Population
genetics and geometry
Population genetics
studies changes in the gene composition of populations from generation to
generation (which is exactly the definition of evolution). The main theoretical
tool in population genetics is mathematical modeling, which allows us to
concentrate on the important details of the process and disregard unimportant.
For the simplest mathematical models of population genetics it is possible to
have a nice geometric interpretation, which will be the subject of my talk. In
a nutshell, evolution (in the simple case of one gene with two distinct forms,
called alleles) geometrically can be represented as a map
acting on a triangle. I will show examples of this "hereditary map"
for some simple evolutionary scenarios. In particular, I will consider the
celebrated Hardy-Weinberg law, which describes the change of population
composition when no evolutionary force acts on the population. No preliminary
background is necessary, and I will cover basic biological facts.