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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.

WYSIWYG
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JMJ
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    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. – Remi.b Apr 29 '16 at 01:30
  • 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)? – JMJ Apr 29 '16 at 04:31
  • 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. – Remi.b Apr 29 '16 at 04:40
  • To those who voted to close: I do not think this question is "too broad" or "primarily-opinion based". The OP is just looking for recommendation of books in population biology. Look for "population biology" on amazon and you get several interesting hits. We just need one person who read these books and can formulate a critic. – Remi.b Apr 29 '16 at 16:16
  • Yes, as Remi.b says, I am not asking for opinions on the subject, but rather which books are commonly used. Having "standard" texts is a common thing in most fields of science and I was simply asking what those are and if people can provide general criticism to direct a newcomer. – JMJ Apr 29 '16 at 20:22
  • @Remi.b I strongly disagree. Although population genetics are important to population dynamics in a broader sense, the examples the OP provides (e.g. Lotka-Volterra, Malthusian growth) have next to nothing to do with genetics but with growth and hunter-pray interactions. There must be better books to suggest here! – RHA Apr 30 '16 at 10:16
  • ®RHA I never said the post that asked for recommendations on population genetics was a duplicate. I just think it is worth mentioning this post as it may interest the OP. I then argued that population dynamics also depend on its evolution (as you did as well). But I recognize the question as being valid (and am the only one who up voted it so far). I am personally not able to offer good book suggestion in this field as I haven't read them. – Remi.b Apr 30 '16 at 16:23
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    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: http://www.springer.com/us/book/9783319030258

    How close is this to SoA?

     – JMJ Apr 30 '16 at 16:35
  • I've also found this good looking book on the SIAM (professional applied math organization) website: http://epubs.siam.org/doi/book/10.1137/1.9781611970005 – JMJ May 01 '16 at 00:44
  • @Remi.b is right, population genetics is a sub field of population biology, the other being population ecology. The two fields are intimately related at their foundations, but diverged long ago to become fairly distinct. A good summary of the historical context can be found in the introduction to Singh, Rama S., and Marcy K. Uyenoyama, eds. The evolution of population biology. Cambridge University Press, 2004. They also include models that may be of interest. But for studying populations as dynamical systems, see my post below. – Michael Andrew Bentley May 16 '16 at 08:49
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    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. (http://www.sinauer.com/a-primer-of-population-biology.html) – David Bahry Oct 07 '16 at 19:55
  • Related: https://biology.stackexchange.com/questions/54796/recommendation-of-ecology-books – Always Confused May 10 '17 at 11:10

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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 :)

Michael Andrew Bentley
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  • 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. – Remi.b May 16 '16 at 01:36
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    @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. – Michael Andrew Bentley May 16 '16 at 08:39
  • 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. – Michael Andrew Bentley May 16 '16 at 08:56
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    All right.... Deal! +1 :) – Remi.b May 16 '16 at 14:22