Evolutionary dynamics by M.A. Nowak

Martin A. Nowak does some of the best work in evolutionary game theory. I enjoy many of his papers, and his general approach to questions in EGT. Thus, I was very happy when I first heard about his introductory book “Evolutionary Dynamics: Exploring the Equations of Life“. After reading the book, I prepared a reading list for the members of the LNSC. I recomend Nowak’s book as a gentle introduction to the field and include my reading list as a review.

Reading list

Here is what I would recommend to read from the book, along with a brief summary:

Cover of Evolutionary Dynamics by Martin A. Nowak

Chapter 2 (2.0 – 2.3) “What evolution is”

  • Covers the basics of evolution: reproduction (2.1), selection (2.2), and mutation (2.3)
  • Introduces the basic equations and phase space. Explains what the simplex is.
  • Section 2.4 is fun, but does not do justice to sexual evolution (and is never references again), so it can be omitted.

Chapter 4 (4.0 – 4.8) “Evolutionary games”

  • This chapter is essential, it covers the basics of EGT.
  • It is important to stress section 4.5 where the replicator equation is introduced.
  • Section 4.9 was fun for me. When I was first starting EGT, I was unaware of many of the classical results and reproved the equivalence of replicator dynamics and Lotka-Volterra, so seeing it was nostalgic. However, in general this section can be omitted.

Chapter 9 (all) “Spatial games”

  • This is the approach that really founded the idea of doing games in a lattice, and is important for everyone to read

Chapter 10 (Optional) “HIV infection”

  • Although not exactly game theory related. It does show the power of differential equations in biology.
  • Given a bit of thought, it is possible to relate the ideas to game theory. In particular, the asymmetric effect between strains of HIV and their suppressors can be thought of as a game. However, Nowak does not mention that in the book.
  • Mostly, it is a part of Nowak’s research that really hit the spot for theory building in biology.

Chapter 11 (Optional) “Evolution of virulence”

  • Also, much like chapter 10 much of this can be interpreted as games, but Nowak does not make the connection explicit.

Chapter 13 (13.3 – 13.6) “Language evolution”

  • The beginning 13.0 – 13.2 is rather weak. It is better if students have their own background in basic linguistics. I don’t think Nowak does a very careful or rigorous introduction. He drops results on the reader, without really making us appreciate them. For instance, he throws down Godel’s theorem for no real reason and without doing it any justice.
  • The later sections are useful. In particular, they show a really fun application of EGT to language coherence, etc.
  • Some of the conclusions are not particularly breathtaking, but it is interesting to see them reached from evolutionary arguments. It gives you much more insight into both EGT and language.
  • Nowak introduces the replicator-mutator equation here. This is a very general and important framework in EGT.

The ‘further reading’ section is one of the best parts of this book. There are a lot of great sources mentioned there.

Sections to omit

As for the omitted chapters and sections:

Chapter 3 is extremely tangential. The quasi-species equation is briefly mentioned again in chapter 13 (when the replicator-mutator equation is introduced) but chapter 13 can easily be understood and enjoyed without chapter 3. Quasi-species work is extremely interesting and promising, but Nowak’s exposition of it is lacking. Chapter 3 is not really worth reading, and might cause more confusion than good.

I omitted chapter 5, even though it is a whole chapter about prisoner’s dilemma. However, only direct reciprocity (iterated PD) is studied in this chapter. Direct reciprocity is pretty well understood as a mechanism for creating cooperation, hence there is not too much excitement here. It does talk about some of the difficulties of iterated PD, but this is not useful if you are interested in one-shot games.

For people that are more biology inclined, it might be good to read Chapters 6,7, and 8. These 3 chapters deal with finite populations in the way that biologists work with them (i.e. via Moran processes). These are very important for understanding the biological parts of EGT, especially neutral drift and fixation probabilities. In a social context though, there will be no fixation or neutral drift since a non-negligible mutation rate should always be included (and there can be no fixation with a mutation rate).

The reason biologists can ignore mutation rates between strategies and social scientists can’t, I think, is quiet simple. The chance of one strategy mutating into another (via genetic changes) is close to null, and hence can be ignored on any reasonable time scale (most mutations will be neutral or will kill you, a random mutation changing something as substantial as a strategy is nearly impossible). However, in social evolution, a person can always change their strategy, or at least they can do it much easier than in biological evolution. Hence, the Moran processes for social evolution will have no absorbing states and thus those 3 chapters on finite populations (which are only of interest because of absorbing states) become irrelevant. However, for people that read a lot of biology papers it is important to go through those chapters.

I found the chapter on evolutionary dynamics of cancer (chapter 12) lacking. It has no really interesting results and a lot of cancer specific set up. I don’t think Nowak has found a good way to apply evolutionary dynamics to cancer, yet. Personally, I prefer the approach of Axelrod and coauthors. Most of this chapter is a bunch of heavy math (which Nowak usually replaces by heuristics) to conclude pretty obvious results.

Conclusion and open problems

As I stated earlier, I think the book is a great introduction. However, I don’t think it equips you with the skills to start doing research. I am not sure how easy the book is to use as a textbook, but Nowak uses it in both his undergraduate and graduate course on mathematical biology.

Do you think this is a good introduction to the field? Is there another text you prefer? Would you like to take or teach a course from this book? Would you like to see a specific chapter reviewed in more depth?