The dynamics of adaptation and evolutionary branching

Stefan A.H. Geritz
Collegium Budapest, Institute for Advanced Studies, 
Szentharomsag 2, 1014 Budapest, Hungary
Stefan.Geritz@zeus.ColBud.hu

J.A.J. Metz
Institute of Evolutionary and Ecological Sciences, 
University of Leiden, Kaiserstraat 63, 2311 GP Leiden, the Netherlands
Metz@rulsfb.LeidenUniv.nl

Eva Kisdi
Department of Genetics, Eotvos University, 
Muzeum krt. 6-8, 1088 Budapest, Hungary
Eva.Kisdi@elte.hu

Geza Meszena
Department of Atomic Physics, 
Eotvos University, Puskin 5-7, 1088 Budapest, Hungary
Geza.Meszena@elte.hu


Abstract

We present a formal framework for modelling evolutionary dynamics
with special emphasis on the generation of diversity through
branching of the evolutionary tree. Fitness is defined as the long
term growth rate which is influenced by the biotic environment
leading to frequency-dependent selection. Evolution can be
described as a dynamics in a space with variable number of
dimensions corresponding to the number of different types present.
The dynamics within a subspace is governed by the local fitness
gradient. Entering a higher dimensional subspace is possible only
at a particular type of attractors where the population undergoes
evolutionary branching.