Evolutionary branching in a two dimensional strategy space

Andras Vukics, Janos Asboth
Department of Biological Physics, Eotvos University 
Pazmany Peter setany 1A, H-1117 Budapest, Hungary
Department of Nonlinear and Quantum Optics
Institute of Solid State Physics and Optics
Hungarian Academy of Sciences, P.O. Box 49,
H-1525 Budapest, Hungary

Geza Meszena 
Department of Biological Physics, Eotvos University 
Pazmany Peter setany 1A, H-1117 Budapest, Hungary
Adaptive Dynamics Network,
International Institute for Applied Systems Analysis
A-2361 Laxenburg, Austria
geza.meszena@elte.hu


In press at the Physical Review E


Abstract

Adaptive dynamics in two dimensional phenotype space is investigated by 
computer simulation. The model assumes Lotka-Voltera type competition and 
a stochastic mutation process. The carrying capacity has a single maximum in 
the origin of the strategy space and the competition coefficient decreases 
with strategy difference. Evolutionary branching, an asexual analogue of 
adaptive speciation, is observed with suitable parameters. The branching at 
the singular point, which is a fixed point of the directional evolution, may 
occur into two or three, but no more directions. Further branchings may occur 
after the initial separation. The probability of 3-branching is studied as a 
function of several parameters. We conclude that the 2-way branching is the 
predominant mode of adaptive speciation.