Title: Discrete Dynamical Systems in Population Genetics

Speaker:
John Franke
Department of Mathematics
North Carolina State University

Abstract:  The classical Crow-Kimura population genetics model will be 
derived using the Hardy-Weinberg Law.  This leads to a discrete, 
deterministic, 2 dimensional model. The stability of equilibria are 
studied.  Interesting dynamics in sue when the genotype fitnesses are 
functions of the total population.  Multiple cyclic attractors appear. 
In fact, as parameters in the model are varied, strange attractors 
appear.  When migration is added to the model a polymorphic equilibrium 
appears.  Hopf bifurcations and pulsating attractors are also present in 
this model.