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.

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

Published at November 26, 2025 ·  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. A few weeks ago, a colleague of mine wrote me to ask the following question (I’m changing it a little, to make it, hopefully, more interesting). He asked: “I am using a power curve to model how the size of the sampling area affects species richness. How can I quantify my knowledge gain?”. This is an interesting question, indeed, although I feel I should provide you with some background information.

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.

Here is why I don't care about the Levene's test

Published at March 15, 2024 ·  5 min read

During my stat courses, I never give my students any information about the Levene’s test (Levene and Howard, 1960), or other similar tests for homoscedasticity, unless I am specifically prompted to do so. It is not that I intend to underrate the tremendous importance of checking for the basic assumptions of linear model! On the contrary, I always show my students several methods for the graphical inspection of model residuals, but I do not share the same aching desire for a P-value, that most of my colleagues seem to possess.