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.