Stochastic Evolution of spatial populations: From configurations to
genealogies and back
The paper reviews the results obtained for spatial population models and the
evolution of the genealogies of these populations during the last decade by the
author and his coworkers. The focus is on their large scale behaviour and on
the analysis of universality classes of large scale behaviour via the methods
of the hierarchical mean-field limit or via the spatial continuum limit and
from another angel, the finite system scheme . We use genealogical information
to analyze the type and location structure and vice versa.
To apply this approach and to explain effects in biological situations we
extend the classical model classes in new directions. Namely we look as
population models here at: Fleming-Viot genealogies in continuum geographic
space, Cannings models with block resampling (reducing diversity),
Fisher-Wright diffusion with coloured seedbanks (enhancing diversity) and
evolving genealogies of Fleming-Viot models with selection and rare mutation.