# Mathematical Biology Seminar

### Tom Alberts

Department of Mathematics, University of Utah

#### The Bak-Sneppen Model of Biological Evolution

#### Wednesday, April 6, 2016, at 3:05pm

LCB 215

Originally motivated by problems in physics, the Bak-Sneppen
model is a simplified description of how the fitness levels of a population
evolves over time due to natural selection, while also taking into account
how the population members are distributed about in space. Experimental
work has shown that it is a reasonable model for describing the fitness
evolution of simple organisms such as *E. Coli*. From a mathematical point of
view Bak-Sneppen is a Markov chain with transition rules that are very easy
to describe, and it is well known that there is a stationary distribution
of the chain that describes the long-time statistical properties of the
population's fitness levels. Analyzing this stationary distribution is a
notoriously difficult task however, and has led to an interesting but
unproved conjecture for its asymptotic properties as the population size
goes to infinity. I will describe some recent work in this direction that
is joint with Ga-Yeong Lee and Mackenzie Simper.