates, where several traits were recorded, including yield (Yield) and weight of thousand kernels (TKW). We might be interested in studying the correlation between those two traits, but we would need to face two fundamental problems:

A trip from variance-covariance to correlation and back

Published at January 24, 2025 ·  6 min read

The variance-covariance and the correlation matrices are two entities that describe the association between the columns of a two-way data matrix. They are very much used, e.g., in agriculture, biology and ecology and they can be easily calculated with base R, as shown in the box below.

data(mtcars)
matr <- mtcars[,1:4]

# Covariances
Sigma <- cov(matr)

# Correlations
R <- cor(matr)

Sigma
##              mpg        cyl       disp        hp
## mpg    36.324103  -9.172379  -633.0972 -320.7321
## cyl    -9.172379   3.189516   199.6603  101.9315
## disp -633.097208 199.660282 15360.7998 6721.1587
## hp   -320.732056 101.931452  6721.1587 4700.8669
R
##             mpg        cyl       disp         hp
## mpg   1.0000000 -0.8521620 -0.8475514 -0.7761684
## cyl  -0.8521620  1.0000000  0.9020329  0.8324475
## disp -0.8475514  0.9020329  1.0000000  0.7909486
## hp   -0.7761684  0.8324475  0.7909486  1.0000000

It is useful to be able to go back and forth from variance-covariance to correlation, without going back to the original data matrix. Let’s consider that the variance-covariance of the two variables X and Y is: