Mechanistic modelling essentials
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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) testable and 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 continuous development, so you can expect additions and further polishing over the next years.

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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 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 60 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 still 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', offering my expertise to clients from industry, contract laboratories, and universities.

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. Toxicokinetic principles

7. Toxicodynamic principles


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