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.
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 :)