Mechanistic modelling essentials
Minimum price
Suggested price

Mechanistic modelling essentials

Principles, mathematics and statistics for building and applying TK and TKTD models

About the Book

In this book, I present the basic principles of modelling, and the bare essentials from mathematics and statistics that you need to build and apply simple models. I am writing from the perspective of TK and TKTD modelling in ecotoxicology, but these basics are applicable to many other scientific fields as well. Furthermore, I am specifically writing about models as tools to answer (applied) scientific questions. I am not so much interested in modelling for the sake of modelling. For me, models are the quantitative tools that make ideas (or theory) applicable to real-world questions. Therefore, this book is not just about mathematics (though there will be equations). It contains elements from philosophy of science, and the intellectual challenge of simplifying real-world complexity into a more manageable representation. Furthermore, statistics will be treated alongside the process models, whereas these topics are usually kept well separated in textbooks and teaching. As soon as we want to compare our model to data, we inevitably have to deal with statistics, so a statistical background is essential for practical modelling.

All of these elements are treated in a somewhat cursory and selective manner. I am focussing on the essential things that you need to get started with TK and TKTD modelling, which differs substantially from what you will get from more general textbooks on mathematics, modelling or statistics. I assume that the reader only has a very limited background in applied modelling, mathematics and statistics. However, I assume that you are familiar with mathematical functions, powers and logarithms, derivatives and integration, and basic probability distributions such as the binomial and the normal.

This book will be used to support courses on dynamic modelling of toxic effects. It is under development, so you can expect additions and further polishing over the next years.

Support page at (includes a version log)

At this moment, this e-book is (unlike my other e-books) not available free of charge. Paying for it gives me the opportunity to continue working on this book, and on other ones (and it keeps Leanpub in the air). Furthermore, you will receive future updates of the book for free. Please note that you can always request a refund from Leanpub within 45 days, no questions asked, if you think the book was not worth the price. If the price is an obstacle for you, please send me a message.

About the Author

Tjalling Jager
Tjalling Jager

Mechanistic modelling is an under-utilised tool in ecotoxicology and stress ecology. It is my passion to promote these models through (applied) scientific projects, providing software solutions, teaching in courses, presentations at conferences, and through writing e-books. The models that I specialise in are so-called toxicokinetic-toxicodynamic (TKTD) models; in particular, models for survival (the GUTS framework) and sublethal effects (based on Dynamic Energy Budget - DEB - theory). These models are based on a rigorous simplification of biological complexity, and have the power to explain (and predict) life-history traits of organisms (e.g., growth, reproduction and survival) over time. Especially when considering exposure to stressors, such dynamic models are indispensable to make sense of the data.

I hold an MSc and PhD in Biology, and have been a professional modeller since 1992, working almost exclusively on DEB- and GUTS-based TKTD modelling since 2002. Currently, I run my own private company 'DEBtox Research'.

More information about Tjalling at DEBtox Research

More information about DEB(tox) and GUTS models

Table of Contents


1. General modelling principles

2. Basics of ODE's

3. Compartment models

4. Error models and likelihood

5. A journey into hyperspace

6. Miscellaneous stuff


The Leanpub 45-day 100% Happiness Guarantee

Within 45 days of purchase you can get a 100% refund on any Leanpub purchase, in two clicks.

See full terms

Do Well. Do Good.

Authors have earned$10,884,695writing, publishing and selling on Leanpub, earning 80% royalties while saving up to 25 million pounds of CO2 and up to 46,000 trees.

Learn more about writing on Leanpub

Free Updates. DRM Free.

If you buy a Leanpub book, you get free updates for as long as the author updates the book! Many authors use Leanpub to publish their books in-progress, while they are writing them. All readers get free updates, regardless of when they bought the book or how much they paid (including free).

Most Leanpub books are available in PDF (for computers), EPUB (for phones and tablets) and MOBI (for Kindle). The formats that a book includes are shown at the top right corner of this page.

Finally, Leanpub books don't have any DRM copy-protection nonsense, so you can easily read them on any supported device.

Learn more about Leanpub's ebook formats and where to read them

Write and Publish on Leanpub

You can use Leanpub to easily write, publish and sell in-progress and completed ebooks and online courses!

Leanpub is a powerful platform for serious authors, combining a simple, elegant writing and publishing workflow with a store focused on selling in-progress ebooks.

Leanpub is a magical typewriter for authors: just write in plain text, and to publish your ebook, just click a button. (Or, if you are producing your ebook your own way, you can even upload your own PDF, EPUB and/or MOBI files and then publish with one click!) It really is that easy.

Learn more about writing on Leanpub