Title: Adaptive dynamics and evolutionary chains


Abstract: 

Adaptive dynamics is a mathematical theory that links population
dynamics to long-term evolution driven by mutation and selection. 
Adaptive dynamics thus deals with processes on two different time 
scales: a fast ecological time scale and a slow evolutionary time scale. 
On the ecological time scale adaptive dynamics addresses questions 
such as which mutant strategies can invade a population of given 
resident strategies, and what will be the outcome of such an invasion in 
terms of which strategies remain and which are eliminated from the 
population when a new population dynamical attractor is reached. 

On the evolutionary time scale adaptive dynamics addresses the 
question how the set of strategies present in a population changes over 
a long time scale as a consequence of many successive  
invasion-elimination events.

In this talk I first present some of the basic ideas and techniques 
of adaptive dynamics. In the second half of the talk I will focus on a 
specific class of difference inclusions (called evolutionary chains) 
as a basic model of long term evolution in adaptive dynamics.