MFET2010
Mathematical Foundations of Evolutionary Theory (Deterministic models)
Nothing in evolution makes sense except
in the light of population genetics
Michael Lynch,
The Origins of Genome Architecture
The recent and welcome infusion of
population genetics theory into a variety of
disciplines associated with the evolutionary
process has not been without some problems.
Perhaps the most important of these is that
it has led to an uncritical use of some
formulas from the theory without due
assessment of whether the formulas
are appropriate to the situation at hand.
Warren J. Ewens
Mathematical Population Genetics.
I. Theoretical Introduction
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.
Suggested textbook for the first several lectures is the book by Joe Felsenstein, "Theoretical Evolutionary Genetics" (pdf). On the mathematical side, the book by Alligood, Sauer, and York, "Chaos – An introduction to dynamical systems," is an ideal reference, which is sufficient (but by no means necessary!). My book can be used as well for the pertinent mathematical theory and some biological applications.
Lectures and problem sets (in Russian):
Для студентов УПМ-511, задания для курсовых работ:
Вопросы для подготовки к зачету для студентов МГУ ФББ: