On October, 2 I start the course “Mathematical Foundations of Evolutionary Theory (Deterministic models)”
Here is the syllabus:
The major emphasis will be put on the modeling assumptions behind the mathematical models and on an accurate derivation of the main results.In the other words, the course is not about a collection of formulas of somewhat obscure origin, as it frequently happens in biologically oriented books, but about the exact assumptions, the proper mathematical tools and theory, and accurate conclusions, which should never go beyond what was originally put in the equations. Contents will hopefully include the Hardy–Weinberg law, selection in one- and multi-locus systems with and without recombination, the Fundamental Theorem of Natural Selection in its full form, the selection–mutation equilibria, the quasispecies model and notion of the error threshold, the hypercycle equation and connections of Population genetics with Statistical physics, the Price equation, the Evolutionary game theory, the replicator equation, the origin of cooperation, and kin and group selection. Prerequisites include some background in ordinary differential equations and linear algebra. We might touch on the mathematical ecology, in particular, the Lotka–Volterra systems.
More can be found at
I also uploaded Lecture 0 (the text is about the basic notions in evolutionary biology, written in Russian)