A simple mathematical model of gradual Darwinian evolution: Emergence of a Gaussian trait distribution in adaptation along a fitness gradient

V. N. Biktashev

Submitted to Evolution 2011/02/01. Submitted to JoMB 2011/10/24. Submitted to JoMB again 2012/08/28. Accepted to JoMB 2013/03/12. Published online 2013/03/30, doi 10.1007/s00285-013-0669-3. Published: JoMB 68(5):1225-1248, April 2014

We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.