I'm an applied mathematician who works in the field of feedback control systems but has been becoming interested in looking at population biology (e.g. Lotka-Volterra, Mathusian growth,etc.) from a mathematical feedback and systems theory standpoint. Since I know almost nothing about biology save for a poor frog I nearly threw up on while trying to dissect in High School, I wanted to ask this community if anyone could provide me with some materials that give a good overview of the current state of this field.

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    $\begingroup$ You will find recommendations for book on population genetics here. The recommendations in General Entry books to population genetics and the 3 first recommendations in Other books treating specific subjects within population genetics can interest you. $\endgroup$ – Remi.b Apr 29 '16 at 1:30
  • $\begingroup$ Can I be dumb and ask whether or not population genetics has anything to do with dynamics (e.g. number of species X in a habitat)? $\endgroup$ – JMJ Apr 29 '16 at 4:31
  • $\begingroup$ Yes, it does. For example, if a population fails to adapt in an environment or if deleterious mutations accumulate in a population due to a too low population size and causes the population to get locally extinct (mutational meltdown). This kind of simple dynamic of species-interaction might be quite different when you add genetics and evolution in the model. So yes, it is very much related. I would call population genetics a subfield of population biology. $\endgroup$ – Remi.b Apr 29 '16 at 4:40
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    $\begingroup$ Remi.b's suggestion has indeed been useful to me; for one, I didn't know that genetics and dynamics were so closely related and am grateful someone took the time to explain this to me. I think I am most interested in learning about simpler models from a mathematical perspective, then diving more fully into population genetics, as undoubtedly getting to the point where I even understand the background in genetics for the latter will be an undertaking! Consider for instance this text, which I have been reading: springer.com/us/book/9783319030258 How close is this to SoA? $\endgroup$ – JMJ Apr 30 '16 at 16:35
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    $\begingroup$ I'm a fan of E. O. Wilson and W. H. Bossert's "A Primer of Population Biology", which has been continuously in print since 1971, as a first introduction. (sinauer.com/a-primer-of-population-biology.html) $\endgroup$ – David Bahry Oct 7 '16 at 19:55

There are three seminal works that will give you an excellent grounding in the study of dynamical systems in population biology.

The first details the foundations of population genetics:

Crow, James F., and Motoo Kimura. An introduction to population genetics theory. (1970).

The second deals with population ecology:

Maynard-Smith, John. Models in ecology. CUP Archive, 1978.

Finally, the field of evolutionary game theory has recently embraced a dynamical systems approach to studying populations under the guise of a new theoretical framework known simply as evolutionary dynamics:

Nowak, Martin A. Evolutionary dynamics. Harvard University Press, 2006.

I would probably read these in reverse order. The introduction to Maynard Smith's book has a nice discussion about some of the interrelations between population genetics and population ecology. Most of the original work was done by Fisher, but you don't want to read his stuff - it's famously inaccessible.

It is probably worth me telling you that a lot of mathematical biologists don't actually use dynamical systems approaches in their work. Instead, they favour optimisation models. A balanced discussion about the benefits of this approach, and some of the limitations of the dynamical systems approach can be found in these papers:

Smith, J. Maynard. "Optimization theory in evolution." Annual Review of Ecology and Systematics 9 (1978): 31-56.

Parker, Geoffrey A., and J. Maynard Smith. "Optimality theory in evolutionary biology." Nature 348.6296 (1990): 27-33.

As it happens, my soon to be submitted doctoral thesis is on dynamical systems in biology. Hopefully one day I will be able to add my own book to this list :)

  • $\begingroup$ Most of the books you cite are really about population genetics and a more in depth review (with IMO better books) can be found here. I don't know "Models in ecology" by J. Maynard-Smith but form its title, it sounds like a good recommendation. $\endgroup$ – Remi.b May 16 '16 at 1:36
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    $\begingroup$ @Remi.b your in-depth review does not answer the OPs question, which is about population biology and dynamical systems. Only a few of the books you posted deal with this explicitly. My answer is focussed and to the point. There is only 1 book on population genetics. It is probably the most cited book on population genetics and a must read for anyone getting into the field (it is not in your list). I presume you were confusing Evolutionary Dynamics with a book about population genetics? Well, it's nothing of the sort. It is a book about modelling frequency-dependent selection in populations. $\endgroup$ – Michael Andrew Bentley May 16 '16 at 8:39
  • $\begingroup$ Too often in biology is mathematical modelling of the evolution of populations conflated with mathematical modelling of the dynamics of populations (from which evolution then occurs). For instance, I recently read Rousset, François. Genetic structure and selection in subdivided populations. Princeton University Press, 2013. It is an excellent book, but it was recommended to me as a book about dynamics, and it barely touches on dynamical systems at all. $\endgroup$ – Michael Andrew Bentley May 16 '16 at 8:56
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    $\begingroup$ All right.... Deal! +1 :) $\endgroup$ – Remi.b May 16 '16 at 14:22

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